simulation engineers

Abstract: In variable-step operator learning, agreement at observed step sizes does not by itself determine predictions at other temporal resolutions. We propose an operator whose step-size dependence is prescribed by a first-order Duhamel approximation of semilinear dynamics. It combines exact linear propagation with a local nonlinear function of the field and its derivatives, allowing evaluation below the observation interval without supervision densely sampled across step sizes. Under suitable conditions and at fixed spatial resolution, we prove that agreement between models at two step sizes controls their prediction differences throughout a prescribed range. We also give conditions for local identifiability of both components from two step sizes, supporting interpretation of the learned structure. A latent extension applies the same construction to learned fields. We evaluate the base model on two synthetic problems and the extension on two real datasets against several baselines.

Abstract: Derivative-free optimization (DFO) addresses problems where derivatives are unavailable or costly to obtain. This setting often arises in simulation-based and experimental applications, where evaluating the black-box objective can itself be costly. Thus, it remains a central challenge in DFO to effectively exploit accumulated observations to select informative evaluation points under a limited budget. In this light, we introduce the NextEval solver, an agent-based DFO solver, which integrates the capabilities of a large language model (LLM) to guide the sequential selection of evaluation points. Specifically, we establish a system that combines an LLM agent with a numerical environment. The environment provides tools for analyzing past evaluations and executing numerical methods, while maintaining a shared evaluation history and method-specific state to support continuation across method switches. Using observations and tool feedback, the LLM agent selects tools, configures their parameters, and allocates the evaluation budget, while numerical methods compute and evaluate candidate points. Building on this system, we also introduce NextEval Bench, a benchmark protocol for comparing agent configurations on shared DFO tasks using the same numerical tools under matched evaluation budgets and information constraints. Numerical results on low-dimensional DFO problems demonstrate that the NextEval solver outperforms the state-of-the-art DFO baselines in function-evaluation efficiency.

Abstract: Predictions with dynamical systems can be computationally expensive---even with reduced models---because reaching future prediction times can require many sequential time integration steps. We propose Flow-Map First-Order Trajectory Matching (FM-FTM), a nonintrusive model reduction approach that accelerates ensemble predictions of stochastic dynamical systems by learning flow maps that replace multiple time-integration steps. Our method uses first-order trajectory matching (FTM) to learn a deterministic representation of the stochastic probability-current dynamics and then reduces its evolution over time into a flow map whose evaluation directly yields predictions over long time horizons. Numerical experiments on evolution problems with stochastic forcing demonstrate that FM-FTM accelerates ensemble predictions by up to two orders of magnitude while accurately predicting time marginals and ensemble statistics.

Abstract: We develop a derivative-free temporal-difference (TD) framework for calibrating black-box simulators using one-step transitions from a target system and noisy simulator-generated continuation values. The calibration parameter is defined through Bellman orthogonality, recovering the physical parameter under correct simulator specification and yielding a near-optimal $L_2$ approximation of the policy value under misspecification. We propose three TD algorithms based on random-direction finite differences, distinguished by their query costs and reuse of noisy simulator evaluations. We establish almost-sure convergence, last-iterate mean-square error bounds, and central limit theorems for Polyak-Ruppert averages across four query-noise regimes. Our analysis reveals a specification-dependent bias phenomenon: for two algorithms, the finite-difference bias of the TD estimating equation vanishes at the calibration target under correct specification, even when the gradient surrogate remains biased. This permits a fixed perturbation radius and rate exponents approaching $1/2$ in the simulator rollout budget, whereas misspecification generally recovers the classical Kiefer-Wolfowitz rates. We also develop a few-replicate online bootstrap that yields Student-$t$ calibrated confidence intervals under negligible query noise, and identify a covariance mismatch that can invalidate conventional multiplier inference along Markov trajectories. Finally, a second-stage TD recursion corrects the remaining value discrepancy without additional simulator queries.

Abstract: Many-query applications such as design optimization, uncertainty quantification and digital twins call for repeated full-field predictions from expensive partial differential equation (PDE) simulations. Grassmannian reduced-order models interpolate parameter-dependent subspaces but commonly vectorize the spatial field, and the ambient dimension then grows with the product of the grid sizes. Tensor-based models preserve the multiway structure but often use shared mode-wise bases or a fixed core across parameters. We propose a Tucker-based surrogate that keeps the spatial directions and time as separate modes. The factor subspaces are interpolated on a product Grassmann manifold, Procrustes alignment places the Tucker cores in one coordinate system, and a truncated singular value decomposition models their variation. Across five PDE benchmarks in two and three spatial dimensions, including public computational fluid dynamics data, the interpolation size is reduced by factors of 13 to 482 and the stored model by factors of 13 to 464 relative to a single-subspace Grassmannian surrogate with the same local interpolation. Cached queries run 3.3 to 8.5 times faster, the mean errors over ten resampled splits differ by at most 0.22 percentage points (0.36 when every model choice is re-selected inside each split), and the prediction-error terms of the two methods differ by less than 0.1 percentage points. The remaining accuracy differences are consistent with the larger representation error of the Tucker format. In a three-dimensional grid study the interpolation-size ratio rises to 2,260 and the query speedup to 11.9 at 64^3.

Abstract: The Well, a 15-terabyte dataset spanning 16 physical simulation domains, provides an extensive benchmark for developing and evaluating machine learning surrogate models for complex physical systems. The baselines released with the benchmark were presented by their authors as illustrative examples obtained at small computational cost, trained with zero to very limited hyperparameter tuning and under a highly constraining 12-hour per-run wall-clock limit. These results have subsequently been treated as fully tuned benchmarks, and in some cases effectively interpreted as unconstrained performance baselines. We perform a short non-exhaustive hyperparameter search for the Tucker-factorized Fourier Neural Operator (TFNO) under the same 12-hour per-run wall-clock limit, while using only a single input timestep rather than the history of up to four used by the published baselines. Despite this more restrictive setup, tuning alone reduces VRMSE below both published FNO and TFNO baselines on 15 of 17 tasks, sometimes by several orders of magnitude. This sensitivity to a modest tuning effort underscores that the released neural operator baselines should not be treated as architectural benchmarks.

Abstract: Understanding and controlling how systems evolve is central to science and engineering, where many problems require reasoning about complete trajectories. Existing approaches typically learn local dynamics or generate trajectories, but objectives constructed from individual transitions can miss dependencies across time, while generative models do not necessarily provide a tractable objective for evaluating and optimizing arbitrary paths. We study $\textit{action learning}$, the problem of recovering a stochastic action from trajectory observations, yielding a common objective for reasoning about dynamical systems. We introduce $\textbf{LEAP}$ ($\textbf{L}$earned $\textbf{E}$nergy on $\textbf{A}$ction $\textbf{P}$aths), which anchors the unknown action to a tractable reference process and learns the remaining correction by comparing observed trajectories with reference trajectories. This construction yields a differentiable objective on path space that can capture both local dynamical structure and nonadditive dependencies across time. Once learned, the same action can be flexibly reused for path ranking and inference, mechanism steering, constrained optimization and sampling. Across stochastic physical systems, many-body orbital dynamics and molecular simulations, LEAP recovers underlying dynamics, captures dependencies across time and enables transfer across inference objectives and physical conditions. We show that $\textit{action learning}$ is a promising framework for turning trajectory observations into reusable objectives for scientific inference and control.

