energy grid operators

Abstract: Electric vehicles produce no tailpipe emissions, but charging them produces emissions that depend on the time-varying generation mix of the electricity consumed. We study an Electric Vehicle Routing Problem with a carbon-aware objective that accounts for charging-related emissions alongside conventional routing costs. The problem determines routing, charging, and waiting decisions, allowing charging demand to be shifted toward periods with lower grid carbon intensity. Because these decisions depend on forecasts of future carbon intensity, we propose a decision-focused learning approach so that the training of the model employed for predicting the carbon intensity of the grid over time is solver-aware. In particular, we train a linear predictor using approximate SPO+ directions and employ a time-limited Large Neighborhood Search followed by exact postprocessing as the underlying solver. Experiments on realistic Germany-based instances show that explicitly considering charging-related emissions reduces realized emissions by 28.76% on average relative to carbon-blind optimization, although at the expense of higher non-carbon operating cost. Moreover, decision-focused training reduces realized total cost by 2.30% on average relative to conventional prediction-focused learning and performs better on 75.5% of the test instances, despite substantially lower pointwise predictive accuracy. Finally, we show that its average advantage remains positive across varied solver configurations and carbon-cost weights.

Abstract: Industrial systems continuously generate time series that vary in sampling frequency, scale, dynamics, and operating regime. Consequently a single time-series foundation model may not be able to represent all regimes effectively and retraining a large model for every new dataset or regime shift is computationally expensive. Modular foundation models address this issue by reusing specialised encoders trained on diverse datasets and by allowing the expansion of capabilities through the addition of new experts. This approach requires compact experts to minimize storage cost and a proper selection mechanism of experts for unseen data. We propose a modular foundation model framework that combines end-to-end Bayesian encoder training with uncertainty based routing. Using Singular Bayesian Neural Networks (SBNNs), we build a collection of compact Bayesian encoders whose epistemic uncertainty guides label-free selection. At the selected ranks, our Bayesian collection uses 63.8\% less storage than its deterministic counterpart. We evaluate this framework on time-series data through distribution shift, encoder selection, and probabilistic forecasting. Across seven incoming datasets, uncertainty-based routing is competitive with distance-based routing in terms of forecast MSE, while reducing average ECE from 0.086 to 0.072 and average NLL from 0.907 to 0.836. It also increases PICP90 from 82.28\% to 89.03\%. In a separate model-family comparison, we evaluate the SBNN pipeline against full-rank Bayes by Backprop, deep ensembles, and MC Dropout. The SBNN pipeline achieves an average MSE of 0.390, comparable with 0.396 for deep ensembles, 0.389 for MC dropout, and 0.443 for the full-rank Bayesian model. It uses 63.9\% fewer parameters than MC dropout, 81.9\% fewer than the full-rank model, and 92.8\% fewer than the deep ensemble.

Abstract: Spatiotemporal forecasting plays an important role in real-world applications, where probabilistic approaches provide uncertainty estimates for decision-making. Real-world systems are inherently non-stationary, leading to distribution shifts between training and test data. However, existing probabilistic methods mainly focus on modeling data distributions under standard settings, while distribution shift methods often handle such shifts in a coarse manner, failing to characterize shift degree and adapt prediction strategy accordingly. As a result, they often produce miscalibrated and unreliable forecasts. To address this issue, we propose REMIND, a retrieval-guided probabilistic framework for spatiotemporal forecasting under distribution shift. REMIND leverages retrieval to estimate how well current observation are supported by historical patterns, enabling adaptive prediction under different shift regimes. It employs spatiotemporal retrieval to construct a memory bank and introduces a dual branch architecture, combining a memory-calibrated probabilistic branch for mild shifts with a deviation-aware probabilistic branch for severe shifts. A shift-adaptive gate, guided by retrieval similarity and memory dispersion, balances the two branches according to shift degree. We further design a hierarchical Gaussian mixture to capture heterogeneous uncertainty over the dual branch predictions, and introduce a memory perturbation training scheme to improve generalization. Experiments on real-world datasets with distribution shifts demonstrate that REMIND consistently outperforms state-of-the-art methods in both forecasting accuracy and probabilistic prediction quality.

Abstract: Sheaf neural networks generalize graph neural networks by assigning each edge a learned linear restriction map that specifies how the local representations of adjacent nodes relate to one another, thereby mitigating oversmoothing. Existing sheaf architectures, however, define the sheaf Laplacian as an instantaneous spatial operator and therefore cannot explicitly model how signals evolve over time on a graph. We first introduce a spectral sheaf Laplacian, defined jointly over space and time, such that a single operator regulates signal propagation across both the spatial graph and the temporal domain. Directly extending this operator's receptive field in space or time would require increasingly complex sheaf structures. Instead, we propose a spectral filter that expands the effective receptive field along both dimensions without enlarging the underlying sheaf. Building on this operator, we introduce ChronoSheaf, a spatio-temporal sheaf network with two key components. First, Transitional Restriction Maps (TRM) decompose each node's restriction map into a spatial term and two temporal frames that independently control its relation to neighboring nodes at the preceding and following timestep, enabling asymmetric temporal influence. Second, the Dual Spectral Filter (DSF) applies a single bounded-degree polynomial filter with an adaptively estimated spectral radius to the joint spatio-temporal sheaf operator. We validate ChronoSheaf on a diverse set of spatio-temporal forecasting benchmarks, where it outperforms state-of-the-art baselines. The code is available at: https://anonymous.4open.science/r/ChronoSheaf-1D7D/.

Abstract: Hierarchical forecasting exploits aggregation structures that expose multiple views of the same underlying spatiotemporal forecasting problem, while ensuring coherence among forecasts. Individual series provide fine-grained information, while progressively coarser aggregates reveal temporal and spatial patterns at different scales. In the associated deep learning architectures, the hierarchy determines which aggregate series are available and how they are processed together with individual series (e.g., through reconciliation or message-passing operators). Different hierarchies thus provide distinct learning signals and inductive biases for forecasting the same collection of time series. Nonetheless, existing architectures are typically trained on a single, often fixed, structure. In this work, we propose a graph deep learning framework that leverages variations across hierarchies as multi-task regularization. We show that jointly learning across these structures can reduce over-specialization to any single hierarchy and improve forecasting performance. Indeed, training across hierarchies provides an inductive bias toward representations that are useful across different structures, and as such, generalize better. Making forecasts coherent with the aggregation constraints for each sampled hierarchy is computationally expensive: to complement the framework, we propose a novel operator-based on a top-down approach-that produces coherent forecasts with linear time and space complexity w.r.t. the hierarchy size. Experiments show that our approach improves forecasting accuracy over training on a single structure and is competitive with current state-of-the-art methods.

Abstract: Spatio-temporal forecasting is fundamental to many real-world systems, yet deployment environments are inherently varying: temporal distributions may evolve, spatial domains may change, and observation availability may shift from training conditions. Existing models are often tightly coupled to their training environments through node-specific representations, predefined spatial support sets, and reliance on consistently available observations, limiting generalization to changing environments. To this end, we propose VaryST, a compact spatio-temporal forecasting model trained from scratch that achieves strong generalization by dynamically constructing predictive context from available long-term observations. To accommodate temporal changes, VaryST derives node representations from long-term histories, capturing current behavior in the context of longer-term patterns. To adapt to spatial changes, it dynamically selects functionally relevant support nodes beyond predefined neighborhoods and integrates their information with recent and long-term target states and global context. To handle varying observation availability, VaryST selectively masks historical patches on which the model relies most during training, encouraging it to exploit alternative temporal and spatial dependencies for accurate forecasting when key observations become unavailable. Extensive experiments on six real-world datasets against seventeen baselines show that VaryST achieves strong in-domain forecasting accuracy, substantially improves zero- and few-shot generalization under spatial and temporal changes, and remains robust to varying observation availability.

