Time Series Forecasting

Accurate, reliable, and deployable wind power forecasting is critical for power system dispatch, renewable energy integration, and electricity market operations. Progress in this field hinges on the ability to empirically and comprehensively benchmark forecasting methods. Yet existing benchmarks fall short of supporting systematic evaluation in four key aspects: 1) limited coverage of wind power scenarios across turbine scale, variable composition, and spatial structure; 2) incomplete coverage of forecasting model families; 3) evaluation metrics misaligned with wind power requirements; and 4) limited structure-aware diagnostics beyond individual temporal patterns. To address these limitations, we propose WPBench, a comprehensive, fair, and extensible benchmark for wind power forecasting. WPBench integrates 26 public datasets organized by turbine scale and variable composition, spanning single-turbine, multi-turbine, univariate, and multivariate settings. Under unified processing, training, and evaluation protocols, it benchmarks 19 representative models covering traditional methods, deep temporal models, spatio-temporal models, and foundation models. Beyond point-wise errors, WPBench assesses forecast-curve fidelity and computational efficiency, and delivers structure-aware diagnostics across temporal, variable-dependency, and spatial-dependency perspectives. Together, these capabilities enable systematic model comparison across diverse wind scenarios and provide a reusable platform for future research.

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.

Long-term time series forecasting has made significant progress by leveraging multi-scale information to capture hierarchical temporal patterns and model long-range dependencies. However, temporal downsampling in existing multi-scale methods inevitably smooths detailed temporal fluctuations, and this information loss is further aggravated by their emphasis on dominant trends across scales, resulting in insufficiently expressive representations. To address this, we propose a Multi-Scale Wavelet Mixing (MWMixer) model, which incorporates a Bidirectional Frequency-Bands Mixing strategy to recover lost temporal details across scales, enabling complementary cross-scale information interactions. Then, a Dynamic Scale-Adaptive Fusion module learns time-varying weights for each scale to fuse multi-scale forecasts into the final prediction, enhancing the flexibility of multi-scale aggregation. In addition, a cross-scale consistency loss aligns each coarse-scale prediction with the interval-averaged fine-scale outputs, while a multi-scale supervision loss enforces prediction accuracy at each scale, promoting consistent learning across scales. Extensive experiments on seven real-world datasets demonstrate that MWMixer achieves competitive performance in long-term forecasting.

Renewable forecasts are evaluated by statistical skill (e.g., CRPS), but grid operators pay for realized dispatch cost. We diagnose what drives dispatch value in a single-period newsvendor-style economic dispatch using real public data from two European transmission systems (CWE, DE-4TSO). Spatial coherence across forecast sites falls below the pre-specified 1% practical-significance threshold: a controlled ablation holding per-zone marginal forecasts bit-identical and varying only cross-zone dependence (10 configurations, 3 seeds, paired-bootstrap confidence intervals) shows a coherence gain of at most 0.64% of dispatch cost, indistinguishable from zero in 3 of 10 configurations, reached only under an unrealistic 8-fold forecast-error stress test. Decision-focused training, an established paradigm in this venue, delivers a robust 2.82-5.19% gain. A parametric Gaussian-copula approximation matches the empirical copula at realistic error magnitudes but performs worse than no dependence under extreme stress. A single-seed sweep shows that a 12% energy-score gain changes cost by less than 0.1%. Results characterize this single-period dispatch class; a lightweight four-period extension supports the same conclusion. For this dispatch class, spatially-correlated scenario generation provides limited operational value on its own; grid operators and forecast vendors should instead evaluate dependence models by downstream decision value and prioritize decision-focused training.