Abstract: Multiply-with-carry (MWC) generators are very fast pseudorandom number generators whose quality depends on the choice of a multiplier, and is usually assessed by applying the spectral test to an associated multiplicative congruential generator. We show that the special form of the modulus imposes structural limitations on the lattice structure of every MWC generator, which the generalized MWC generators of Goresky and Klapper mitigate; in our tests, xoring each output with its carry removes them. Since these limitations make the usual worst-case criterion useless, we rank candidates by a weighted geometric mean of their figures of merit, which does not depend on their normalization, and suggest multipliers for generators with 64 to 256 bits of state. Along the way, we correct some errors in the literature. In the end, we propose MWC192X, a 64-bit generator with 192 bits of state that passes all tests we are aware of, and emits an output in half a nanosecond.

Abstract: Neural Posterior Estimation (NPE) fits an amortized conditional density estimator to a simulated training set of complete-data realizations. NPE's training objective, log-likelihood, favors posterior approximations that assign arbitrarily high density to the training points, and typical families of amortized conditional density estimators (e.g., normalizing flows, Gaussian encoders) are flexible enough to oblige. The resulting policy of extreme overconfidence translates poorly to held-out data. Early stopping and other regularizers can prevent this degeneracy, but they are limited to selecting posterior approximations along an unfavorable optimization trajectory set by in-sample residuals, where the posterior mean is underfit while the posterior variance is overfit. To avoid this trade-off, we propose Cross-Fitting NPE (CF-NPE), which uses sample splitting to separate conditional-mean estimation from the estimation of the posterior's higher moments. Using $K$-fold cross-fitting, CF-NPE fits $K$ posterior-mean regressors and then fits a conditional density estimator to the resulting out-of-fold residuals. In experiments with synthetic data and in a cosmological application, CF-NPE achieves higher held-out log-likelihood than standard NPE and typically improves calibration. CF-NPE is most useful in high-dimensional, simulation-limited settings.

Abstract: Neural PDE solvers commonly generate multi-step predictions through autoregressive rollout, recursively applying a learned evolution operator and feeding each prediction back as input for the next step. Approximation errors can therefore propagate through the rollout, causing predictions at a shared target time to depend on their temporal origins and rollout depths. For a well-posed deterministic PDE flow, however, states at different times along the same physical trajectory should, under exact evolution, reach the same target state. To this end, we propose Align Latent Rollout (ALR), a regularization approach that promotes consistency across rollout origins through the neural PDE solver's internal representations. A second-order Taylor analysis of latent discrepancy propagation motivates two objectives: zeroth-order latent state consistency, which aligns representations at a shared target time, and first-order latent dynamics consistency, which aligns local evolution responses to shared perturbations. ALR can be integrated into different neural PDE solvers by regularizing suitable internal representations, without modifying their backbone architectures. Experiments across multiple PDE benchmarks and neural-operator backbones show that ALR improves prediction accuracy while reducing shared-target discrepancies across rollout origins.

Abstract: Neural emulation need not require learning a substitute for known physics. We investigate PolyNets that couple a continuous-time neural representation of polynomial dynamics with a simple recurrent network for discrete-time integration. When the governing coefficients are known, the resulting tensor graph requires no training and preserves the prescribed numerical scheme while enabling efficient hardware execution and parallel simulation. Using the one-dimensional Korteweg-de Vries equation, we compare PolyNet with CPU and GPU finite-difference Runge-Kutta solvers and three trained neural models: a state-map emulator, a physics-informed predictor, and a learned-tendency integrator. Analytical soliton solutions provide a reference for amplitude and phase errors across grid resolutions, 10^6 dispersively scaled time steps, ensembles of up to 10^4 trajectories, and varying initial amplitudes. PolyNet achieves accuracy comparable to the numerical solvers, including at amplitudes outside the learned models' training conditions. It combines this fidelity with high GPU throughput, approximately constant over the tested resolution range, and favorable ensemble scaling.

Abstract: Generating LiDAR point clouds from multi-view camera images is a valuable task with applications in controllable data synthesis, cross-modal simulation and various perception tasks. However, most existing methods are not specifically designed for this task, and the quality of their generated LiDAR remains limited. Moreover, these methods typically focus only on semantic cues in images or generate LiDAR from a monocular camera image. In this work, we introduce LiFi (LiDAR From images), a dedicated framework for generating visually and geometrically aligned LiDAR scenes from multi-view camera images. LiFi guides the latent diffusion process through two complementary branches: geometry and semantics. The geometry branch constructs scene features from images through a reverse sampling algorithm and an uncertainty-aware geometric encoder combined with DepthAnything3, whereas the semantic branch provides high-level semantic representations via a cross-view interaction module. We further introduce a dual-branch balanced classifier-free guidance (CFG) strategy, which enhances the model's conditional generation capability while preserving the independent learning and collaborative controllability of the two branches. Extensive experiments demonstrate that LiFi outperforms state-of-the-art methods in generating high-fidelity LiDAR scenes. The code will be publicly available at: https://github.com/szzhou88/LiFi.

Abstract: Neural surrogates for Partial Differential Equations (PDEs) are usually trained on synthetic data from numerical simulators. As models grow and scaling laws demand larger datasets, the cost of data generation often outweighs the training cost and becomes the bottleneck in the scaling quest. Unlike data in other domains, however, each PDE sample has a tunable cost that depends on its numerical fidelity, with the resulting cost-accuracy trade-off governed by known convergence rates. We exploit this property by formalizing neural surrogate training as a function of both data quantity and fidelity under a fixed data generation compute budget, treating fidelity as a fine-grained discrete spectrum rather than a binary distinction. Building on this, we show that multi-fidelity training enables Pareto-optimal error scaling against data generation compute. By using simulations at lower fidelities as an additional training signal, training on the optimal fidelity mixture matches the accuracy of high-fidelity-only training, with up to $6.3\times$ less data generation compute across our settings. We validate these findings across six PDE problems spanning structured grids and unstructured meshes, two distinct error sources (discretization and iterative-solver error), and four surrogate architectures, totaling over 7,000 training runs.