Abstract: Hierarchical time series forecasting requires generating accurate predictions that are coherent across multiple levels of aggregation. Existing methods either rely on two-stage pipelines with post-hoc reconciliation or on end-to-end models that often lack statistical guarantees. We introduce a unified framework that formulates hierarchical forecasting as a multivariate regression problem in a vector-valued reproducing kernel Hilbert space. By designing structured operator-valued kernels, our approach enforces coherence directly within the hypothesis space, ensuring that all predictions satisfy hierarchical constraints by construction. We further propose tailored kernel constructions for hierarchical data and derive excess risk bounds that characterize generalization performance. Empirical results on synthetic and real-world datasets demonstrate the relevance of the proposed method.

Abstract: Day-ahead (DA) electricity price forecasting is usually posed per market, with a separate model fitted to each grid's own history. This caps accuracy: statistical and tree-based baselines saturate, while higher-capacity sequence models need more training data than a single market's few years of hourly prices can supply. Such methods also treat each node as an independent series, discarding the spatial dependencies induced by network topology and congestion. Because price formation across independent system operators (ISOs) is driven by shared physics and largely common market design, we instead treat cross-market history as a pretraining corpus. We present MetaGrid, a topology-aware transformer, meta-trained across markets so that a single zone-count-independent parameter set adapts to an unseen grid. On a leak-free benchmark of five U.S. ISOs, where every model receives the same prices, DA load forecasts and calendar features, MetaGrid attains the lowest average MAE, improving on the best baseline by 3.1\% and on the same architecture trained from scratch by 7.7\%.

Abstract: Time-series forecasting plays a vital role in a wide range of real-world applications. Recent approaches have achieved strong performance by modeling temporal correlations and cross-channel dependencies, yet most forecasting benchmarks still represent time series primarily as numerical histories. In practice, time series are observations of complex real-world processes, and their trajectories may reflect events, interventions, disruptions, and changes in measurement or reporting that cannot always be inferred from past values alone. A central barrier to studying context-aware forecasting is therefore the lack of large-scale datasets that align real-world events with the individual series they affect. We present World2TS, a scalable construction framework and large-scale dataset for time-series forecasting with real-world event context. We first develop world2ts-core, a reusable tool that combines agent-led semantic reasoning and Web search, command-line execution and validation, and human review within a feedback-driven discovery workflow. Given heterogeneous time series with semantic descriptions, the workflow discovers candidate events, consolidates retrieved evidence into verified events, and links them to relevant series under explicit temporal and semantic scopes. Using this framework, we construct world2ts-data, which contains 31 datasets across six domains, comprising 4,179 series, 97.1 million observations, 1,159 events, and 56,846 event-series links. We further conduct extensive data analyses and controlled comparative experiments to characterize the dataset and demonstrate the utility of the collected context for improving forecasting accuracy. World2TS provides a reusable data foundation for developing and evaluating context-aware forecasting models and agents. The project homepage is available at https://world2ts.github.io/.

Abstract: Time-series foundation models (TSFMs) have achieved strong forecasting performance across domains. However, most adaptation methods remain static. Existing all-in-one methods learn a single set of dataset-level parameter updates and apply the same adapted model to every input. As a result, they cannot adapt the model parameters to the temporal patterns, seasonality and dynamics of each input time series. This limits their ability to produce forecasts that are tailored to heterogeneous inputs. To address this limitation, we propose AdaCast, a conditional parameter generation framework for time-series forecasting. AdaCast uses a generator to produce input-specific low-rank parameter updates for a frozen pretrained TSFM. These updates adapt the model to each input during both training and inference. Across six public benchmarks, AdaCast consistently outperforms static adaptation baseline in in-domain forecasting and improves zero-shot generalization to held-out datasets across domains. These results demonstrate that conditional parameter generation provides an effective approach for adaptive forecasting.

Abstract: Distributionally robust optimization (DRO) protects decisions against distributional uncertainty by optimizing over an ambiguity set, but poorly aligned set geometry can require large radii and yield overly conservative decisions. We introduce diagnostic-transport DRO (DT-DRO), which uses held-out calibration data to adapt the ambiguity-set geometry to observed predictive errors. DT-DRO uses the conditional probability integral transform cumulative distribution function to diagnose systematic probability misallocation and translates this information into an outcome-level transport that jointly adjusts the ambiguity-set center and ground cost. The resulting formulation admits a computationally tractable dual reformulation. Theoretically, we derive valid ambiguity radii and decision-risk guarantees that tighten as estimation and approximation errors vanish, and show that DT-DRO can eliminate the nonvanishing robustness floor caused by model misspecification. Synthetic experiments and a power-outage application demonstrate improved decision quality, particularly under structural and tail misspecification.

Abstract: With the rise of univariate time series foundation models (e.g., Sundial, Timer), initial efforts have been made to extend them to multivariate settings. However, these models mainly focus on modeling correlations among variables. When they are applied to multi-station weather forecasting, two important factors are often overlooked: (1) the spatial information of stations, and (2) different error priors of different stations relative to the foundation model. In this paper, we propose WxFM-XL, a model for adapting univariate time series foundation models to multi-station weather forecasting. WxFM-XL introduces a cross-station error correlation prior graph to capture stationwise error priors with respect to the foundation model. Building on this, we further propose a dynamic fusion mechanism that adaptively integrates a spatial correlation graph with the error correlation prior graph. Experiments on multiple datasets demonstrate that our model outperforms state of the art baselines.

Abstract: Recent advances in mean-field games and its multi-population variants enable large-scale heterogeneous multi-agent systems to be modeled through representative agents and their associated mean-field distributions. However, existing approaches do not explicitly account for uncertainty in the behavior of other populations. To this end, we introduce a new paradigm: risk-averse multi-population mean-field games, where each population optimizes a worst-case expected reward over dynamically feasible ambiguity sets of mean-field flows of a subset of the other populations. Employing an occupation-measure formulation along with tools from set-valued analysis, we establish, under mild assumptions, several theoretical properties of the multi-population game, including the geometric properties of the ambiguity sets and the existence of a novel risk-averse multi-population mean-field equilibrium. Further, we derive contractivity results of the fixed-point operator under entropy regularization and show that it can be utilized to learn the equilibrium. Finally, we propose a risk-averse fictitious-play scheme and show that exploitability decays to zero, despite the additional nonlinearity introduced by the worst-case objective. We report several numerical experiments to illustrate convergence and risk-averse behavior.

Abstract: The scenario approach is a well-established statistical framework for data-driven decision-making. In particular, in data-driven optimization, the scenario approach unveils how the problem structure governs out-of-sample generalization, and offers a principled basis for assessing and certifying the reliability of the optimal solution as per constraint satisfaction. Despite its strong theoretical development and wide applicability, no software toolbox has been available to date that enables user-friendly, data-driven convex optimization within the scenario-approach framework. In this paper, we introduce Scen-Opt, an open-source software tool that integrates convex programming with data samples while providing statistical guarantees grounded in scenario theory. Scen-Opt is implemented in Python, supporting data-driven linear, quadratic, and semidefinite programming, and offers a Python-based web application with an intuitive and reactive graphical user interface (GUI) built using modern web technologies. Scen-Opt can be used directly through its online interface or installed locally, accommodating both manual input and data-file uploads (CSV, JSON, TXT, TSV, MAT, Excel, NPY, NPZ, Parquet). Built on a Python backend with a modern JavaScript frontend, Scen-Opt offers a highly user-friendly experience and efficient usability across desktops, laptops, tablets, and mobile devices. In this paper, Scen-Opt is applied to a set of representative benchmarks, demonstrating its practical effectiveness for data-driven convex optimization with guaranteed performance.