Probabilistic forecasting requires accurate central predictions and calibrated uncertainty estimates. This paper presents TEMPER, the Temporal Encoder-Masked Probabilistic Ensemble Regressor, a univariate time-series forecasting algorithm that combines a temporal autoencoder, a differentiable masked neural decision forest, continuous ranked probability score (CRPS) training, and Gaussian-mixture post-processing. The R implementation is built on torch for R and returns horizon-wise density, distribution, quantile, and sampler functions. We evaluate TEMPER on three deterministic synthetic level series with trend, periodic, regime-switching, nonlinear-threshold, and heteroskedastic components. Across 96 rolling-origin forecasts at horizons t + 1, t + 5, t + 20, and t + 60, TEMPER obtains 2.824% mean CRPS normalized by origin level, 3.635% median absolute error, and 68.8% empirical 90% interval coverage after training with a 300-epoch cap and early-stopping patience of 100. A naive persistence bootstrap has the best aggregate CRPS, 2.763%, while TEMPER has the best median absolute error and the best CRPS at t+1 and t+5. The ablation study uses matched series-origin-horizon cells, horizon-wise CRPS deltas, endpoint sensitivity summaries, and a calibration-specific interval study. Relaxing the learned mask improves average CRPS by 0.472 percentage points on the ablation subset, mainly through long-horizon gains. A twofold interval inflation improves held-out coverage from 54.2% to 91.7% and gives the best 90% interval score among tested calibration rules. The results identify calibration, horizon-specific tuning, and component selection as the central research priorities.

Patch-based autoregressive time-series forecasting often ties input representation, learned transitions, and recursive execution to one patch length. We ask which of these roles can be adjusted separately. A supporting atomic-encoding study finds greater sensitivity to model width than to atom grouping on the evaluated grid. Our main finding is that a frozen parent's recursive trajectory is easier to fit than the observed future with lightweight parallel exits. Autoregressive Trajectory Distillation (ATD) turns this into selectable ATD-1/2/4/8 execution, with ATD-1 exactly recovering the parent. On a paired four-data-set comparison, ATD-8 reaches $5.54\times$ end-to-end speedup with stable quality across widths. Fewer calls do not automatically remove the parent's existing forecast error: ATD improves trajectory fidelity in all 21 seed runs but forecast accuracy in only 15 against matched clean-future supervision. We further find a correctable residual projection along a train-selected periodic history direction. Spectrum Tangent applies this correction without adding neural parameters or Transformer calls. At horizon 720, it reduces mean squared error (MSE) and mean absolute error (MAE) by 2.54% and 2.33% over seven data sets and two output widths, while remaining $3.24\times$ faster than recursive inference. Level and shape projections sometimes disagree. Trajectory compressibility, the fidelity-accuracy mismatch, and the correction recur across three public AR parents. Together these results separate representation, transition, and execution as AR design axes. Code is available at https://github.com/RowanFFF/ATD-Spectrum-Tangent.

Financial time series evolve across multiple temporal resolutions, challenging forecasting systems to incorporate newly available information without repeatedly recomputing unchanged representations. We introduce HARN, a Hierarchical Associative Resonance Network for event-driven multi-timeframe forecasting. HARN maintains persistent representations across temporal levels and updates each level only when its corresponding completed bar becomes available. The architecture combines causal multi-scale temporal encoding, gated associative memory, cross-level resonance, and hierarchical evidence aggregation, with forecasting performed in basis-point space and reconstructed to the original price scale. We evaluate HARN on four assets spanning equity, foreign exchange, and commodity markets using multiple random seeds and component ablations. HARN achieves competitive reconstructed-price forecasting errors against single-timeframe PatchTST and TimeXer baselines, while ablations reveal the effects of removing individual components across assets and timeframes. A code-level audit further examines consistency between the implementation and the defined event-driven causal protocol. The results position HARN as a persistent multi-timeframe forecasting framework rather than evidence of universal predictive superiority.