Abstract: Neural operator splitting composes a library of neural operators, one per physical mechanism, into zero-shot simulators of new equations. Existing approaches, however, require these mechanisms and their labels to be specified in advance. We ask whether a pretrained library can instead be adapted and grown from unlabeled trajectories in which multiple mechanisms act simultaneously. We introduce SPLICE, a framework that discovers operators without mechanism labels on mixture data. The contributions of the candidate operators to each trajectory are inferred by solving a convex optimization problem. A calibrated test then assigns each discovered operator the mechanism it implements. Failure cases are also detectable, when the library lacks the required physics or when mechanisms are insufficiently separable. Across one and two dimensional systems, the discovered operators recover mechanisms from unlabeled mixtures and compose into zero-shot simulators of unseen equations; a frozen library can also grow an operator for physics absent from pretraining, without labels and without forgetting. On Navier-Stokes, the discovered operators compose about as accurately as their supervised counterparts.

Abstract: We introduce IND-Eval, a public benchmark that organizes industrial time series across domains into source-specific forecasting tasks. Relative to established benchmarks such as GIFT-Eval, it emphasizes finer sampling resolutions and a greater prevalence of multivariate forecasting. Evaluating Chronos-2, TiRex-2, and TimesFM-3, we find that TimesFM-3 achieves the lowest source-balanced aggregate nMASE and nCRPS and leads seven of nine sources under each metric; source-specific exceptions reinforce the need for domain-representative evaluation for model selection. These findings also motivate improving domain alignment during pretraining, where real industrial data are often too scarce to close domain-specific gaps directly; we therefore investigate whether a domain's statistical structure can guide simulator design. In a case study on two offshore well-monitoring regimes, we improve a general simulator's coverage using an oscillator-augmented simulation pipeline. This lowers forecasting error in the target domain but reduces performance on the subset of GIFT-Eval with natively univariate targets. A 50/50 mixture of the general and augmented simulation recipes achieves the lowest error among the three training recipes for all four event-metric pairs in the case study while recovering most of the lost GIFT-Eval performance. Together, these results illustrate how domain-representative evaluation can guide model selection and the composition of simulated data while revealing a trade-off between specialization and generality.

Abstract: Video-based interactive world models aim to enable real-time, user-controllable environments. Yet most existing systems are trained and rolled out at a fixed temporal rate, limiting both runtime-rate adaptation and physical-horizon coverage -- a limitation we term temporal-rate coupling. Specifically, when runtime generation throughput differs from the learned temporal rate, the generated world evolves unintentionally more slowly or quickly. Moreover, using a single temporal rate imposes an inherent trade-off between temporal granularity and physical horizon: higher rates capture finer motion but cover a shorter duration under a fixed context window. To address both limitations, we introduce Rate-Adaptive Rollout (RAR), a framework that enables interactive world models to roll out at controllable temporal rates. At its core, Stride-RoPE aligns latent frames sampled at different rates on a shared physical-time coordinate, enabling consistent multi-rate rollout, unseen-rate generalization, and online rate switching without discarding history. Meanwhile, RAR uses multi-stride video sampling to enable joint learning of fine-grained dynamics and long-horizon evolution. Across action- and camera-controlled environments, RAR achieves temporally consistent multi-rate rollout and online rate switching while preserving high-rate generation quality and extending physical horizons under matched training budgets. RAR also transfers to pretrained world models while preserving perceptual quality.

Abstract: Deploying language-model agents onboard mobile robots requires task reasoning and responsive execution within limited compute and memory. We propose BT-Agent, an onboard architecture combining LLM-driven task decisions with predefined behavior-tree (BT) skills. These skills enforce execution conditions and return structured failure feedback. We demonstrate fully onboard operation with a 9B model on a quadruped across five task categories. Intervention tests show that local checks stop ongoing navigation without waiting for another model decision, while the agent remains active to retry or report constraints. To compare agent designs efficiently, we introduce a 161-task multi-fidelity benchmark, evaluated in text on all tasks and in Habitat on 39. Text supports 10.9$\times$ higher evaluation throughput, while simulation reveals how perception and motion failures change task outcomes. BT-Agent's largest success gains over the strongest Act/ReAct baseline occur at 4B and 9B: approximately 10 and 5 percentage points. Ablations identify structured tool calls and informative failure feedback as the most useful components.

Abstract: Physics foundation models are an increasingly popular approach for building versatile emulators for spatiotemporal systems. They require tokenisation layers that lift physical field data into a latent representation suitable for dynamic processing. A typical choice for this layer is a convolutional encoder, which lifts field information in a locality-aware way and can be trained very efficiently. However, this choice cannot be applied to a large class of scientific computing problems where data are represented on unstructured meshes, for example simulations on domains with curved boundaries. Such data typically require graph neural network architectures, which are more expensive to train and, in the form currently used, encode information differently from their CNN counterparts, thus limiting the portability of physics emulators between these data regimes. In this work we introduce Mesh-Native Convolution (MNC), a locality-aware tokenisation layer that encodes unstructured mesh-based data in a way that is analogous to CNNs. This approach leads to models that can be trained once on mesh data and then deployed to arbitrary unstructured meshes, even if these are irregular, with minimal retraining. We show that this tokenisation approach can be used to retrofit grid-pretrained foundation models efficiently on unstructured meshes and provide theoretical results to confirm the consistency of this approach with classical CNN encoders. We demonstrate the favourable performance of this retrofitting approach, which in many cases reaches acceptable accuracy even in zero-shot deployment, and outperforms existing baselines after only a few epochs of fine-tuning, thus providing an efficient bridge between the two data regimes.

Abstract: Complete orthogonal predictive coordinates do not by themselves bind a latent direction to a named intervention. We present a mathematical and synthetic audit motivated by vascular device-vessel suitcordance. Capacity-matched least-squares predictors were exactly equivalent under complete fixed output transforms, whereas an anchor-only observer recovered interpretations only within the span of known perturbation signatures. Six three-dimensional configurations across 64 seeds gave a maximum paired prediction discrepancy of 6.7e-15 but a median untransported edit error of 1.513. Coordinate transport removed that error. Noisy and weak anchors constrained calibration stability, and changing the representation basis required recalibration or verified transport. Across 256 additional fits in dimensions 3-24, prediction equivalence persisted within 4.0e-15. We then evaluated nine deliberate runnable fault classes across 64 seeds. All 576 faulty executions completed, but each violated at least one reconstruction, prediction, delivered-edit or scope contract; all 320 valid control records passed. Repeating a faulty implementation gave exact self-agreement despite error against the separately computed simulator expectation. For one omitted-direction defect, probe coverage followed its analytic law, and rank-aware abstention protected unsupported interpretations. Scalar-noise experiments exposed both missed weak faults and excessive rejection under narrow relative tolerances. These controls provide an executable separation of prediction, semantic support and scientific acceptance. They are synthetic numerical audits, not clinical validation, neural JEPA-Anything replication, agent learning or patient treatment-effect estimation.