Abstract: Deep learning has revolutionised weather forecasting in recent years, especially through atmospheric foundation models, which offer competitive skill for a fraction of the computational costs of classic physics-based models. However, most existing foundation models are deterministic, limiting the generation of large ensembles for accurate uncertainty quantification, extreme weather risk assessment, and long-range weather forecasting. Furthermore, these models incur a large, often prohibitive, computational overhead to train from scratch. To address these shortcomings, we turn a pretrained deterministic prior model, namely the Aurora foundation model, into a generative ensemble-prediction model. To that end, we introduce a novel generative method, Denoising Stochastic Interpolants, combined with a replay buffer for Stochastic Differential Equation (SDE) rollout, enabling probabilistic training of SDE trajectories. Our stochastic foundation model, Xaurora, is finetuned from the small Aurora version, yet it approaches the state-of-the-art on global ensemble metrics and is competitive with the large version of Aurora. Our method is parameter and sample efficient, and generates skilful 15-day forecasts in 13 minutes. Our results demonstrate that deterministic foundation models can be efficiently extended into even stronger stochastic models.

Abstract: Event-informed forecasting requires translating reports and historical responses into changes to a numerical forecast. We propose TIMBRE (Temporal Integration of Memory-Based Responses and Evidence), which combines source-aware representation, state-conditioned response transfer, and reliability-guided fusion before a frozen forecast head. A separate readout adjusts interval widths while preserving the median. In a single-seed, one-epoch development study of 13 tasks, TIMBRE improves MAE over ordinary fusion on eight tasks but over native Chronos-2 on only two. Disabling response transfer in the trained model reduces BTC and AULF MAE by 47.04% and 6.81%, respectively. These findings identify sensitivity to learned response transfer rather than a general forecasting advantage. Missing development-set scores and the absence of retrained ablations limit attribution to individual evidence mechanisms.

Abstract: Precise constraint satisfaction is a prerequisite to deploying learned models in many areas, motivating methods that repair raw neural predictions with a repair procedure. Current methods unroll multiple repair steps in training and softly penalize constraint violations that remain after the unroll. This is compute- and memory-intensive, lacks robustness when the repair fails to converge, and surrenders most of the constraint satisfaction work to the repair. Our central finding is that, contrary to common practice, a single detached projection step suffices in training. We accomplish this with a Projection-Adaptive Loss (PAL), which uses the constraint residual after this single step to adaptively weigh constraint penalties on the raw prediction. In experiments, PAL is the only method that retains virtually perfect feasibility on extremely nonlinear constraints, and matches or outperforms current methods on synthetic and engineering benchmarks. Because it only requires a single detached projection step, PAL trains 2.5x faster than the canonical repair-based method (DC3) on its own ACOPF benchmark. PAL can also be trained when constraints are expensive to evaluate (e.g., via neural surrogates), a setting where current unrolled methods are memory-intractable.

Abstract: Deploying a new decision policy creates a cold-start problem for prediction models whose targets depend on the policy's actions: historical observations reflect earlier policies, while real observations under the new policy are not yet available. Simulation offers a way to address this gap by rolling out the target policy across counterfactual scenarios and using the resulting trajectories to learn how the system responds to those controls. The simulation-to-reality (Sim2Real) transfer of this simulator-trained model can then be backtested by evaluating it against real observations from past deployments. Using two real-world inventory-control deployments, we evaluate this process from three angles: simulator fidelity, zero-shot transfer to real behavior, and adaptation as real target-policy observations accumulate. The simulator-trained forecaster achieves lower point-estimate mean absolute percentage error (MAPE) than the same architecture trained on historical real data, reducing MAPE by 1.2-3.1 percentage points in Study 1 and 12.5-18.7 points in Study 2. After deployment, lightweight calibration using early real observations further reduces error by up to 2.5 percentage points. These results provide empirical evidence that simulator-generated counterfactual data can support cold-start forecasting under a new policy, and the resulting model can be further refined as real deployment data become available.

Abstract: Existing machine learning weather forecasting models typically generate forecasts through autoregressive rollouts at a fixed temporal resolution. While highly efficient for long-range prediction, this formulation can suffer from severe error accumulation when used with shorter time steps and does not explicitly encode the locality and temporal continuity of atmospheric dynamics. To address these limitations, we introduce **SDECast**, a Neural Stochastic Differential Equation (SDE) framework for continuous-time probabilistic weather forecasting. SDECast extends SDE Matching to learn stochastic dynamics directly in physical space, without requiring repeated SDE simulation during training. On a simulated geophysical flow, we show that SDECast recovers meaningful drift dynamics and faithfully reproduces the underlying continuous-time behavior. We then demonstrate its scalability to global weather forecasting at hourly resolution, where SDECast produces skillful probabilistic forecasts for lead times of up to five days.

Abstract: The subseasonal-to-seasonal (S2S) timescale, roughly from two weeks to two months ahead, is a critical forecast window for sectors such as agriculture, energy, and water management. Yet, it is widely known as the `predictability desert'. Recent AI weather models excel up to two weeks ahead but deteriorate beyond, largely because they are trained to predict fine-scale details that are neither predictable nor essential at S2S timescales. We argue that a more physically grounded objective is to forecast only the slowly varying components that remain predictable. Computer vision reached the same conclusion with the Joint-Embedding Predictive Architecture (JEPA), which predicts in latent space, discarding unpredictable details. In this work, we introduce S2S-JEPA, which brings the JEPA paradigm to S2S forecasting. It is tailored to this task through design elements from state-of-the-art AI weather models. S2S-JEPA achieves comparable skill to the gold-standard ECMWF physics-based ensemble and surpasses it on multiple metrics at weeks 5 to 6.

Abstract: Time series forecasting (TSF) increasingly drives decisions in transportation, energy, finance, healthcare, and infrastructure, yet current evaluation remains overly narrow: standard benchmarks reward low held-out error, while robustness studies typically reduce failure to Gaussian noise, random masking, or bounded adversarial perturbations. This obscures the real failure modes of deployed forecasting systems. Input-side anomalies are not merely noisier inputs: they often reflect structured events that alter temporal dynamics, break cross-variable dependencies, induce regime shifts, or propagate from faulty sensors to downstream decisions. These semantic, causal, and system-level failures cannot be faithfully captured by i.i.d. perturbations alone. The rise of TSF foundation models makes this evaluation gap more urgent, as unauditable pretraining corpora make held-out generalization increasingly unreliable. We therefore advocate scenario-grounded stress testing. Each test instance should include historical inputs and future targets, together with a semantic scenario, an explicit failure operator, and a measurable difficulty level. This shift makes evaluation interpretable, attributable, and deployment-relevant and friendly, enabling the community to ask not only which model is accurate, but under what conditions it fails and why.

Abstract: Balancing electricity demand and supply is increasingly difficult due to the inherent intermittency of renewable power generation and the stochastic power consumption. Grid operators require fine-grained, decision-relevant insights into household energy consumption to manage peak loads and design responsive tariffs, but increased transparency at this level raises significant privacy concerns. Traditional methods for explainable AI (XAI) can reveal sensitive information, while standard privacy techniques often reduce the usefulness of explanations. To address this issue, we introduce HXAI, a hierarchical framework that preserves privacy while enabling reasonable explainable analysis for grid-level demand management. HXAI consists of two main components: (1) a local model that generates fine-grained explanations within a secure, private environment, and (2) a zonal model that aggregates these explanations to support grid-level analysis while enforcing privacy through flexible privacy-budget management. We explicitly limit cumulative privacy exposure under repeated operator queries and show that the proposed framework preserves decision-relevant information without compromising household privacy. Experiments on both simulated and real-world energy datasets demonstrate that HXAI provides useful insights for zonal load management while ensuring that appliance-level consumption remains local and is never transmitted to grid operators. Our results show that preserving the semantic structure of explanations, rather than minimizing numerical error, is the key to XAI under differential privacy. This framework provides a way to achieve both privacy and explainability in energy management.

