energy market analysts

Abstract: We study the inverse problem of recovering unknown parameters governing the dynamics and rewards of Mean Field Games (MFGs) from partial observations of population trajectories, made stochastic by common noise. The observer seeks to recover a consistent parameter $θ$ via Bayesian inference, facing the challenge that evaluating the likelihood requires solving a new Nash equilibrium (NE) for each candidate $θ$. Due to common noise, the mean-field evolution is stochastic and equilibrium policies are population dependent, which makes solving for each parameter computationally expensive. To overcome this, we introduce the Bayesian-Extended Mean Field Game (BE-MFG), whose single NE simultaneously encodes equilibrium policies for all parameters, enabling efficient learning of the conditional density of mean-field trajectories. We formalize parameter consistency and identifiability in MFGs with common noise and investigate conditions under which consistent parameter recovery is guaranteed. On three synthetic environments of various complexity, we recover the ground-truth parameter accurately from a small number of partial, stochastic observations, outperforming an adaptation of inverse reinforcement learning for MFGs. A fourth experiment, on public electricity market data, suggests that the approach can also be applied to real-world data.

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: Test-time adaptation (TTA) enables time series forecasters to update after deployment as new observations become available. However, adaptation objectives that focus primarily on prediction errors at individual time steps do not fully address the needs of financial time series forecasting. In addition to pointwise return fitting, return direction and the price trajectories reconstructed from sequences of returns are also important. To better account for these properties, we introduce Direction- and Price-Aware Adaptation Loss (DPAL), which combines pointwise return fitting with directional and price-calibration terms. We apply DPAL within existing TSF-TTA frameworks without modifying the source forecaster or the adapter architecture. Across a diverse collection of financial datasets, DPAL reduces reconstructed-price mean squared error in most evaluated settings.

Abstract: Public redispatch records provide empirical data for grid congestion forecasting, but delayed reporting, zero-inflated distributions, and temporal shift present major modeling challenges. We assess the accuracy and reliability of probabilistic machine-learning forecasts using published German transmission records under experimentally imposed information-age constraints. The benchmark evaluates eight daily series of upward and downward intervention energy across four German transmission system operators from 2021 to 2024 (48,242 eligible records; 354 evaluation dates in 2024). We compare seasonal empirical, regularized autoregressive (ARX), quantile LightGBM, GRU, and Transformer models under a minimum seven-day target-latency constraint. Neural architectures use a zero-censored output head to accommodate exact-zero outcomes. Static, rolling, and adaptive delayed-feedback calibration are evaluated using normalized weighted interval score (nWIS), empirical coverage, and block-bootstrap inference. Raw LightGBM achieved nWIS 0.7952, outperforming ARX (1.0604) and the seasonal baseline (0.8739) by 25.0% and 9.0%, respectively (Holm-adjusted p<0.005). Rolling calibration improved LightGBM to nWIS 0.7767 versus 0.8251 for static calibration (p=0.0092), with 91.81% coverage for nominal 90% intervals. The zero-censored Transformer achieved nWIS 0.8161, with no significant difference from LightGBM (p=0.260). However, aggregate coverage concealed substantial undercoverage during high-volume interventions (61.91% coverage among above-threshold events). These results show that boosted-tree models with rolling calibration provide accurate probabilistic forecasts of aggregate redispatch volumes under target delays, while nominal aggregate validity does not ensure reliability during extreme congestion events.

Abstract: Power markets are a natural testbed for multi-agent reinforcement learning (MARL), where multiple self-interested participants repeatedly submit bids. A market-clearing mechanism then determines dispatch and prices subject to power grid constraints and market settlement rules. However, existing MARL environments typically focus on a single market setting, implement simplified clearing mechanisms, or rely on CPU-based optimization solvers that slow large-scale training and limit the systematic study of bidding strategies and market behavior. We introduce PowerMarketJax, a benchmark suite for MARL across five power markets: day-ahead wholesale, real-time balancing, ancillary services, peer-to-peer double auctions, and local flexibility. Each environment implements its own clearing, pricing, and settlement rules while providing a common framework for learning and evaluation. We find that learned bidding behavior depends strongly on the market design: independent learners can miss better strategies when gains require many agents to change together, when more profitable strategies lie beyond a region of lower profit, or when profits disappear as more agents adopt the same strategy. PowerMarketJax implements both market simulation and policy training in JAX, allowing the entire pipeline to run on the GPU with 1,024 X 1,200 parallelisms across both environments and market participants, achieving up to 33X speedup over CPU-based baselines. Our open-source benchmark is available at: https://github.com/powermarketjax/PowerMarketJax.

Abstract: Causal inference guides operational and managerial decisions but remains challenging in high-dimensional panel or tensor settings, where decisions may depend on the joint conditional distribution of missing control outcomes. We develop \emph{Counterfactual Tucker Diffusion} (\CFTDiff), which integrates the treatment mask and latent Tucker structure into conditional diffusion to recover this distribution given observed control outcomes through efficient nonlinear score learning in a low-dimensional core. The masked Tucker score preserves dependence across tensor modes while reducing the dimension of nonlinear score learning from the product of mode dimensions to the much smaller product of Tucker ranks. We establish high-probability error bounds for conditional score estimation that depend on the Tucker ranks, largest mode dimension, and the factor-strength-adjusted number of missing outcomes, and show how these bounds translate into recovery guaranties for the conditional distribution of the missing control outcomes. Across missing rates, simulations show more accurate point recovery than common causal panel and matrix/tensor completion methods; comparisons with nested diffusion specifications further demonstrate the gains from masked conditioning and Tucker dimension reduction. In Norway's iFlex experiment, \CFTDiff recovers missing outcomes more accurately than competing methods; when applied to causal analysis, its estimated conditional distributions yield counterfactual prediction intervals and target-attainment probabilities, allowing pricing interventions to be evaluated by demand-reduction magnitude and reliability.