Recursive differenced forecasting, the standard remedy for non-stationarity, predicts one-step changes and integrates them by cumulative summation. We show that this reconstruction is a discrete integrator with a pole on the unit circle, so the biased increment errors of a learned nonlinear model are summed without bound and the rollout diverges: at 336 steps its normalised MAE reaches 1.6-3.8 for every neural architecture tested, against 0.80 for a stable linear recursion. We then introduce leaky-integrator reconstruction, a training-free fix that moves the pole inside the unit circle with H(z) = 1/(1 - gamma z^-1), gamma < 1, bounding the accumulation of the model's own increment errors. Applied post hoc with a single fixed gamma=0.9 (no retraining, a two-line change to any deployed one-step or foundation-model forecaster), it beats the traditional recursive integrator at every horizon, with the mean gain over seven diverging architectures and twenty datasets growing from ~3% at H=24 to 23% at H=96, 37% at H=192 and 51% at H=336 (43-75% across those architectures; 78% with an oracle pole), bringing all of them to 0.87-0.97. Based on these extensive empirical experiments, adding a leaky integrator thus improves recursive differenced time-series forecasting.

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.

Day-ahead electricity price forecasts support trading and storage decisions, but for battery arbitrage predicting intraday price spreads is more relevant than predicting individual hourly prices. Here we show that a temporal hierarchy forecasting (THieF) framework that jointly reconciles forecasts of hourly electricity prices and all intraday price spreads consistently improves performance across two major European electricity markets and three different forecasting architectures. Using five years of out-of-sample data from Germany and Spain, we obtain accuracy improvements of up to 19.7% and profit gains of up to 10.4% relative to unreconciled hourly price forecasts. The gains persist even for a highly accurate pretrained TabPFN foundation model. Our results demonstrate that exploiting coherent relationships between economically relevant forecasting targets can improve both predictive accuracy and decision value, and that better statistical forecasts do not necessarily imply better economic decisions.

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.

In this paper, a comparative review of different hybrid models for short-term forecasting of building thermal demand is carried out. Particularly, the assessment tackles the comparison of data-driven models enhanced with other state-of-the-art techniques. At the first step, the existing techniques reported in the literature are analysed. It is concluded that Metaheuristics or a data-driven model are used to identify the parameters of the basic model. The qualitative evaluation includes for each method the input and output features, main advantages and drawbacks. At the second step, an existing dataset of historical thermal demand from Scottish households, as well as historical weather forecasts are utilized to assess additionally the performance of existing hybrid methods. From the assessment of 13 hybrid methods, the Empirical Modal Decomposition - long short-term memory - Markov (EMD-LSTM-Markov) model can predict with the highest accuracy the day-ahead power pattern of heating and domestic hot water (DHW) demands. Though local power peaks are also accurately predicted, high power swells and spikes are underestimated. Other methods, such as Support Vector Machine - Simulated Annealing (SVM-SA) and Random Forest - Improved Sparrow Search Algorithm - LSTM (RF-ISSA-LSTM) predict a smooth pattern of heating and DHW demand profiles with rapid changes underestimating most power peaks.

Time series foundation models (TSFMs) have recently delivered impressive zero-shot performance across diverse forecasting tasks. However, real-world decision-making frequently relies on \emph{irregular multivariate time series} (IMTS), where inconsistent inter-observation intervals and asynchronous sampling across variables coexist with informative missingness. Existing TSFMs handle such inputs either through imputation that injects spurious values or through index-based positional encodings that ignore continuous time. There is still a gap in the foundation model that follows the original IMTS patterns. In this paper, we propose a hybrid attention model that learns a unified time-aware patch representation for IMTS forecasting. We first design a \emph{time-aware patch encoding} that maps a variable number of intra-patch timestamps into a fixed-size embedding, producing a uniform format for irregular patches without resorting to imputation. We then introduce a \emph{time bias attention} mechanism that calibrates inter-patch temporal misalignment and asynchronous cross-channel dependencies as auxiliary attention offset. Finally, on top of a decoder-only Transformer backbone, we adopt a \emph{hybrid causal mask} that preserves a bidirectional full view over the historical context while keeping the forecast horizon strictly autoregressive. To support large-scale pretraining under irregular settings, we also curate VersaTSA, an archive of $30$B observations that retains the native sampling sparsity of its sources. Experiments on three IMTS benchmarks and a standard regular-MTS benchmark show that our model achieves state-of-the-art zero-shot performance on IMTS and remains competitive when transferred to regular forecasting.