Abstract: Real-world time-series applications increasingly require models that can handle time series forecasting, context-conditioned prediction, and language-based temporal reasoning. Yet current time-series foundation models remain fragmented across these capabilities: numerical specialists often provide the strongest forecasts, while language-based models offer broader contextual understanding and analysis. A central challenge is to unify these heterogeneous capabilities without reducing their individual performance. We introduce OpenTSLM TeeMoE, a generalist time-series language model that can forecast directly from observed time series, reason over textual context and temporal patterns, and synthesize and refine predictions from external numerical forecasting specialists. We independently train three low-rank experts for forecast aggregation, native forecasting, and temporal analysis over a shared backbone. A learned LoRA mixture-of-experts controller then weights their frozen parameter updates for each request. Our proposed model achieves strong performance on widely used benchmarks for time series forecasting, context-conditioned prediction, and language-based temporal reasoning, ranking among the top three on GIFT-Eval by mean MASE rank, Context is Key by RCRPS, and TimeSeriesExam by accuracy.

Abstract: Pretrained time-series foundation models (TSFMs) are evaluated as forecasters of future values, yet for sparse series many decisions depend only on which future periods contain activity. Standard benchmarks do not assess this. On five sparse datasets, we rank positions within forecast windows that contain both events and zeros. The released point forecasts of 12 TSFMs improve chance-corrected average precision over training-free references by at most 0.031, and in chance-corrected AUC the median TSFM falls below them on every dataset. With event supervision, linear probes of six frozen backbones improve on their backbone's point forecast in 29 of 30 backbone--dataset pairs. Averaging the predicted quantiles instead of taking their median improves the ranking of most TSFMs that forecast the median, and on two datasets the strongest such outputs rival the probes. The probes' advantage over raw-context learners depends on the dataset, and under the same probe, pretrained features outperform randomly initialized ones for five of six backbones. For sparse-event ranking, released point forecasts thus add little over simple references, whereas lightweight event heads on frozen TSFMs rank events better than these forecasts, and the best of them exceed gradient-boosted trees trained on the raw context on three of the five datasets. More broadly, assessing pretrained forecasters on tasks beyond value forecasting requires reporting their outputs, supervised probes of their representations, and raw-context and randomized controls side by side, since each supports a different conclusion.

Abstract: Diffusion models have recently shown strong potential for probabilistic multivariate time-series forecasting by modeling complex conditional distributions. Recent decoupled diffusion frameworks further separate forecasting into deterministic prediction and stochastic residual generation, making it natural to derive dependency graphs from deterministic representations and use them to guide residual diffusion. However, we show that this direct structural transfer is unreliable. Although deterministic-derived graphs encode useful global dependency priors, they exhibit substantial edge-level misalignment with residual dependency structures, introducing inaccurate or redundant conditions during residual generation. This reveals a previously overlooked deterministic-to-residual structural alignment problem in decoupled diffusion forecasting. To address this problem, we propose GARDiff, a Graph-Aligned Residual Diffusion framework for probabilistic multivariate time-series forecasting. Instead of treating deterministic-derived graphs as fixed diffusion conditions, GARDiff progressively adapts them to residual generation. Specifically, GARDiff estimates residual uncertainty to distinguish high- and low-uncertainty regions, enabling uncertainty-aware structural refinement, and further performs timestep-aware edge sparsification during reverse diffusion to evolve graph conditions from broad dependency aggregation to localized residual refinement. Extensive experiments on six real-world benchmarks demonstrate that GARDiff consistently improves probabilistic forecasting performance and uncertainty calibration over strong baselines.

Abstract: Neural Koopman autoencoder models have been shown to successfully build a latent embedding with linear dynamics for arbitrary dynamical systems, enabling strong performance in long-term time series forecasting. However, these models usually work in a deterministic setting, which does not allow the quantification of the uncertainty of their predictions. Thus, we propose the new Variational Augmented Invertible Koopman AutoEncoder (VAIKAE), in which the latent embedding follows a Gaussian distribution instead of being deterministic. A key property of the VAIKAE architecture is that it leverages normalizing flow models, enabling the use of likelihood computations in the state space of dynamical systems for training a model. We further propose new strategies for uncertainty-aware latent data assimilation with a trained VAIKAE model. The effectiveness of our methods is demonstrated in a series of experiments on long-term time series forecasting benchmarks.

Abstract: Time series modeling increasingly demands high-quality supervision, yet target observations remain scarce - exogenous inputs are broadly available, but target measurements are often unavailable due to cost, infrastructure, or accessibility constraints. Can models trained on observed locations reconstruct target time series where measurements have never been collected? We term this zero-shot time series reconstruction. A naive approach - directly mapping exogenous inputs to targets - can yield predictions at unobserved locations, but without target signals, such models fail to capture the intrinsic dynamics of the target variable, producing overly smooth outputs that underestimate extremes. This reveals systematic errors that call for explicit modeling and calibration. We propose ZeroDiff, which constructs an informed prior from exogenous variables alone, then learns to calibrate reconstruction errors through diffusion - training on observed locations and generalizing to unobserved ones. Experiments across diverse real-world datasets demonstrate significant improvements over existing approaches. Our code is available at https://github.com/YingdaFan/ZeroDiff-ICML2026.

Abstract: Covariate effects vary across contexts and shift over time, requiring forecasters to assess how to use them for each forecasting context. As forecasting proceeds, observations for earlier forecasts become available, providing feedback on past covariate use for subsequent forecasts. However, when multiple covariates act together, the forecast error reveals the numerical discrepancy from the observation but not how the covariates should have been used. We introduce JudgeCast, an experience-based framework for time series forecasting with covariates. Following the judgmental adjustment practice, a frozen TSFM provides the base forecast, while a frozen LLM uses the current context and relevant experience to adjust it. Within the adjustment, assessing covariate effects and determining the numerical adjustment serve distinct roles, so JudgeCast first forms explicit covariate-wise judgments and then determines the adjustment. After observation, JudgeCast uses the observed residual of the base forecast to reconstruct alternative judgments and evaluates the original and alternatives through their resulting adjustments. The best-performing decision is selected and retained as validated experience for subsequent forecasts. Across diverse real-world datasets, JudgeCast outperforms strong baselines. Ablations show that explicit covariate-wise judgment can improve forecast-time adjustment, while residual-guided experience construction yields more reliable forecasting gains than retaining raw decisions as experience.

Abstract: Recent power measurements provide valuable information for photovoltaic(PV) power forecasting, but directly extrapolating short-term trends can introduce substantial errors over longer forecast horizons. To address this challenge, we propose state transport routing (STR), a lightweight adapter that refines the predictions of a frozen forecasting model. STR combines the original forecast with two complementary trajectories derived from the latest measured power level and its recent trend. A horizon-conditioned router adjusts their contributions over the first 120 min, while leaving subsequent predictions unchanged. Experiments on four public PV datasets show that STR consistently outperforms a parameter-matched residual adapter. On PVDAQ, the same approach improves five neural forecasting backbones, reducing all-horizon normalized mean absolute error by 0.0201-0.2364 percentage points, with paired 95% confidence intervals excluding zero. No reliable improvement is observed for LightGBM. These findings demonstrate the potential of structured state adaptation to improve short-term forecasting across different neural architectures without retraining the underlying models or altering their longer-horizon predictions.

Abstract: Multivariate time series forecasting (MTSF) is critical across many real-world domains. Existing deep learning approaches fall into two paradigms with distinct limitations: channel-independent (CI) methods unconditionally ignore cross-variable dependencies and model only temporal dynamics, while channel-dependent (CD) methods consider both but typically rely on architectural compromises to mitigate overfitting and computational overhead. We therefore propose Chameleon, a specialized CD state space model (SSM) that enables data-dependent, fine-grained interactions across variables while scaling linearly with their number. By connecting selective SSMs with the Kalman filter, we leverage the missing measurement update in the former for cross-variable modeling while preserving the SSM backbone for robust temporal modeling. We further identify favorable inductive biases of GatedDeltaNet for time series, adapt it as our backbone, and improve generalization through additional techniques, including a previously unexplored stochastic perturbation of reversible instance normalization. On strongly dependent ODE and PEMS datasets, Chameleon achieves the best MSE and MAE across all settings, while its CI ablation and prior CD methods incur 61-178% higher MSE on average. Across 28 standard benchmark settings, Chameleon also achieves better MSE and MAE than each baseline in at least 27 and 22 cases, respectively. Training-time and peak-memory analyses on Traffic and ETT further demonstrate competitive efficiency and favorable memory scalability across different variable counts.