Abstract: Physics-informed neural PDE solvers adapt their parameters to satisfy governing equations, yet their representational structure typically remains fixed throughout training. This rigidity is poorly matched to PDE solutions with strongly heterogeneous complexity across space and space--time, leaving capacity insufficient where the physics is difficult and redundant where it is simple. We introduce physics-informed neural plasticity, a paradigm in which the representation itself reshapes during optimization in response to unresolved physics. We instantiate this principle with Representation Capacity Adaptation for PDEs (ReCAP), a Gaussian-localized solver that dynamically redistributes capacity through local enrichment, residual-directed splitting, gate-based pruning, and function-aware merging. ReCAP uses responsibility-weighted error indicators and the geometry of residual energy to determine where and how to refine. To limit the disturbance introduced by splitting, we introduce quiet-child refinement, which initializes new components by transporting the parent representation while controlling instantaneous functional perturbation. We further establish conditional a posteriori reliability and structural-stability guarantees linking localized physics residuals to solution error and stable refinement. Across five challenging 3D and 4D PDE benchmarks against 11 physics-informed solvers, ReCAP achieves the lowest relative $L^2$ error on every problem, reducing error by $10.7\%$--$27.5\%$ relative to the strongest competing result. These results suggest that physics-informed solvers need not merely learn their parameters---they can learn how their representational capacity should be organized.

Abstract: This work examines the transfer of a co-evolved communication mechanism between two robotic agents from a discrete two-dimensional (2D) simulator to a three-dimensional simulator with real physics (3D). The study focuses on whether a communication mechanism co-evolved in a 2D environment retains its functional role after transfer to a 3D physics-based simulator. To support this analysis, the effects of the episode time budget, the social cue, and the asymmetry between the two co-evolved roles were examined. The results indicate that the success rate increased approximately linearly with the evaluated time budgets, with no evidence of a plateau between 2,000 and 6,000 physics steps, suggesting that evaluations based on shorter episodes may underestimate the performance of the trained controllers. In both simulators, the social cue functioned primarily as a jam- assistance mechanism rather than as a navigation guide, although with a more pronounced effect in 2D. Analysis of eight independent evolutionary runs revealed a consistent direction of asymmetry, although its magnitude varied across runs. Controlling the processing order between agents allowed us to rule out an artifact of the physics engine. Finally, the results are discussed in terms of the factors that may contribute to the remaining performance gap observed after transfer.

Abstract: Bidirectional video diffusion models denoise entire videos in parallel, yet when trained on effectively unlimited in-distribution data from procedural generators, continue to violate physical laws and simple symbolic rules. We introduce Serial-to-Parallel Diffusion (S2PD), which performs autoregressive diffusion at high noise before switching to parallel diffusion at low noise. The autoregressive phase provides the serial computation needed to coordinate interdependent events and produce valid state transitions while the parallel phase jointly refines the entire video and reduces sampling time relative to fully serial generation. We implement S2PD with two architectures: a pixel-space diffusion transformer trained from scratch and a pretrained video model adapted through LoRA fine-tuning with causal attention. Across games, physical simulations, and real video, S2PD follows rules more reliably than matched bidirectional baselines and generates videos with greater temporal stability and sampling efficiency than other serial methods.

Abstract: Realistic environment replicas are increasingly valuable for training and evaluating LLM agents, yet the original systems may be inaccessible or impractical to reproduce. We explore agentic language world modeling: rather than rebuilding an executable environment, a world model agent serves as the environment for a task agent and supports faithful and stateful simulation. We instantiate this paradigm with Trace2Env, a learning-free framework for settings where the original system is unavailable but historical interaction traces remain accessible. Trace2Env reconstructs these traces into a reusable environment worldbook containing environment schemas, grounded evidence, and induced behavioral knowledge. At runtime, the world model agent actively consults the worldbook together with persistent episodic state to infer each action's observation and lasting state effects. Across nine environments, Trace2Env improves both next-observation fidelity and long-horizon interaction consistency over conventional prompt-based LWMs. In multi-turn interaction, task agent actions generated against Trace2Env remain valid more often when replayed in the real environment, indicating that its simulated dynamics better preserve the consequences of earlier actions across successive turns. These results establish agentic language world modeling as an alternative direction for building realistic environment replicas without reconstructing the original executable system.

Abstract: Operator learning methods such as DeepONets and FNOs often struggle with PDE families featuring sharp interfaces, heterogeneous coefficients, and localized multiscale structures. We introduce a partition-of-unity (POU) mixture-of-experts framework for localized operator learning, in which geometry-aware gating networks produce smooth spatial partitions which blend the contributions of local expert networks. Our main contribution is HiRefPOU, a residual-style hierarchical POU architecture for DeepONets that organizes localized representations through nested parent-child partitions while preserving global continuity. We also show that the same POU principle can be incorporated into Fourier Neural Operators to introduce spatial adaptivity without modifying the underlying spectral layers. On heterogeneous Darcy and reaction-diffusion benchmarks, HiRefPOU achieves substantially lower error than global DeepONet and static POU-MoE baselines, while the broader operator-learning experiments show that the benefits of localization depend on the PDE structure and the chosen neural-operator backbone. The learned partitions are interpretable and align with interfaces and regions of rapid solution variation. These results show that explicit geometric localization can improve both accuracy and interpretability in neural operator learning.

Abstract: Neural surrogate models for Partial Differential Equations (PDEs) on unstructured 3D geometries are often limited by poor generalization and the high cost of generating large-scale training datasets. Consequently, pre-training on massive datasets of related PDE dynamics has emerged as a critical alternative to enhance the robustness and scalability of these models. However, this strategy is neither compute- nor data-efficient, as it relies on massive pre-computed data that is very costly to generate. In this work, we introduce a disk-data-free pre-training framework tailored to both steady-state and transient regimes. For steady-state problems, we propose a geometry-driven strategy that leverages intrinsic shape descriptors to learn representations of complex 3D domains. For transient problems, we introduce a physics-driven approach based on online generation of synthetic PDE data, enabling scalable pre-training without reliance on expensive datasets. Across multiple experiments, our approach achieves faster convergence, greater data efficiency, and higher accuracy during fine-tuning, particularly under realistic low-data regimes. This methodology provides a practical pathway toward data-efficient neural emulators for large-scale simulations.

Abstract: World Action Models (WAMs) predict visual futures and robot actions, yet they remain susceptible to task-incomplete imagination, where plausible, action-consistent predictions omit the transition needed for task completion. In this paper, we show that this failure is not inherent to the world model backbone, but emerges when adapted for short-chunk control, which can repeatedly favor plausible local continuations over task-completing transitions. To address this, we introduce Completion Aware Guidance (CAG), a training-free sampling method that guides generation toward task completion. Across representative WAMs, CAG improves success from 64% to 70% on a RoboTwin 2.0 subset and from 69% to 75% in zero-shot simulation, while reducing task-incomplete imagination from 79% to 40%.