Average squared error cannot reveal whether forecasting performance degrades because the future becomes less predictable or because forecasts move farther from the conditional mean. We introduce paired, mechanism-controlled stress tests that decompose changes in expected squared error at each lead time into environmental risk and forecast-oracle distance, using an origin-conditioned predictive oracle unavailable to the evaluated models. Three end-to-end controls have known attribution. Specifically, the null, environmental-only, and information-gap controls verify that the pipeline assigns changes to the correct component. We then apply the benchmark to 24 deployable forecasters. Under frequent switching, 14 methods have higher realized MSE but lower oracle distance; under outlier-variance feedback, 19 have higher MSE but lower scale-standardized MSE. Short- and long-lead stress-response rankings have Spearman correlation 0.624, revealing substantial horizon-dependent reordering. We then study multivariate relation shifts. Across six models and three coupling severities, oracle distance accounts for only 0.7-3.9% of the decomposed expected-risk increase, and environmental-risk majority persists in an eight-channel system and a matched-difficulty audit of Ring, Block, and Hub relations. Finally, prespecified contrasts on independent data-generating process (DGP) realizations show that several visually compelling discovery profiles, including trend accumulation and the hypothesized switching reversal, do not replicate. The benchmark thus combines component-wise diagnosis with a held-out stability audit. It complements real-data out-of-distribution evaluation, which measures performance under realistic shifts when exact oracle attribution is unavailable.

Accurate flood forecasts several days in advance are essential for flood control, water-resource management, and emergency response. A central challenge is to produce high-resolution forecasts across continental domains where hydrological behavior varies widely from place to place. We developed Hapi, a U-Net Swin Transformer that uses fine three-dimensional patches and hierarchical shifted-window attention to forecast river discharge, surface runoff, snow water equivalent, and soil wetness index across the contiguous United States. The model produces medium-range forecasts (24--72~h) at $0.05^{\circ}$ resolution with adaptive task weighting and required only 0.11 seconds for a four-variable 72-h CONUS forecast on one A100 GPU. In a held-out 2024 potential-skill evaluation with ERA5-Land inputs prescribed over the forecast horizon, Hapi achieved the highest F1-score for floods in 20 of 21 comparisons across seven GloFAS return periods and three forecast leads. Independent validation against observed daily discharge at 3{,}881 U.S. Geological Survey gauges showed that Hapi achieved the highest median Nash--Sutcliffe efficiency at every lead, supported by regional-cluster bootstrap intervals. In a matched 24-h comparison of loss formulations, adaptive task balancing produced the lowest discharge errors and the highest F1-score for floods.

Forecasting a long horizon from only the first observations of a sequence is ill-posed: many trajectories are consistent with the same short history. We study this problem in oil and gas production forecasting, where forecasts made after roughly the first fifth of a well's producing life drive development and abandonment decisions, and where a usable forecast must describe a monotone decline. We present Physics-SIMS-TS, a conditional diffusion forecaster that combines negative guidance against synthetic artifacts, decline-curve constraints and an isotonic projection applied during sampling, spatial training augmentation, and an ensembled stochastic sampler yielding a full predictive distribution. Across three jurisdictions and more than 35,000 wells, under a shared-space, validation-frozen protocol, Physics-SIMS-TS is the most accurate diffusion forecaster in the comparison and is competitive with, but not superior to, ensembled transformer forecasters. Its forecasts are monotone by construction at a cost of at most 0.5% in mean squared error, and its trajectory ensemble yields calibrated intervals after one dispersion factor is fitted per jurisdiction. On six standard benchmarks a reversible-instance-normalization variant of the backbone is the leading diffusion baseline. We also quantify four protocol choices on which the measured ranking depends. Code and evaluation artifacts are released.