Abstract: Deep forecasters predict from a fixed-length lookback window, and lengthening it gives diminishing returns at a growing cost. Retrieval augmentation instead shows the model how similar past situations continued. Retrieving a whole past window gives every variate the continuation of the same past moment. In multivariate series, however, the best past match differs from variate to variate. We present GNA (Granular Neighbor Assembly), a retrieval layer for forecasting backbones that assembles neighbors at two granularities: whole past windows, which keep the variates coherent, and per-variate neighbors, in which each variate takes its future from its own best-matching past. A learned gate decides, per forecast step and variate, how much to trust these futures against a persistence forecast, next to the backbone's own forecast. Candidates come from an embedding trained to predict each window's future, and retrieval is strictly causal: a past window is used only once its future has been observed. With the same lookback for every model and the same retrieval constants for all datasets, GNA improves two Transformer backbones in 85 of 96 dataset-horizon settings, gives the lowest MSE on 8 of 12 standard benchmarks and beats its backbone in every seed on 10 of them. Both granularities are needed, and neighbors of mismatched queries are worse than none. Retrieval helps most where the lookback says least: the gate shifts trust to retrieved futures further ahead. Where it fails, on hourly non-stationary series at long horizons, the loss is consistent with a drifting level of the retrieved futures.

Abstract: Spatial-temporal (ST) forecasting underpins many real-world systems such as traffic, climate, and energy networks. While existing methods implicitly assume strong spatiotemporal coupling, we observe that real-world ST data exhibits distinct coupling regimes, ranging from temporal-dominated and spatial-dominated to strongly coupled patterns. This mismatch causes current models to suffer from spurious dependencies and degraded performance when one correlation dominates. To overcome this limitation, we aim to dynamically modulate spatial and temporal modeling based on the data's inherent coupling structure. However, three key challenges exist: unknown coupling structure, heterogeneous coupling dynamics, and suboptimal spatial modeling. We propose AdaST, an adaptive ST forecasting framework that tackles these challenges through a decompose-recompose paradigm. AdaST factorizes inputs into components capturing different coupling patterns using heterogeneity-aware experts. Each component is processed by role-aligned modules, and a correlation-informed adaptive recomposer integrates them for final prediction. Extensive experiments confirm that AdaST significantly outperforms state-of-the-art baselines, validating the necessity of an adaptive approach.

Abstract: Artificial intelligence is increasingly deployed in critical industrial domains, including healthcare, energy grids, subsurface exploration, where failures can have severe consequences for human safety, system stability, and economic outcomes. Yet AI is still evaluated primarily through benchmark accuracy, a model-centric metric that fails to capture the structural complexity and risks of real-world deployment. We propose a framework that views industrial AI reliability as a problem of structural alignment across four interacting worlds: physical, representational, machine, and human cognitive. These worlds are connected through two interfaces: digitalization, linking physical reality to computational representations, and goal encoding, translating human cognition to the machine objectives. Together, they define the space of admissible solutions. We characterize the solution space through four attributes: existence, non-uniqueness, robustness, and interpretability and show how mismatches arise at interfaces and propagate across worlds to produce reliability failures. Applications to healthcare, energy grids, and subsurface exploration illustrate that although dominant failure modes differ across domains, for example, interpretability in healthcare, robustness in energy grids, and non-uniqueness in subsurface exploration, all originate from a shared structural mechanism. By shifting the focus from model-centric evaluation to system-level alignment, this framework offers a principled foundation for assessing and governing reliability in industrial AI systems.

Abstract: Online Resource Allocation (ORA) is a fundamental framework for sequential decision-making problems under budget constraints. Classical ORA models typically assume that resources are monotonic, meaning that selecting actions can only decrease the available budget. In this work, we study a more general setting with replenishable budgets, in which actions may either consume or replenish resources over time. This extension is necessary to capture scenarios such as inventory systems or energy markets in which capacity can be actively recovered. We develop a dual-based algorithm that recovers best-of-both-worlds guarantees for standard ORA when the replenishment factor $β= 0$, and improves them when $β> 0$. In particular, our algorithm attains $\widetilde{\mathcal O}(\sqrt{T})$ regret in the stochastic setting and $\widetilde{\mathcal O}(\sqrt{T})$ $α$-regret in the adversarial setting, where $α$ depends on the per-round budget and on the replenishment factor of the void action. Moreover, the algorithm ensures strict satisfaction of the budget constraints.

Abstract: Existing multimodal time series foundation models (TSFMs) typically model heterogeneous modalities through largely shared mechanisms, overlooking the distinct forecasting roles of endogenous and exogenous modalities. In this work, we propose QiYao-M, a role-aware multimodal TSFM that models the two types of modalities separately. For endogenous modalities, to capture how they evolve along with the underlying temporal dynamics, we introduce an Endo-Multimodal Predictor and Endo-Multimodal Supervision to explicitly learn their evolution from history to the future. For exogenous modalities, to generalize across domains and across various modality types and numbers under the scarcity of exo-multimodal pretraining data, we propose an Exo-Multimodal Retrieval Enhancer that enables rapid downstream adaptation without updating the TSFM parameters. We further introduce Endo-Modality Proxy Training to train this retrieval module without exogenous multimodal pretraining data. Extensive experiments across unimodal and multimodal benchmarks demonstrate strong forecasting performance in scenarios both with and without exogenous modalities.

Abstract: Longer histories can improve time-series foundation models (TSFMs), but require substantially higher inference cost. We therefore ask whether contextual information can be provided more efficiently through a compact set of learned token embeddings. We introduce PaCTS, which generates a small set of instance-adaptive latent prompts in the form of continuous embedding tokens conditioned on the visible context. These prompts serve as compact context surrogates for frozen TSFMs. PaCTS constructs them from instance-specific global statistics and further refines them with segment-level temporal information, capturing both global characteristics and local temporal variations. The prompt module is jointly trained and deployed across heterogeneous time series with the frozen backbone. Extensive experiments demonstrate the effectiveness of prompts as context, consistently improving forecasting across context lengths and model architectures. With a shorter input context, PaCTS can outperform the same frozen backbone using double context while requiring substantially less inference computation. Compared with weight-space adaptation methods, PaCTS achieves stronger improvements and better out-of-distribution generalization.

Abstract: LLM-based agents are increasingly used for time-series forecasting because they can organise contextual information, perform multi-step analysis, and guide the sequence of actions required to complete forecasting tasks. Most existing agents focus only on the current forecasting instance. However, in real-world deployments, forecasting commonly operates online, with new forecasts issued from the currently available history as the forecast origin advances and the ground-truth targets of earlier instances progressively become available. These targets provide feedback on the actions taken in earlier instances, yet existing agents generally do not preserve or utilise this information to adapt their subsequent actions. To address this limitation, we introduce FASE, a Feedback-Aware Self-Evolving forecasting agent that converts such feedback into task-specific experience for subsequent forecasting instances. FASE combines episodic memory, which retrieves relevant completed instances, with online policy learning, which summarises the feedback accumulated across instances into ranking guidance. The proposed framework is evaluated on 29 dataset configurations selected from the GIFT-Eval benchmark. Across these 29 configurations, FASE attains the strongest aggregate point forecasting performance among the evaluated methods and reduces the normalised MAE by 9.1% relative to the best individual foundation model baseline. The results further indicate that the cumulative advantage of FASE increases as delayed feedback accumulates. Together, these findings demonstrate that FASE can continually self-evolve through feedback from completed forecasting instances without updating the parameters of the LLM.

