Spatiotemporal Forecasting

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39 papers in the last four weeks, up 290% on the four weeks before. 0.4% of all new papers.

Jul 13Week of Sep 28

Latest papers 279

Jun 20, 2026cs.LG

Beyond Time Series: Spatial Reasoning for Epidemic Forecasting via Multimodal Learning

Epidemic forecasting models typically rely on surveillance data reported over administrative regions, treating them as atomic units, thereby obscuring sub-regional spatial structure that shapes disease dynamics. We introduce a spatially structured multimodal epidemic forecasting setting that integrates region-level temporal surveillance data with spatially localized auxiliary signals that are misaligned in resolution and structure, reflecting realistic public health reporting constraints. Building on this formulation, we propose M-SPICE (Multimodal SPatIal Context for Epidemic Forecasting), a structure-aware spatiotemporal forecasting framework that performs joint reasoning over temporal disease dynamics and spatial context via attention-based multimodal fusion, allowing spatial signals to selectively condition temporal representations across forecast horizons. We evaluate our approach on real-world COVID-19, influenza, and influenza-like illness (ILI) forecasting tasks under realistic real-time evaluation protocols. Across all forecasting settings, our method consistently outperforms state-of-the-art multivariate time-series, multimodal, and epidemiological forecasting baselines while maintaining strong probabilistic forecasting performance. Finally, interpretability analyses reveal when, where, and how spatial signals are leveraged, highlighting settings in which purely temporal, region-aggregated models are most likely to fail.

Diana Guadalupe Gomez, Chenwei Wu, Zhiyi Wang +2

University of Michigan Ann Arbor, MI, USA

Epidemic Forecasting Spatiotemporal Reasoning Probabilistic Forecasting Spatiotemporal Forecasting Multimodal Fusion

Jun 19, 2026cs.LG

An Efficient and Effective Architecture for Large-Scale Traffic Prediction via Geometry-Adaptive Square Partitioning

Traffic prediction is a core task in intelligent transportation systems and urban-scale decision making. Despite the effectiveness of mainstream neural-network based methods, their deployment in real-world settings with thousands of traffic sensors is jeopardized severely by their poor computational scalability. To address this, the community has attempted to incorporate spatial database partitioning techniques (e.g., Grid, Quadtree, and K-D Tree) to improve model scalability. However, these approaches rely on handcrafted geometric heuristics and often produce irregular or imbalanced data partitions, leading to boundary fragmentation, excessive padding overheads, and degraded model accuracy. In this paper, we propose SqLinear, an efficient and effective architecture for large-scale traffic prediction. First, we design Square Partition, a geometry-adaptive algorithm that partitions massive traffic sensors into balanced, non-overlapping, and near-square spatial regions. Unlike existing heuristic-based designs, Square Partition is theoretically grounded and provides provable guarantees on aspect ratio, balance, and partition utilization, establishing a high-quality foundation for downstream spatiotemporal modeling. Next, we propose a Hierarchical Linear Interaction (HLI) module that abandons the costly attention mechanisms commonly used in Transformer-based spatio-temporal models. HLI efficiently captures both local intra-region dynamics and global inter-region dependencies through a lightweight linear interaction scheme, enabling effective spatiotemporal modeling with linear computational complexity. Extensive experiments on four large-scale traffic datasets and 10 baselines show that SqLinear reduces MAE by 2.30% on average under standard setting and by 5.81% under extreme scalability settings, while reducing training runtime by 13.27%--30.84% in spatial- and horizon-scaling scenarios.

Yongfeng Su, Hongwen Li, Zijian Zhang +3

Zhejiang University, China · Southeast University, China · Aalborg University, Denmark

Traffic Flow Estimation Spatiotemporal Forecasting Traffic Forecasting

Jun 19, 2026cs.LG

Structure-Aware Graph Multi-Task Learning for Dynamic Sparse OD Demand Prediction

Origin-Destination (OD) demand prediction is fundamental to intelligent transportation systems, yet real-world OD flows are often dynamically sparse, long-tailed, and characterized by heterogeneous zero-flow patterns. These properties make it difficult to distinguish whether an OD connection is active from how much demand it generates once activated. Many existing methods primarily treat OD prediction as a single flow regression task, which limits their ability to model low-frequency, intermittent, and long-tailed OD interactions. To address these challenges, we propose SAGMTL, a Structure-Aware Graph Multi-Task Learning framework for dynamic sparse OD demand prediction. SAGMTL decomposes OD prediction into structural state modeling and flow intensity estimation, jointly learning regional activity states, OD connection activity, and edge-level flow intensity within a unified framework. Specifically, a node-edge collaborative representation module captures regional semantics, temporal dynamics, and spatial priors through interactive node-edge updates, producing structure-aware representations for dynamic OD interactions. Based on these representations, SAGMTL estimates OD flows by jointly modeling stable demand patterns and short-term fluctuations. A multi-constraint objective further improves sparsity awareness and structural consistency. Experiments on three real-world urban mobility datasets from Beijing, Chengdu, and Nanjing show that SAGMTL achieves superior overall performance compared with state-of-the-art baselines. Further analysis demonstrates that explicitly modeling regional activity, connection states, and flow intensity improves the robustness of dynamic sparse OD demand prediction.