Financial time-series forecasting must capture price dynamics across heterogeneous assets while incorporating news available at prediction time. We introduce DualCast, a dual-path framework that extends a frozen language model with a discrete financial vocabulary. Each log-return patch is represented by a learned summary token and three residual shape tokens, preserving local drift and volatility while allowing shape patterns to be shared across assets. To improve codebook utilization, we develop adaptive frequency-equalizing residual vector quantization, which rebalances overloaded codewords without compromising reconstruction accuracy. The fast path trains only the new financial-token embeddings and output heads on a frozen Qwen3-8B backbone. A toggleable LoRA adapter enables a slow path that conditions on the fast forecast and news available at the forecast origin to produce a revised prediction. The reviser is initialized by supervised fine-tuning and further optimized with a return-space group relative policy optimization objective that rewards improvements over the fast forecast. In zero-shot evaluations covering equities and energy prices at five-minute, daily, and weekly resolutions, the slow path achieves the lowest mean absolute percentage error among the compared methods in 8 of 12 dataset-horizon settings, including every longest-horizon setting. News ablations indicate additional gains in most tested settings, although their magnitude varies across markets. DualCast thus combines a fast numerical forecaster with an optional text-conditioned revision mechanism.

Accurate time series forecasting is critical across various domains, yet traditional ensemble methods often suffer from the disproportionate influence of extreme forecasts. We introduce the Conformal Adversarial Generative Ensemble (CAGE), a novel framework that combines generative modeling, adversarial discrimination, and conformal prediction to enhance forecast reliability and accuracy. CAGE employs multiple generative models to produce initial forecasts, which are then evaluated by a discriminative component using conformal prediction techniques. P-values derived from nonconformity scores help dynamically adjust model weights, minimizing the impact of unreliable forecasts. This approach ensures that only the most credible predictions contribute to the final ensemble output. Our empirical and statistical analyses of time series data from New Zealand's milk collection and the global health data from the public owid-monkeypox dataset show that the CAGE outperforms traditional ensemble methods, especially in handling outliers and noisy data. By incorporating conformal prediction, CAGE delivers accurate and statistically rigorous forecasts, enhancing decision-making. We have demonstrated performance on two different datasets deliberately to showcase that the proposed method offers a versatile solution potentially applicable across finance, weather, and supply chain management.

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.

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.

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.

Time series forecasting has seen signicant advancements with the emergence of new deep learning models. However, forecasting time series in applications involving physical processes remains a major challenge. Despite the apparition of Physics Informed Neural Networks (PINN), recent models do not estimate unobservable intermediate physical variables, which are important for domain experts to understand the target behavior. To this end, we propose a Physics Informed Recurrent Neural Network (PIRNN) which predicts, along the target, unobservable variables on both historic data and forecast target. This approach enhances the model robustness and results interpretation using domain knowledge. Our method is easily adaptable to any physical model using several equations, each having its own set of unobservable variables, to describe it-self. As a case study, we incorporate physical equations used for groundwater levels predictions by the physical model called Gardenia. This model uses transfers equations between reservoirs, optimized with data assimilation, to simulate the evolution of groundwater levels. Evaluation includes several well known neural network models and the Gardenia model compared on twelve real world datasets. In addition, we study the impact of each component through an ablation study. Our model outperforms other models on ve out of the twelve datasets and our ablation study underlines the importance of having a physical background in our time series forecasting task. Finally, the coherence of the physical variables predicted by our neural network is assessed by a domain expert.

Federated learning (FL) enables privacy-preserving, on-device training across heterogeneous Internet-of-Things (IoT) deployments such as smart-city water-metering networks, where each smart meter observes a household-specific consumption time series. Under such statistical heterogeneity, the standard Federated Averaging (FedAvg) aggregation averages dissimilar local models into a single global model that may fail to capture client-specific patterns. We address this by forming client coalitions directly in the local-weight space and aggregating at the coalition level. Extending a prior weight-driven coalition-formation scheme, we model coalition formation as a Hegselmann-Krause (HK) bounded-confidence opinion-dynamics process acting on the local weights, and develop variants of the HK interaction based on Euclidean-distance and cosine-similarity confidence criteria. The framework is applied to short-term water-consumption forecasting with local Long Short-Term Memory (LSTM) models and evaluated against FedAvg, Per-FedAvg, FedProx, and FedAvg with Euclidean-distance or cosine-similarity coalition formation. Experiments on a real smart-metering dataset of water consumption show that the proposed HK-based coalition formation produces stable, endogenous coalition structures within at most ten inner iterations, incurs no additional client-side computation or communication compared to FedAvg, and reduces the average MAE by up to 54% relative to FedAvg, 39% relative to FedProx, and 24% relative to Per-FedAvg, while achieving the highest global accuracy (83-85%).