Abstract: Decision-focused learning (DFL) trains predictors for downstream decision quality, but often relies on optimal reference decisions that are expensive to obtain. We present PolyStepOR, which trains directly from realized decision costs without pre-computed optima and extends to in-constraint predictions through repair or infeasibility penalties. To handle piecewise-constant losses, PolyStepOR perturbs predictor parameters, evaluates the resulting decisions, and uses optimal transport to favor lower-cost directions, requiring no derivatives. Without task-specific tuning, PolyStepOR performs strongly on classical optimization benchmarks and competitively on predicted-constraint and real-world problems. Theoretically, we characterize decision-preserving perturbations and boundary detection, bound sensitivity to cost errors, and establish stationarity guarantees for a smoothed objective. PolyStepOR thus replaces optimal reference decisions and derivatives with forward evaluations.

Abstract: Safe reinforcement learning (RL) commonly enforces expected-cost constraints, but such expectation safety may fail to control the probability of rare high-cost trajectories. Chance-constrained MDPs (CCMDPs) impose a stronger probability-level requirement, but are widely viewed as harder because the chance constraint is nonconvex and depends on the full trajectory rather than a Bellman-linear expectation. In this paper, we reveal that this computational difficulty does not necessarily imply a higher statistical price. For tabular discounted CCMDPs with fixed bounded successor support and access to a certified planning oracle, we establish a model-based upper bound, with a matching lower bound up to logarithmic terms. Technically, our key idea is the \emph{Bellman distributional certificate}, which constructs a Bellman recursion for constraint violation probabilities before policy selection. The certificate can be reused across candidate policies; combined with shared row-wise reverse-KL confidence sets, it gives a policy-uniform trajectory-KL transfer without a union bound over policies or time--budget Bellman tables. For stochastic policies, we give a model-free variance-reduced policy-gradient algorithm with a finite-sample expected KKT-residual guarantee and independent validation of every accepted policy. Numerical experiments on synthetic CCMDPs and an IEEE 14-bus energy storage control benchmark illustrate the safety and mechanism behavior of the proposed algorithms.

Abstract: Graph-structured optimization with linear constraints is fundamental to critical infrastructure but faces scalability limits due to massive strict hard constraints and high dimensionality. While recent projection-based methods such as Trainable Sampling Kaczmarz-Motzkin Net (T-SKM-Net) guarantee feasibility, they face high computational costs in dynamic environments by processing the entire constraint set and requiring expensive matrix factorizations. To bridge this gap, we propose the Accelerated Trainable-SKM (AT-SKM) Net framework. To concentrate computation on the active constraints and eliminate redundant calculations, we introduce a hybrid sampling strategy guided by a topology-aware heterogeneous GNN model. To efficiently handle topological shifts in graph-based constraints, we employ a Cholesky Update mechanism that theoretically reduces the equality projection complexity from O(N^3) to O(N^2) under low-rank perturbations. Experiments on random geometric graphs, N-1 Security-Constrained DC-OPF, and minimum-cost gas transport problem demonstrate that AT-SKM reduces iteration counts by up to 85% and achieves 2.95x-7.29x SKM layer speedups, while maintaining zero constraint violations.

Abstract: We present TimeBraid, a series of unified time-series and language models that align pretrained language models and pretrained time-series foundation models through interleaved global residual attention layers. Each model inherits knowledge, instruction following, and reasoning from one side, continuous-signal perception and zero-shot forecasting from the other, and fuses the two in a shared representation space where both modalities are understood and generated. We study the design choices that make such unified modeling work: where to align the two representation spaces, how to ground language in temporal structure, how to balance understanding with generation, and how to keep joint optimization stable. The resulting recipe combines a unified prompting scheme for diverse time-series and text tasks, stabilized joint training, and supervision from 2.2M curated series--text pairs and 4.9M instruction-tuning samples. Across benchmarks spanning time-series perception, understanding, reasoning, and both context-aided and unimodal forecasting, TimeBraid remains competitive with far larger general-purpose models and task-specific counterparts.

Abstract: Time-series foundation models (TSFMs) provide forecasts for operational decisions, but accuracy alone does not determine their value. Evaluating agents that use these models requires measuring decision quality and forecast cost. FWBench evaluates this capability on 1,251 electricity and cycle-hire cases using fixed forecast tools and simulated capacity contracts. Agents select models, histories and horizons, then submit capacities to minimize a stated loss-cost objective. We evaluated two hosted and eight local configurations, including small language models, and tested local models with and without TSFMs. GPT-6 Astra bought inexpensive short-horizon forecasts selectively, using 2.5% of the budget, and outperformed fixed policies when the saved decisions were scored with three loss-cost weightings. FWBench enables reproducible evaluation of how language models select and use time-series forecasts to make decisions under cost constraints.

Abstract: Short-horizon forecasts of atmospheric temperature are needed to support climate-aware digital-twin systems, but such forecasts must be produced where thermal observations are incomplete. This study evaluates a physics-informed neural network for potential-temperature forecasting, constrained by a pressure-coordinate thermodynamic advection-source equation and a diabatic-source closure fit from the preceding 12-hour period and frozen before future-time training. Using hourly ERA5 reanalysis at three pressure levels, the model is evaluated as a conditional hindcast at lead times of one, two and three hours against persistence, local-trend, and two matched neural-network baselines, one of which receives the same future meteorological forcing as the PINN, helping distinguish the physical constraint from access to future forcing. In an Oklahoma development case, mean RMSE improvement over the strongest baseline grew from 8.1\% at one hour to 23.8\% at three hours; under an observation-density sweep down to 5\% of candidate locations, this 3-hour advantage remained 14.6--16.9\%, with no evidence that lower density improves performance. Under a fixed protocol transferred to an Alabama heat event with three virtual-observation layouts, three-hour improvement ranged 19.7-24.4\% with consistent origin-level wins. A parallel Montana stress test, in which fixed pressure levels intersected complex terrain, produced a three-hour degradation of roughly 17.5\%, identifying a terrain-related applicability limit of the formulation. Together, these results indicate that the physics constraint's benefit grows with forecast horizon, persists under severe observation sparsity, and transfers across regions, but is bounded by the validity of a fixed vertical-coordinate representation over complex terrain, evidence relevant to physics-constrained components of climate-aware forecasting and digital-twin systems.

Abstract: Probabilistic time series foundation models (TSFMs) provide coordinate-wise predictive distributions, but these marginals do not determine a joint distribution over multivariate future trajectories. We study training-free coupling of frozen TSFM marginals into multivariate forecast sample paths. Our primary evaluation fixes the empirical marginal sample multiset at every channel--horizon coordinate across methods, isolating the effect of coupling alone. Historical temporal and channel relations substantially improve their corresponding dependence diagnostics. The same pattern persists when the fixed-marginal constraint is removed and paths are sampled directly, and remains present under native multivariate backbone inference. These results support treating dependence reconstruction as a distinct post-processing problem for probabilistic TSFMs.

Abstract: Accurate multi-step traffic forecasting remains challenging because observed traffic signals contain heterogeneous temporal dynamics with different characteristics and levels of predictability. Existing approaches typically model these dynamics within a unified representation or rely on predefined decomposition rules, which may limit their ability to flexibly separate persistent patterns from rapidly varying fluctuations. To address this issue, we propose the Adaptive Decomposition Network (ADNet), a component-specific forecasting framework that adaptively disentangles traffic dynamics into dominant and residual components. ADNet introduces a learnable complementary spectral decomposition mechanism that determines the contribution of each frequency bin to the two components. Unlike hard frequency partitioning, every frequency bin can contribute to both components with different learned proportions, allowing the decomposition to be optimized jointly with the forecasting objective. The reconstructed components are then modeled by two dedicated spatiotemporal forecasting branches, and their predictions are integrated to generate the final multi-step forecast. Experiments on the Alameda and Orange regions of the TraffiDent dataset show that ADNet achieves the best performance in 20 of the 24 reported region-horizon-metric comparisons, with particularly clear gains at longer forecasting horizons. Capacity-controlled ablation experiments further show that the learnable decomposition substantially outperforms a fixed decomposition and provides additional improvements beyond the dual-branch architecture alone. These results demonstrate the effectiveness of adaptive decomposition and component-specific modeling for multi-step traffic forecasting.