Ming Xu, Jiawei Cao

Software College, Liaoning Technical University, Huludao, Liaoning 125100, China

Intelligent Transportation Systems Multi-Task Learning Spatiotemporal Forecasting Spatiotemporal GNNs

Jun 18, 2026cs.LG

Enhancing Graph Neural Networks Using Proximity Graphs for Dust Source Emission Forecasting

Accurate prediction of dust source emissions is critical for mitigating the significant environmental and health hazards posed by dust storms. Traditional forecasting methods often struggle to capture the complex spatiotemporal dynamics of these phenomena. In this paper, we demonstrate that proximity graphs enable Graph Neural Networks (GNNs) to effectively model the intricate spatial and temporal relationships between data points. Specifically, we use proximity graphs--such as Delaunay triangulation, Gabriel graph, k-Nearest Neighbor graph, and Yao graph--as the input for GNNs (including GraphSAGE, Graph Convolutional Networks, and Graph Attention Networks) to perform message passing. Our approach highlights the effectiveness of integrating proximity graphs with GNNs for robust and accurate dust source forecasting. To emphasize the importance of proximity graph representations, we compare our method against GNNs using random graphs for message passing. The results show that GNNs with proximity graphs significantly outperform those with random graphs and are also far superior to Long Short-Term Memory (LSTM) model in dust source emission forecasting.

Maryam Sanisales, Zahed Rahmati, Ali Darvishi Boloorani +1

Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran · Department of Remote Sensing and GIS, Faculty of Geography, University of Tehran, Tehran, Iran

Graph Neural Networks Spatiotemporal Forecasting

Jun 17, 2026cs.LG

Understanding Key Features of Time Series Foundation Models from Epidemic Forecasting

Seasonal influenza infects millions of people and causes substantial morbidity and mortality in the United States each year, making accurate short-term forecasting a core public-health need. Reliable forecasts of epidemic time series can inform vaccination timing, hospital staffing, and resource allocation, yet the comparative behavior of modern forecasting architectures on infectious-disease surveillance data remains insufficiently characterized. We address this gap through a systematic evaluation of regional influenza forecasting using influenza-like illness surveillance and influenza-associated hospitalization time series under both temporal and spatial generalization settings for 1-4-week-ahead prediction. We compare classical neural network architectures, numerical transformer-based models, pretrained time series foundation models, and LLM-based forecasting approaches. Across tasks, we demonstrate that a mixture-of-experts model that fuses multiple pretrained forecasters achieves the strongest overall performance, indicating that heterogeneous pretrained representations provide complementary predictive information. Our results further show that numerical transformer-based models produce reliable forecasts, while pretraining provides the largest gains at longer horizons, particularly when the pretraining domain is mechanistically aligned with influenza dynamics. In contrast, LLM-based time series methods underperform relative to numerical forecasters in this setting. Finally, we examine hospitalization information as both an auxiliary covariate and a pretraining source. Hospitalization signals provide complementary improvements in selected settings and clarify when additional surveillance streams enhance the robustness of multi-horizon forecasting. These findings provide actionable guidance on model selection, pretraining strategy, and auxiliary-signal use for influenza preparedness.

Alireza Jafari, Judy Fox, Geoffrey C. Fox +2

Department of Computer Science, School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22904 USA · School of Data Science, University of Virginia, Charlottesville, VA 22904 USA · Biocomplexity Institute and the Department of Computer Science, School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22904 USA +1

Epidemic Forecasting LLM-Based Time Series Forecasting Spatiotemporal Forecasting Time-Series Foundation Models

Jun 17, 2026cs.LG

INDEQS: Informed Neural controlled Differential EQuationS

Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a modification to graph-based NCDE forecasting methods that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, and offers both a lightweight graph-constrained variant and a more expressive variant, learning additional graph connections from data via adaptive graph convolutions. To systematically study when graph informedness is beneficial in forecasting, we devise a continuous advection simulation on directed graphs, yielding synthetic spatio-temporal datasets with known ground-truth flow structure. We then evaluate INDEQS on two real-world tasks: river discharge forecasting on a hydrological network and traffic flow prediction on PeMS08. Across the synthetic and the river-discharge tasks, outer informedness consistently improves mean absolute error over an uninformed NCDE with comparable parameter count, particularly on larger graphs, while inner informedness offers a more parameter-efficient alternative when strict adherence to a known adjacency is desired. A comparison of discrete convolutional and continuous-time decoders further shows that continuous decoders yield better accuracy and greater temporal flexibility on real-world tasks. An implementation of INDEQS and the advection simulation is available at https://github.com/mitchi1/indeqs .