Abstract: Large Language Models (LLMs) are increasingly used as probabilistic generators for simulation, synthetic data generation, and decision support in settings where real-world data are unavailable. Yet, the structure and reliability of the distributions they produce remain understudied. Here, we systematically analyze LLM-generated distributions of preferences for air travel, restaurants, and consumer products. Encouragingly, all models considered in our analysis exhibit self-coherence, with the most probable outcomes stabilizing rapidly under repeated sampling. At the same time, we observe substantial discordance across both model families and scales, with little consensus even among their most probable outcomes. These patterns hold across nine open-weight models, three choice domains, and show robustness under temperature changes, greedy decoding, and perturbations of prompt and ordering. Our findings indicate that outcomes are influenced more by the choice of model than by the wording of the prompt, challenging the common assumption that sufficiently capable LLMs produce similar preference distributions when used as stand-ins for survey respondents.

Abstract: Uncertainty quantification is critical in scientific machine learning, where black-box, image-based models are increasingly deployed in high-stakes settings. In many such applications, model outputs inform costly decisions, yet most methods provide only point estimates without quantifying predictive uncertainty. This challenge is compounded by the limited accessibility and interpretability of model internals, making it difficult to assess reliability across different regions of the input space. As a result, there is a growing need for methods that can provide input-dependent uncertainty estimates to guide both model development and downstream experimentation. To address this need, we propose Adaptive Conformal Prediction using Nearest Neighbors (ACPNN), an input-adaptive conformal framework for image regression. ACPNN leverages information from neighboring samples to produce locally adaptive uncertainty estimates while maintaining low computational cost. The neighborhood structure is defined using a scaled distance metric learned via a Gaussian Process with an automatic relevance determination (ARD) kernel. We demonstrate the effectiveness of ACPNN on a diffusion model for emulating inertial confinement fusion (ICF) simulations, showing that it achieves reliable and adaptive uncertainty quantification.

Abstract: Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FFM) extends Flow Matching to this setting, learning a velocity field whose flow transports a Gaussian prior to the data distribution, but it inherits the independent endpoint pairing of standard Flow Matching: in each batch, prior and data samples are matched arbitrarily, so the conditional bridge must traverse both the shared global structure of the dataset and instance-specific residuals. In function space this is harder to fix than in finite dimensions, since optimal transport (OT) on function spaces is delicate to formulate and a flat Euclidean surrogate ignores the geometry that distinguishes function-valued data. We propose kernel Functional Flow Matching (kFFM), which replaces the independent pairing by entropic OT under a kernel-induced cost, the coupling underlying the Hilbert Sinkhorn Divergence (HSD), leaving the FFM neural-operator architecture unchanged. We prove that the kernel cost and the HSD objective are uniformly bounded and well-posed on Banach ambient spaces, derive an error decomposition against quadratic-cost OT on compact metric spaces that isolates an irreducible kernel-cost mismatch term, and prove a discretization-invariance bound whose rate is governed by Sobolev regularity. Empirically, kFFM improves distributional matching over FFM, diffusion, adversarial, and finite-dimensional OT baselines on time-series and PDE benchmarks, with significant paired-seed gains over FFM and improvements that persist under non-kernel and physics-based diagnostics, including a turbulent Navier-Stokes benchmark. Bounded kernel costs already outperform raw $L^2$ Sinkhorn, and function-space-aware kernels (signature, Sobolev RBF) give further gains on rough or path-valued data.

Abstract: Dynamic simulations are an entrenched way of gaining insight into the evolution of system dynamics. Their computational cost however is often prohibitively high, especially in cases of stochastic frameworks. Machine learning algorithms are especially suited as simulation surrogates. Nevertheless, they face some very distinct limitations. Firstly, the sheer dimensionality of these systems, however, precludes the use of traditional time series models who struggle with high dimensional feature spaces. Additionally, traditional time series focus exclusively on either long or short range effects, causing local or global drift given enough time. In this paper, we propose a framework that addresses those limitations. Our framework combines a Variational Autoencoder, with a convolutional or graph basis that reduces the dimensionality of the system. This latent vector is propagated in time using a Temporal Fusion Transformer model, which includes both long range and short range effect encoding, as well as static covariate support. We test our framework on three distinct cases, to prove its robustness and in all three we have achieved practically identical to the simulation results at a fraction of the time. Further, our framework is flexible enough to be adapted to any new system and provides an inbuilt uncertainty quantification for targeted experiment design.

Abstract: Recovering complete physical fields from sparse observations is challenging because the measurements may not uniquely determine the underlying state. Diffusion-based PDE solvers address this problem through iterative sampling whereas neural operators provide deterministic one-pass predictions. We propose SCOPE (Sparse-Context Observability-aware Predictive Embeddings) to recover complete PDE fields from sparse observations by coupling full-field latent prediction with physical reconstruction. A shared decoder reconstructs fields from both predicted and complete-view representations so that representation learning is guided by both physical recovery and latent matching. We derive a quadratic risk decomposition at fixed teacher-decoder pairs showing why optimal latent prediction need not yield optimal field reconstruction. We also establish sufficient conditions for decoder improvements on complete inputs to transfer to recovery from partial observations. Experiments across five PDE settings show that SCOPE outperforms mask-aware neural operators on all ten forward and inverse tasks and achieves lower errors than those reported for diffusion-based solvers including DiffusionPDE and FunDPS. Decoder-only adaptation further improves recovery without retraining the backbone while retaining deterministic single-pass inference.

Abstract: Learning PDE operators on complex domains requires capturing interactions among fields on vertices, edges, and faces, alongside global responses shaped by topology. Existing neural operators accommodate irregular geometries but often overlook these distinct field supports or their condition-dependent coupling. We introduce the Dynamic Kuramoto--Hodge Operator (DKHO), which combines topology-constrained interactions with learned coordination. DKHO encodes conditions on their native cochain supports, evolves Kuramoto-inspired relation states through the boundary and coboundary operators that compose the Dirac operator, and decodes non-harmonic and harmonic responses in orthogonal Hodge subspaces. Topology thus determines where information can flow, while learned dynamics adapts how it is exchanged to each PDE instance. Across porous-medium Darcy flow, torus transport--diffusion, and cavity magnetostatics, DKHO-large reduces prediction error by approximately 61% on average over leading baselines, while DKHO-small remains competitive using only 11.5--24.3% as many parameters. These results suggest that coupling topological structure with adaptive dynamics provides an effective inductive bias for accurate and parameter-efficient PDE operator learning on complex geometries and topologies.

Abstract: Deep generative models are used to solve partial differential equations and model distributions of physical system states, but ensuring that the generated samples satisfy the governing laws remains challenging. Projection-based flow-matching methods enforce physics by correcting the flow from an unconstrained noise distribution. These corrections shift the generated samples away from the distribution of target solutions, especially in high noise regions. To address this limitation, we propose Source Anchoring for Physical Consistency (SAPC), a Functional Flow Matching method that encodes the physical constraints into the source noise before generation begins. We evaluate SAPC on five systems governed by partial differential equations, covering six tasks with linear and non-linear dynamics, and compare results against five baselines and the unconstrained backbone. Anchoring the source reduces the need for large corrections that drive samples onto admissible but off-distribution states, and SAPC reproduces the target distributions most accurately on every evaluated task, while matching the constraint precision of the best projection-based baselines. Ablation experiments show that this gain arises from pairing source projection with a matched training objective that regresses toward the projected source. These results identify the source distribution as a key design choice for physically consistent generative modelling.