TW3Cast is a time-series forecasting system that reaches position 3 of 130 entries on the GIFT-Eval benchmark by mean MASE rank, as of 2026-09-14. The two entries above it belong to the leaderboard's agentic category, multi-step systems that use agents or language models to reason about, generate or select forecasts. TW3Cast runs no agent and no language model. Its selection is a table computed once on the training split and then frozen, and its experts are public foundation models lightly fine-tuned on those training splits. For each of the 97 dataset, frequency and horizon configurations, the table serves one of four modes: a specialist, which is a LoRA or full fine-tune of Chronos-2, TiRex or Toto whose training data was cleaned and enriched by explicit rules; a quantile blend that contains a specialist; a blend of base models; or a selection tournament played on a backtest carved from the training split. Every decision in the table was taken on that backtest. A specialist is admitted the moment it beats the tournament there, so a candidate costs a few megabytes and minutes of GPU time, and a failed candidate changes nothing. Three guarded mechanisms protect the selection from its own biases: a dual accuracy and calibration criterion, an asymmetric margin against candidates that saw the series during training, and conservative per-window gates. The selection rules themselves were chosen inside a temporal meta-backtest. The best base model served alone reaches a mean MASE rank of 33.8, the tournament served on every configuration reaches 38.0, and the full router reaches 19.4. The routing table, the expert index, the pinned base-model revisions, the submitted score file and the dated snapshot of the public scores are released, and every leaderboard number in this paper regenerates from them by one script.

For distribution system operators, short-term load forecasting (STLF) supports congestion management, voltage control, and asset protection. Most existing approaches focus on overall accuracy across all time steps and neglect performance during high-demand (HD) periods, where larger forecast errors can increase the risk of congestion and voltage violations. In this paper, we study peak-aware STLF across three operator-relevant distribution grid aggregation levels, area codes (AC), secondary substations (SUB), and low-voltage (LV) feeders, using open datasets from the United Kingdom and Switzerland. We compare statistical baselines, machine learning models (LightGBM and XGBoost), and recent time-series foundation models (Chronos Bolt and Chronos-2) under a peak-aware evaluation framework that reports both overall and HD forecasting performance using NMAE and MAPE. The results show that Chronos-2 achieves the best HD performance across all aggregation levels, with HD-NMAE and HD-MAPE of 0.039 and 4.53% at AC, 0.080 and 9.45% at SUB, and 0.138 and 16.14% at LV, while Chronos-Bolt consistently ranks second best. Compared with the gradient boosted ML models, Chronos-2 reduces mean HD-NMAE by about 20-51% across levels while remaining best or near-best on the overall metrics. A quantile analysis of the probabilistic Chronos outputs further identifies aggregation-specific operating points, and runtime measurements indicate that foundation model inference is fast enough for practical deployment. Overall, the findings highlight peak-aware evaluation and aggregation specific quantile selection as a practical pathway toward more operationally relevant STLF in distribution networks.

Joint-embedding predictive architectures (JEPA) have emerged as a promising self-supervised pretraining paradigm for time series, learning representations by predicting target embeddings in latent space rather than reconstructing raw signals. Yet evidence on their benefits remains mixed, and most studies test only a single backbone or a narrow set of architectures, leaving unclear whether JEPA pretraining is a reliable improvement or one that depends heavily on the downstream model. We address this gap through a large scale evaluation of one JEPA instantiation across nine backbones and eleven benchmarks spanning temporal and spatio-temporal forecasting, the most extensive cross architecture assessment of JEPA for time series to date. We find that the benefit of this instantiation varies sharply across backbones, producing consistent gains for some architectures and consistent degradation for others, even on the same dataset. This pattern holds across both task families, indicating the variability is a general property of this instantiation rather than a dataset specific artifact worth accounting for when choosing a backbone in practice.