Abstract: Data centers are being developed at an unprecedented pace, yet their energy and water impacts, and the spatial and temporal distribution of these impacts, remain poorly characterized. Data centers consume water for cooling (direct) and through electricity generation (indirect). Decisions on siting and cooling technology result in water-energy trade-offs that extend impacts beyond the facility's location. Existing assessment frameworks rely on facility efficiency metrics and average grid water intensity factors, suppressing the temporal impacts of data center load and generation availability. They also attribute indirect consumption to the facility's location rather than to the generators (and corresponding hydrologic regions) that respond to the added load, misattributing spatial impacts. To close this gap, we develop a computational model of the data center-energy-water nexus that links facility cooling and electricity demand with hourly economic dispatch, generator-level water consumption, and monthly subbasin depletion. Built on open-source data, the model resolves where and when water is consumed, and where this consumption compounds existing water risk or creates new risk. Using the model, we study different cooling configurations and proposed developments in the state of Michigan. Air-cooled data centers halve total water consumption relative to evaporative cooling, but increase electricity demand and raise indirect water consumption by one-third, shifting the water footprint from the facility to generators. Mapping these changes to subbasins reveals depletion increases beyond the data center sites, in regions that facility-level reporting may overlook. These results show that data center water and energy impacts cannot be assessed in isolation, motivating the need for integrated modeling to inform siting, design, and reporting practices.

Abstract: Energy networks face a paradigm shift driven by renewable integration, uncertainty about required flexibility, distributed markets, and smart demand. Increasing asset interactions, cyber dependencies on communication and computation systems, and the deployment of AI agents demand a holistic, system-wide approach to understand the system's emergent behaviour. These transformations affect energy generation, demand adaptation, grid operations, and market dynamics, forming a complex engineered \emph{system of systems}. We argue that a complex-systems perspective can help to understand this evolution. Drawing lessons from two highly successful large-scale engineered systems, the Internet and agile software engineering, we highlight how prioritising design for evolution over traditional design for functionality enables energy systems to adapt to net-zero dynamics and handle unforeseen uncertainties. We discuss how the notion of federated energy communities (FEC), which aims for an open energy system with distributed coordination, aligns with this perspective. In FECs, each EC produces, stores, and manages its own energy, enabling it to trade with peers, respect grid constraints, and reach fair agreements. Beyond regulatory issues, the main challenge is identifying constraints that can orchestrate EC operations at the scale and reliability standards required of power networks, without unnecessarily limiting the innovation needed for system evolution. We then conclude with tentative design principles for future decentralised, self-organised energy networks through the lens of design for evolution, and how to apply them to a bottom-up architecture of autonomous energy communities.

Abstract: Multivariate time-series forecasting is essential to many real-world applications. Recent large vision models (LVMs) offer a promising paradigm by transferring cross-domain visual priors to time-series forecasting. However, existing LVM-based methods face two key challenges: balancing independent visual representation spaces with cross-variable dependency modeling, and adapting vision backbones pretrained on natural images to the distinct temporal semantics of time-series images. To address these challenges, we propose MUSE, a dependency-aware adaptation framework built on a fully frozen pretrained MAE. First, the Variable Context Refinement Module (VCR) aggregates shared temporal information within each variable and models cross-variable contextual dependencies while preserving independent visual spaces. Second, the Temporal-Periodic Refinement Module (TPR) performs lightweight refinement at different encoder depths and explicitly models across-period temporal dependencies and within-period periodic dependencies. The two modules independently produce forecasts, which are fused through a learnable prediction-level gate. Experiments on 10 real-world datasets demonstrate that MUSE achieves state-of-the-art performance.

Abstract: Most existing time series forecasting methods rely solely on numerical observations, overlooking rich contextual information from auxiliary texts. Recent multimodal approaches attempt to incorporate textual signals, but they often treat text as static features or use large language models as forecasting backbones, limiting their ability to capture temporal dynamics and increasing computational cost. To address these challenges, we propose TAC-Time, a unified framework that transforms textual information into additional temporal channels. By modeling text features jointly with numerical sequences in a shared temporal backbone, TAC-Time preserves temporal continuity and periodic structures while remaining efficient and scalable. This formulation also enables systematic interpretability analyses. We show strong cross-modal dependencies through attention and frequency-domain analyses, and identify predictive textual signals whose correlation-aware alignment yields partial forecasting improvements. Extensive experiments on real-world multimodal benchmarks demonstrate that TAC-Time outperforms prior methods.

Abstract: Time series forecasting underpins critical decision-making across diverse domains. While large language models (LLMs) offer promising reasoning capabilities, existing LLM-based time series forecasting approaches either reduce them to numerical predictors that bypass their strengths, or allow direct forecast generation that destabilizes predictions in non-stationary settings. We introduce CTRL, a framework that decouples semantic reasoning from quantitative prediction. A frozen backbone generates base forecasts, while specialized LLM agents function as controllers that analyze backbone prediction errors through decomposed trend, seasonal, and irregular components, grounding reasoning in interpretable temporal structure. Each agent outputs compact control signals that a lightweight residual decoder translates into forecast corrections. CTRL incorporates label-free test-time adaptation that detects distribution shift from input statistics alone and readapts control signals with only 3-24 LLM calls via caching. CTRL is explicitly designed to improve robustness under non-stationary temporal dynamics and distribution shift, while remaining competitive on highly stationary time series where adaptive correction provides limited additional benefit.

Abstract: Forecasters often know an event is imminent but not the shape, size, or timing of its effect. We introduce Event Signature Transfer (EST), a training-free, model-agnostic operator that turns a completed past event into an explicit forecast scenario. EST removes a source event's own trend and seasonality, then scales and retimes the remaining event signature onto a native forecast, preserving the forecast's linked structure and reducing to it exactly at zero strength. Because it reads only output quantiles, EST applies to any quantile forecaster, with no training, no model internals, at transfer time. Across twelve real episodes and ten synthetic scenarios on Chronos-2, TimesFM-2.5 and Toto-2.0, manually configured EST reduces real-episode WQL by 21.7-90\% in-sample. On Chronos-2, it leads eleven of twelve matched comparisons against covariate conditioning, activation editing and raw replay. The operator builds a scenario; it does not estimate its likelihood.

Abstract: Covariate-rich time-series forecasting requires deciding how external variables enter the target forecasting path. Existing Transformer-based forecasters usually build a covariate representation and pass it to the encoder without an explicit admission stage. This paper studies pre-encoder covariate admission as an input-side interface that regulates that representation immediately before encoder processing. We implement the interface with a lightweight representation-level pre-encoder gate that assigns sigmoid scores to representation units, and we also study a usage-regularized variant that penalizes average admission. The interface is evaluated as a plug-in module for TimeXer, Inverted Transformer (iTransformer), and Patch Time Series Transformer (PatchTST) under a zero-extra-tuning protocol, where each gated model inherits the corresponding baseline configuration. Experiments on the Electricity Transformer Temperature minute-level (ETTm1 and ETTm2) datasets, Traffic, Energy, and influenza-like illness (ILI) include paired forecasting comparisons, gate-placement ablation, initialization ablation, controlled covariate-admission analysis, and a variance inflation factor (VIF)-informed permutation feature importance (PFI) diagnostic case study. In the tested settings, the gate is competitive with the corresponding baselines, and the usage penalty reduces average admission scores while keeping forecasting errors close to the unpenalized TimeXer setting.