Abstract: Video world models are emerging as data engines, action planners, and generative simulators for autonomous driving, but existing benchmarks primarily assess visual fidelity and coarse physical plausibility, providing limited evidence on whether generated driving futures obey realistic vehicle kinematics and dynamics. This limitation is further compounded by the lack of datasets in which vehicle, road, maneuver, and speed conditions are independently controlled, and ground-truth vehicle states are recorded in synchrony with videos. We introduce VehDyn, a driving world model benchmark for vehicle dynamics. VehDyn is built on a CARLA-CarSim co-simulation platform where photorealistic rendering is coupled with a validated multi-body dynamics model, and it contains 10,080 configurations from a full factorial design over five vehicle types, four tire-road friction coefficients, three maneuvers, four target speeds, 14 scenes, and three illuminations, each paired with synchronized position, velocity, and attitude sequences. Built on this dataset, VehDyn introduces a hierarchical evaluation framework that measures trajectory alignment, kinematic consistency, and dynamic consistency, and benchmarks 12 state-of-the-art video world models. We further assess the video quality using two established protocols and correlate it with the VehDyn score. Trajectory-level metrics are nearly saturated, with ten of twelve models within 20\% of ground truth, while no model reaches 92\% of ground truth on dynamic consistency, and visual-quality metrics are only weakly correlated with vehicle-dynamics fidelity. DrivingWorld achieves the highest VehDyn score, followed by Cosmos 3 Nano and LTX-Video 2.5, and the VehDyn score agrees closely with human judgment. VehDyn provides a systematic foundation for developing driving world models that are physically consistent and visually realistic.

Abstract: High-fidelity simulations of time-dependent partial differential equations (PDEs) are computationally expensive, motivating data-driven reduced-order surrogates for many-query tasks such as uncertainty quantification, design optimization, data assimilation, and optimal control. However, existing surrogate models often exhibit poor temporal stability, which can lead to unstable rollouts and exploding gradients during backpropagation, especially in multistep long-horizon forecasting. To address this, we propose SMORE, a mesh-agnostic framework for model order reduction of time-dependent PDEs. Its latent dynamics are trained with Lyapunov-guided stability regularization, which promotes stable long-horizon rollouts. We provide theoretical guarantees under the stated structural assumptions. Beyond forecasting PDE evolution, the learned latent dynamics, which are interpretable and linear or linear-quadratic, could bring benefits for downstream tasks such as data assimilation and optimal control. Moreover, our framework is capable of predicting continuous PDE solution fields from sparse measurements of the initial condition. We evaluate SMORE on a range of problems, including wave propagation, the Navier-Stokes equations, and the shallow water equations. Our results show that it improves long-horizon rollout generalization and empirical robustness, and achieves competitive accuracy at comparable parameter budgets relative to competitive baselines including DINo, FNO, CNO, and Transolver.

Abstract: General Game Playing across arbitrary games from rules alone remains challenging due to differing algorithmic requirements across game classes and strict decision-time constraints. Rather than hand-designing search heuristics for specific domains, can we leverage Large Language Models (LLMs) to discover general game-playing algorithms? Because language models can propose and refactor structured code, they provide an expressive proposal engine for exploring the space of algorithmic designs. We introduce a multi-agent LLM meta-learning system to co-evolve game-agnostic procedural search mechanisms in C++ alongside domain heuristics synthesized directly from game rules. Controlling the compute budget, we benchmark the discovered mechanisms across more than 400 diverse environments, including OpenSpiel training and held-out games, procedural simulation engines, and games with deep neural policy-value representations trained via PPO. Evaluated via AlphaRank stationary distributions and Soft Condorcet Optimization (SCO) against 15 established MCTS baselines, the discovered search mechanisms consistently achieve top-tier ratings and pairwise ballot majorities over most baselines across independent evolutionary runs, generalizing to unseen human-designed and procedurally synthesized games and remaining competitive with baselines on frozen neural network representations.

Abstract: World models are moving from generating realistic frames to generating playable worlds, yet whether a delivered world can keep running is not tested anywhere. Existing evaluations stop at generation, at delivery, or at single-step transitions, and each stops at a different point along the way. Correct local state transitions or intermediate outcomes do not guarantee a correctly organized causal event flow. We propose the world agent task, which moves the evaluation point of world generation from the moment of delivery to the continued operation that follows. In this task, a model is not asked to generate a world. It is held responsible for keeping the world running, which requires coordinating events and carrying forward their consequences to constrain subsequent evolution. We instantiate the task in WorldAgent-Benchmark with two complementary tracks. In the maintenance track, the model must ground the events of a continuous narrative into correct transitions of the explicit world state while respecting causal, temporal, and concurrency constraints. In the deduction track, the model must predict how the world will evolve under partial observations and act toward a goal. The maintenance track combines LLM-assisted semantic judgments with programmatic validation and scoring, while the deduction track is evaluated entirely programmatically. Individual judgments are auditable against world states and execution logs, and scores can be recomputed from the saved judgments and execution records. Across 8 models, scores decline steadily as pre-built structure is removed from the world, and causal-relation checking is the weakest component for every model. The benchmark makes the continued operation of a world measurable and distinguishes local completion from failures in event organization. Code and dataset will be released on https://github.com/HCPLab-SYSU/WorldAgent-Benchmark.

Abstract: A agentic story world is a dynamic system simulating who learned what, when, and from whom -- yet the standard design gives each character a private memory stream. A shared event is therefore stored once per witness, large duplication will be incurred in terms of storage. We present Agentsensus, a story-world simulation framework in which there is an unified long-term memory. Records of the same event merge into one owned by all its witnesses, and semantically relevant memory records are linked. We evaluate on four worlds -- two classical Chinese novels, Hamlet, and a real-world conflict timeline -- run for 40 to 80 rounds against three per-character memory designs under an equal-granularity protocol. Agentsensus writes 22-44% fewer entries than the closest baseline and is the only design whose memory becomes shared (14-28% of records held by more than one character, some by 10) and linked (94-99%), at judged simulation quality indistinguishable or even better than the baselines. An ablation attributes this to the merge itself: disabling it multiplies the store by 3.1x and takes sharing to exactly zero. Sharing also compounds with the horizon rather than saturating early, rising 6% to 9% to 14% as one world is re-run at 10, 20 and 40 rounds.