Weekly influenza surveillance counts guide vaccine distribution and public-health alerts, yet they are hard to forecast. Each region offers only a few seasons, waves shift in timing and height every year, and information that helps while a wave grows misleads after its peak, whereas last season's shape stays informative for a year. Existing epidemic graph models and general forecasters read a short fixed window and treat all past information alike, so they neither exploit earlier seasons nor discard stale associations when the epidemic phase changes. To address these limitations, we propose TERN, a forecaster built around a delta-rule fast-weight memory that decays channel-wise and erases along a learned address under gates driven by local epidemic-phase features, combined with an explicit seasonal reference and online adaptation. On three Cola-GNN influenza benchmarks, TERN outperformed epidemic graph models and general forecasters, matched or exceeded seasonal references, and a controlled comparison confirmed the contribution of the memory itself.

The Koopman operator has been widely used for time-series prediction in dynamical systems. However, prior work that learns latent ``Koopman spaces'' using neural networks often did not construct a valid Koopman space for forecasting, as these representations may be mathematically inconsistent with the operator-theoretic formulation and fail to capture the intrinsic low-rank structure of system dynamics. To address this issue, we introduce K$^2$SVD, a method that explicitly learns the leading singular functions of the Koopman operator by optimizing a Hilbert-Schmidt objective. This yields a well-defined low-rank approximation of the Koopman operator with an interpretable linear combination, featuring a compact latent space with less than $10\%$ of the dimensions used in previous work. In the learned Koopman space, K$^2$SVD further captures temporal evolution with a linear Gaussian state-space model and performs inference via Kalman filtering, mitigating noise accumulation during multi-step prediction. Empirical results show that K$^2$SVD outperforms state-of-the-art methods across multiple datasets, with significantly faster prediction speeds and lower computational cost than previous efficiency-focused models. This highlights the benefits of principled low-rank Koopman representations and opens up broader potential for applications.

We present NanoForecast v0.5, a 6.5M-parameter forecaster that competes with models 31x its size (TimesFM, 200M parameters) after training pipeline fixes and no architecture change. Retraining the v0.3 architecture with corrected loss-scope handling, tensor shape alignment, and wider augmentation coverage cuts overall Mean Absolute Scaled Error by 43.8% under one fixed protocol (MASE 3.030 to 1.704) on the same data and compute budget. NanoForecast v0.5 beats TimesFM on all three ETT datasets (MASE 0.676/1.110/0.287 vs. 0.705/1.360/0.545) and on exchange rate (4.317 vs. 4.383); TimesFM keeps a clear lead on the high-cardinality electricity and traffic sets. Against PatchTST (15M+ parameters, official configuration), v0.5 wins all three ETT sets. Training takes about 12 hours on a single cloud GPU (NVIDIA T4, Google Colab) and inference needs no GPU (measurements in this paper are on an Apple M4 CPU). We release all code, pretrained checkpoints, and evaluation framework under Apache 2.0 at https://github.com/eulogik/NanoForecast

Traditional energy forecasting solutions rely on task-specific supervision and energy asset representations, limiting transferability and the ability to capture general temporal dynamics across heterogeneous assets. We address this by proposing a distributed Joint Embedding Predictive Architecture (JEPA) for self-supervised learning from heterogeneous energy time-series. The framework predicts latent representations of masked temporal segments while integrating temporal observations and contextual information within a shared embedding space. To prevent representation collapse, training combines a latent-space predictive objective with covariance and temporal variance regularization. The evaluation was conducted on energy consumption and generation datasets under data-degradation scenarios and compared with a Transformer forecasting baseline. The learned representations remained stable (cosine similarity $\approx 0.98$; effective rank 185-235). JEPA achieved performance comparable to a Transformer on building energy data, higher $R^2$ in 3/5 consumer clusters, and outperformed the baseline on 9/10 unseen PVs ($R^2$=0.73-0.88 vs. <0.45), while showing greater robustness to missing data.