Abstract: Quantum long short-term memory (QLSTM) models extend recurrent sequence learning with variational quantum circuits, but their optimization behavior can vary substantially across random initializations and temporal contexts. This paper evaluates a recursive QLSTM architecture against a standard QLSTM for one-step-ahead prediction of daily minimum and maximum temperature. Using daily weather observations from Toronto and identical training settings, we compare convergence, predictive accuracy, and generalization across input windows of 8, 16, and 32 days over 20 random seeds. The recursive model consistently reaches a near-optimal test loss earlier, reduces mean absolute error and root mean squared error, and exhibits a smaller generalization gap. These results indicate that recursive quantum feature transformations can improve stability and out-of-sample performance for compact hybrid quantum--classical temporal models.

Abstract: Long-term multivariate time series plays a significant role in many application areas such as power systems, trading, etc. However, their accurate prediction is quite difficult for conventional forecasting methods as they often exhibit high dimensionality and complex relationships. Recent works show that transformer-based approaches are quite effective for long-term forecasting thanks to their attention mechanism. However, in the presence of complex high-dimensional inputs, they show evidence of oversmoothing, limited capacity, and opacity. To this end, this paper introduces SETTer, a transformer-based model that addresses these challenges by incorporating novel techniques for decoupled self-attention and hybrid masking. The proposed techniques enable SETTer to effectively capture the dominant short- and long-term patterns across the temporal and channel dimensions. In addition, we enrich the model layers with simple explainable structures that indicate the discriminative pattern of SETTer. We show that with a single-layer transformer architecture, SETTer can effectively model long-term dependencies in the presence of varying data complexities. Extensive experiments on real-word benchmark datasets for long-term multivariate time series forecasting demonstrate that SETTer outperforms state-of-the-art models in 88% of the scenarios.

Abstract: An ensemble can improve photovoltaic forecasts while adding components that contribute little or increase computation. We assess these effects through matched comparisons and ablations of a fixed heterogeneous predictor bank. Hourly experiments use GEFCom2014 and three additional public datasets, with chronological partitions and three seeds. Under retrospective ERA5 assistance, static fusion reduces scaled mean absolute error against matched boosting by 1.11%, 4.41%, and 1.63% on PVDAQ, OPSD, and Ausgrid; only OPSD remains supported after multiple-comparison correction. Weather gating offers no consistent incremental benefit. Exploratory member removals show group-level dependence alongside individual redundancy. A separate, previously inspected fifteen-minute case replaces one neural member with a tree predictor: normalized error falls by 1.72%, but measured inference is slower. These findings support component-wise evaluation with explicit limits on weather availability and test-set reuse.

Abstract: Earth system modeling is shifting from task-specific predictors toward foundation models with general spatiotemporal representation capabilities. Although these models can jointly encode dynamic Earth fields, external forcings, and static geographic context for multistep forecasting, accurate point predictions or statistically calibrated intervals alone are insufficient for high-impact applications such as extremeweather warning, flood control, renewable-energy dispatch, and emergency resource allocation. What matters in practice is whether predictive uncertainty can be translated into reliable decision risk under specific actions, loss functions, and risk preferences. We propose a decision-oriented uncertainty quantification framework for Earth system spatiotemporal foundation models. The framework produces predictive distributions of future states and uses a decision risk adapter to map forecast samples, decision context, and utility functions into action-conditional risks. A utility-aware calibration module further enforces reliability at the downstream decision-loss level rather than only at the forecast-value level. Calibrated risks are then used to select warning, dispatch, inspection, or resource-allocation actions. Compared with the strongest baseline, the proposed method reduces decision regret by 18.7%, lowers the missed-event rate from 14.2% to 9.1%, and improves expected utility by 11.6%, while maintaining 90.4% predictive coverage and reducing decision calibration error from 0.083 to 0.047. These results suggest that decision-oriented uncertainty quantification can improve the robustness and operational value of Earth system foundation models in risk-sensitive applications.

Abstract: Managing drawdown, the peak-to-trough decline in an investment portfolio's value, is a precondition for long-term survival in practical investment management. However, mainstream stock forecasting methods predominantly optimize returns or Sharpe ratios under the independent and identically distributed (i.i.d.) assumption. Real markets do not follow this assumption, triggering catastrophic drawdowns. We propose a cross-asset state-space trading system (CAST), consisting of two components: The predictor, Cross-Asset Collaborative Kalman Filter (CoKF), estimates each asset's latent state online, coupling all assets through their correlations and adaptively fusing multiple integrated-random-walk orders. The controller, Model Predictive Control (MPC), converts the predictor's forecast into trades, using forecast uncertainty as an explicit risk penalty that controls drawdown. We evaluate CAST on four real-world stock markets over a 15-year test window and show that it consistently occupies the return-drawdown Pareto frontier, achieving strong risk-adjusted performance while maintaining substantially lower maximum drawdown than competitive baselines. A stress test across crisis periods further demonstrates robust behavior under market shocks and distribution shift. Because the predictor and controller interact only through the predicted price path, both are plug-and-play, making CAST a modular, interpretable trading system. The code is available at https://github.com/FanBroWell/CAST

Abstract: The increasing penetration of renewable energy and rising electricity demand are driving the need to integrate new buses and transmission lines into transmission grids. These trends are reshaping transmission expansion planning (TEP), motivating the development of effective methodologies to manage the resulting complexity. This paper introduces the longest shortest-path connection (LSPC) algorithm, a graph-based method to enhance the mixed-integer linear programming disjunctive formulation of TEP using valid inequalities (VIs). Traditional approaches for determining big-M coefficients in disconnected TEP networks typically rely on solving the computationally intensive longest path problem (LPP). In contrast, LSPC circumvents these limitations by efficiently identifying relevant power-flow paths between disconnected buses within the expansion network. We demonstrate that the VIs generated from these identified paths dominate those derived from LPP-based methods and other existing approaches.

Abstract: Machine-learning weather models (MLWMs) now match or outperform operational numerical weather prediction (NWP) at global medium-range forecasting, at far lower inference cost. Many deployed MLWMs are deterministic, producing a single forecast with no estimate of its own uncertainty, whereas a growing family of trained-probabilistic models generate calibrated ensembles directly, at the price of a dedicated training run. We ask instead how much uncertainty can be extracted from a deterministic checkpoint that already exists, without retraining it. Where physical ensembles represent model uncertainty by stochastically perturbing parametrisation tendencies, we perturb the network's raw weight tensors at inference time, a scheme we call stochastically perturbed weights (SPW). We also ask whether it works, where and on which scales to inject the noise, and where it fails. A three-phase ablation across four deterministic backbones, Aurora, GraphCast, SFNO, and AIFS, selects one production baseline per model, benchmarked against the trained-probabilistic AIFS-ENS, FourCastNet 3 and Atlas as well as the operational ECMWF ensemble (IFS-ENS) over 112 initialisation times. At a 240 h (10-day) lead time the SPW ensembles reach continuous ranked probability skill scores (CRPSS) between 0.04 and 0.13 below the best trained-probabilistic baseline, at zero marginal training cost. No injection site works across models: the productive tensor group is architecture-specific, so SPW is at present a tuning procedure rather than a plug-and-play recipe. Its main failure mode is a coherent whole-field offset that overdisperses the domain mean, and restricting the noise to coarse scales or perturbing the initial conditions each repair part of it.

Abstract: Generalized Nash Equilibrium Problems (GNEPs) often arise in multi-agent engineering applications that require distributed algorithms. Unlike traditional approaches that enforce consensus on multipliers, our method removes the need to share multipliers, reducing communication and improving privacy. As a result, different initializations can lead to different GNEs, including non-variational ones. We establish convergence under sufficient conditions using an input-to-state stability (ISS) framework.