Abstract: Efficient sampling from Boltzmann distributions is central to modelling complex physical systems. Markov Chain Monte Carlo (MCMC) methods suffer from critical slowing down, high autocorrelation, and poor mode-mixing, limiting their scalability. Recent advances, like Boltzmann Generators, offer a promising alternative but remain constrained by costly MCMC-based training, inefficient sampling, and poor ergodicity. We introduce an algorithm for learning Boltzmann distributions that does not require any true samples for training. Our approach draws inspiration from flow matching but departs fundamentally from sample-trajectory matching to distribution-trajectory matching. The algorithm iteratively reshapes the target distribution, using model generated samples to guide learning and ensure comprehensive mode coverage. We validate our method on standard benchmarks, including a 2D Gaussian mixture, Many-Well distributions, and high-dimensional scalar $φ^4$ theory. The proposed approach not only improves sampling performance and accuracy over traditional MCMC and flow-based baselines but also establishes a new method for sample-free learning of complex physical distributions.

Abstract: We introduce Distance-Residual Physics-Informed Neural Networks (DR-PINNs), a physics-informed learning framework for approximating solutions of ordinary and partial differential inclusions (DIs), governing laws in which a differential operator is constrained to lie in a set-valued map rather than equaling a prescribed function. The method replaces the classical pointwise PDE/ODE residual by the squared distance from the differential operator to the admissible set. This distance vanishes exactly when the inclusion is satisfied and measures the infimal correction needed for the operator to enter the admissible set. For a fixed closed convex admissible set, the squared distance is differentiable with respect to the operator value, with gradient given by the metric projection. When the admissible set also depends on the network state, that dependence is included through the chain rule. The framework encompasses ordinary and partial DIs with set-valued reaction terms. For both settings we prove consistency: under the stated closedness, measurability, convexity, and growth assumptions, any sequence of candidates satisfying the initial (and, in the parabolic case, boundary) conditions whose continuous distance-residual functional tends to zero admits a subsequence converging to an exact solution of the target inclusion. These are conditional statements for the continuous distance-residual functional; they do not cover the finite-collocation training loss, the behavior of the optimizer, or convergence rates. For admissible sets given as convex hulls of finitely many vertices, projection onto the set reduces to a small convex quadratic program, making the loss efficiently computable inside the training loop. Numerical experiments demonstrate high accuracy on the differential-inclusion benchmarks.

Abstract: Physical systems evolve continuously in time, yet their states are typically observed only at discrete times. Generating trajectories consistent with their probability densities from such observations therefore requires capturing the continuous-time evolution rather than only learning transition mappings between consecutive observations. We propose PhiBE-Flow, a framework that directly estimates the probability velocity field induced by the stochastic differential equation (SDE) which governs this continuous-time distributional evolution. PhiBE-Flow learns from discrete observations using a model-free approach requiring neither known SDE coefficients nor score estimation. We establish convergence guarantees for the method, accounting for both time-discretization and finite-sample errors. We evaluate PhiBE-Flow on systems of increasing complexity, from controlled stochastic numerical systems to Navier--Stokes dynamics and real-world videos. Our results show that PhiBE-Flow accurately recovers probability flows of stochastic dynamics, preserves multiscale physical statistics, and improves video generation performance over representative baselines. The code is available at https://github.com/R1fe/PhiBE-Flow.

Abstract: We present a neural method for adaptive triangle mesh refinement, in which an autoregressive model adds geometric detail to selected regions of an input mesh while leaving the rest unchanged, a key capability for efficiently allocating mesh budget. Existing upsampling methods struggle to achieve this. Classical subdivision schemes refine triangulation without semantic awareness of the underlying shape or the ability to recover geometric details missing from a coarse input. Recent neural mesh models generate shapes globally, sacrificing region-specific control. We propose a novel tokenizer that yields combinatorially many valid upsampling trajectories from a single mesh. Trained on such data, our locally-conditioned autoregressive architecture allows for direct manipulation of topology and geometry within target regions of an input mesh. We validate our method against state-of-the-art approaches and demonstrate its ability to perform adaptive upsampling with region-selective control, a capability absent from existing approaches. This unlocks inference-time view-dependent refinement, physics-aware region refinement, and coarse-shape conditioned novel mesh synthesis. We provide code at https://github.com/seanxzhan/learned-localized-mesh-refinement/.

Abstract: Physics-Informed Neural Networks (PINNs) are trained by optimising a composite objective that combines data fitting with physics-based constraints, typically resulting in a highly imbalanced multi-task optimisation problem. Under these conditions, existing optimisation strategies are affected by conflicting task gradients, leading to slow convergence and unstable training, particularly for stiff and high-frequency partial differential equations. We analyse gradient conflicts throughout training of PINNs with standard optimiser and investigate Multi-Task Deep Learning (MTDL) optimisation methods. In our analysis across four benchmark problems we observed that PINN optimisation exhibits three distinct phases in which angle- and magnitude-based gradient conflicts alternate, with only one present at a time. Building on these observations, we propose PAM-GS, a physics-aware gradient surgery method that adaptively mitigates task interference during training according to the observed conflict types. Experiments on four representative PDE benchmarks demonstrate that PAM-GS combines competitive solution accuracy with consistently strong task-balanced performance, outperforming existing methods on most problems.

Abstract: High-fidelity simulation of control-conditioned multi-event physical systems is computationally expensive, especially across broad control spaces and long trajectories. In these systems, macroscopic evolution emerges from localized discrete events whose intensities and effects depend on process controls and evolving local states, while the available system knowledge is typically expressed as event-attribute descriptions. Purely data-driven surrogates must infer these event effects from limited trajectory coverage, which can hinder generalization to unseen control regimes. Physics-guided methods instead primarily build on equation-level constraints or differentiable solvers rather than discrete event-rule priors. We therefore propose NEMSim (Neural Event-Mechanism Simulator), which compiles predefined event-attribute descriptions into an executable transition structure linking control-dependent event intensities, prior-guided mechanism attribution, and state-dependent responses. To enable evaluation of control-conditioned multi-event dynamics with explicit system knowledge, we construct a 3D KMC-based benchmark pairing high-fidelity trajectories with explicit event rules, standardized splits, and evaluation protocols. Across three settings, NEMSim reduces Avg. RMSE by 58.9%-81.3% relative to the strongest baseline in each setting. It also remains best in the data-efficiency study with training-data fractions down to 10%. Mechanism analyses further show that these gains arise from executable rule integration rather than prior access or architecture alone.

Abstract: Latent neural surrogate solvers, or latent dynamics models, accelerate simulations of time-dependent physical systems by evolving a compressed latent space rather than resolving full-resolution fields directly. In principle this reduces computational cost and simplifies learning, but in practice errors often accumulate rapidly during long autoregressive rollouts, limiting predictive utility. We show that this instability does not stem from the latent representation itself, but arises when it is trained solely for reconstruction, producing representations poorly suited to long-horizon forecasting. We systematically evaluate training-level interventions that align latent representations with long-horizon rollout: Koopman operator learning and Hamming noise injection during autoencoder training to improve compression, together with noise injection and multi-step rollout fine-tuning to improve dynamics. Interventions that improve long-horizon rollout stability often degrade conventional training metrics, including reconstruction and one-step prediction accuracy. Collectively, these interventions reduce long-rollout error by approximately 40\% and match or exceed the accuracy of full-resolution models on two physics benchmarks, while requiring 2 orders of magnitude fewer floating point operations and half the GPU memory. Applied to mesoscale crystal-plasticity simulations of high-cycle fatigue, the resulting surrogate achieves stable extrapolation over horizons orders of magnitude beyond those observed during training. More broadly, these results show that neural compression should be designed not merely to reduce dimensionality, but to restructure the solution space for stable dynamical evolution, a key requirement for reliable, efficient neural surrogates in scientific applications.

Abstract: Large language models (LLMs) are increasingly used as natural-language interfaces for robotic systems, yet their integration with Robot Operating System (ROS)-based navigation remains limited by two gaps. First, navigation data such as occupancy grids are represented as raw geometric messages that are difficult for LLMs to use directly as spatial or semantic context. Second, adding LLM-driven capabilities often requires custom wrappers or robot-specific interfaces, limiting reuse across systems. To address these challenges, we propose a non-invasive framework that connects LLM reasoning with ROS-based navigation through a navigation-oriented representation layer, exposed through the Model Context Protocol (MCP) as standardized, reusable tools so that any MCP-compatible LLM can access them without robot-specific wrappers. The visual map modules transform occupancy grids into metric, pose-aware images for goal reasoning, while the semantic annotation modules record waypoint-level observations with robot poses. We evaluate the framework on three tasks: autonomous mapping, spatial reasoning-based navigation, and semantic reasoning-based navigation. The results show that the evaluated LLM backends use these representations to achieve over 97% map coverage and select spatial or semantic navigation targets from natural-language instructions in a simulated indoor environment. This demonstrates representation-mediated LLM navigation without modifying the existing ROS navigation stack.

Abstract: Drifting provides a direct route to one-step generative models, but applying it directly to stochastic transition modeling requires multiple samples of the next state conditioned on the same current state. Standard trajectory data, however, typically provide only one realized next state for each observed current state and therefore do not provide an empirical approximation of the corresponding conditional distribution over possible next states. We introduce block-triangular joint drifting, which instead applies a projected drift field to the empirically accessible joint distribution of consecutive states. Importantly, the block-triangular architecture preserves the current-state marginal while making its second component a direct sampler of the conditional distribution of possible next states. The resulting surrogate generates stochastic trajectories with one model evaluation per time step, without auxiliary generative steps between time steps. Numerical experiments demonstrate accurate marginal and trajectory-dependent statistics and favorable accuracy-cost tradeoffs compared with deterministic, diffusion-, flow-, and distillation-based generative surrogate models.

Abstract: Rigid-body interpenetration frequently occurs in procedurally assembled and generated scenes and must be removed before downstream applications such as physical simulation. We present S4R (Scaling for Rigid-Body Interpenetration Resolution), a scale-continuation method for static interpenetration repair. S4R first uniformly shrinks each body about a fixed reference center to a small initial scale, at which the layout is penetration-free, and then restores full scale through a sequence of minimum-norm convex contact quadratic programs (QPs) that target the linearized separation margin during continuation. Resolution thereby replaces one deep correction with a sequence of shallow-contact subproblems. A conservative scale-event bound and frozen-witness gap predictions cut the number of exact mesh queries; the continuation then ends with a full-scale evaluator check and bounded tail refinement. We evaluate S4R on Kubric, HY3D-Bench, and Thingi10K using a shared mesh-level evaluator and a unified per-scene timing protocol. In the main comparisons on all three benchmarks, up to N=5000 bodies, S4R reaches zero reported penetration with displacement that stays small and nearly independent of scene size, and at the lowest wall time within each hardware tier among the compared methods. A GPU implementation extends these results to large-scale scenes. Our code and data can be found on our project page: https://frank-zy-dou.github.io/projects/S4R/index.html.

Abstract: The enforcement of essential boundary conditions is a fundamental challenge in unfitted boundary methods. This paper presents a non-intrusive, black-box strategy for imposing such conditions in unfitted meshes. The approach is intended for situations where the user does not have access to the solver's source code or its mathematical formulation, which is often the case when using commercial software. The proposed algorithm allows solvers originally designed for body-fitted meshes to be used in unfitted cases, provided that four conditions are satisfied: (i) the solver must support user customization by means of scripting, (ii) allow the imposition of Dirichlet boundary conditions at the node level through scripting, (iii) permit the deactivation of elements outside the physical domain, and (iv) provide access to the solution gradient within active elements. The last condition can also be satisfied by externally reconstructing the gradient from nodal values and connectivity information, provided the element formulation is known, making it optional in practice. These requirements are very fair demands and are satisfied by the vast majority of production-ready, possibly commercial, codes. In the current work, we show the application of this non-intrusive algorithm in the context of the Finite Element Method (FEM) and Isogeometric Analysis (IGA) discretizations, demonstrating optimal $L^2$-norm error convergence. This is demonstrated using the Kratos Multiphysics code (release \texttt{v10.1}) \emph{from the user API, simply leveraging the capabilities mentioned above.}

Abstract: Automatically generating high-quality conforming hexahedral (hex) meshes from general input boundaries remains a challenging problem, despite the numerical advantages hex elements offer in simulation. Grid-based adaptive refinement, followed by hanging-node removal, is the most robust fully automatic choice. Among two-refinement methods, primal templates have better mesh quality than dual templates but depend on a strong balancing condition that over-refines the grid; neither family guarantees planar quadrilateral (quad) faces. This paper generalizes recent primal three-refinement templates to a two-refinement scheme under a moderate balancing condition, a relaxation of the strong one. 32 special and five fundamental patterns resolve all 144 symmetry-reduced configurations, followed by either a fast greedy algorithm or an integer linear programming (ILP) algorithm that trades extra runtime for a further reduction in element count. The scheme is the first two-refinement method in which all hexes have planar faces, and its meshes feed directly into a recent quality-guaranteed hex mesh reconstruction algorithm. At comparable element counts, it attains a similar Hausdorff ratio (HR) and a higher minimum scaled Jacobian (min SJ) than its three-refinement counterpart.

Abstract: Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(σ_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $σ_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

Abstract: Independent evaluation can reject harmful policy updates yet also prevent useful continual learning. We argue that update admission must be assessed through both error control and retained learning opportunities at a stated interaction budget. We identify a concrete failure: a range-based confidence gate cannot certify unchanged old-task behavior within otherwise substantial budgets. A standard paired-binomial construction reduces this burden when outcome disagreements are rare. We also specify certified historical-reference promotion and a round-level missed-opportunity metric. In a constructed one-step pushing diagnostic with 32 seeds, fresh paired checks admit 31.6% of a common update stream at 2,000 episodes per stage, versus zero for the range-based gate; unconditional replay nevertheless learns better in closed-loop runs. A separate learned-dynamics stress test distinguishes model bias from feedback-selection error. The contribution is an admission-audit protocol with analytical and synthetic evidence; physical-robot and VLA validation remain open.