Michael Detzel, Gabriel Nobis, Kristiyan Blagov +3

Fraunhofer Heinrich Hertz Institute · Technische Universität Berlin

Neural Controlled Differential Equations Spatiotemporal Forecasting Neural ODEs Traffic Forecasting Spatiotemporal GNNs

Jun 17, 2026cs.LG

Investigating Inductive Biases for Machine Learning Emulation of Sudden Stratospheric Warmings in Idealised Isca Simulations

Machine-learning emulators are increasingly used for weather prediction and have the potential to extend skill on subseasonal-to-seasonal timescales by learning dynamically important sources of predictability. A key challenge is whether the models can exploit predictability anchors, such as stratospheric variability, that influence tropospheric circulation beyond short lead times. We test how architectural inductive bias affects emulation of sudden stratospheric warming (SSW) dynamics using paired idealised Isca simulations that differ only in an imposed wave-2 heating perturbation. Across convolutional, transformer, and graph-based architectures trained for one-step prediction, model differences are modest when the stratosphere is dynamically quiet but widen substantially when SSW-like variability is active. Our results identify explicit three-dimensional vertical coupling as a key inductive bias for machine-learning emulation of stratospheric dynamics. However, Eliassen-Palm flux diagnostics show that low forecast error does not guarantee physically faithful wave-mean-flow interaction, with coherent errors remaining in stratospheric wave-driving structure.

Oskar Bohn Lassen, Simon Driscoll, Stephen I. Thomson +2

Department of Technology, Management, and Economics Technical University of Denmark · Department of Applied Mathematics and Theoretical Physics University of Cambridge · Department of Mathematics and Statistics University of Exeter

Neural Surrogate Modeling Climate Science Inductive Bias Scientific ML Spatiotemporal Forecasting

Jun 16, 2026cs.LG

ASTEROID: A Spatiotemporal Information Transformer for Forecasting Multi-Step Time Series of Molecular Dynamics

Molecular dynamics (MD) simulation is computationally demanding, particularly for large-scale systems requiring long-term analysis. Accurate forecast of the outcomes of a MD simulation is not only an attractive scientific challenge but also has substantial practical value. In this work, we developed a data-driven framework, termed ASTEROID (Advanced Spatiotemporal TransformER fOr Inferring Dynamics), that can directly predict multi-step atomic coordinates, avoiding conventional iterative integration. For this purpose, our ASTEROID reformulates MD trajectories as high-dimensional spatiotemporal sequences and integrates the Spatiotemporal Information (STI) Transformation equation into a Transformer architecture. The core innovation of ASTEROID lies in its ability to model multiscale spatiotemporal dependencies. In particular, for spatial dependencies, a local-global self-attention mechanism captures both short- and long-range interactions. For temporal dependencies, an encoder-decoder structure integrates global context with autoregressive forecasting. ASTEROID was evaluated on several quantum-mechanics derived molecular datasets. Our results indicate that ASTEROID achieved not only a higher level of accuracy in multi-step prediction than existing methods on various benchmarks, but also significantly reduced computational cost of conventional MD simulation. Moreover, the model supports iterative multi-step forecasting over an extended time scale. This work establishes a robust and generalizable data-driven paradigm for accelerating MD simulations.

Kexin Wu, Luonan Chen, Renxiao Wang

Department of Medicinal Chemistry, School of Pharmaceutical Sciences, Fudan University, 826 Zhangheng Road, Shanghai 201203, People's Republic of China · School of Mathematical Sciences and School of AI, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China

Spatiotemporal Forecasting Molecular Dynamics Simulation Trajectory Prediction Time Series Transformers Multiscale Time-Series Modeling

Jun 15, 2026cs.LG

Towards Fast GNN Surrogates for CO2 Migration in Complex Geological Formations

This chapter discusses how a data-driven machine learning approach can reproduce key aspects of the physical behavior of multiphase flows in complex geological formations. We propose an end-to-end graph neural surrogate tailored to CO

_2

plume migration forecasting in geological storage. The method is evaluated on the SPE11A benchmark, a well-known industry test case designed to assess CO

_2

storage scenarios and characterized by sharp gas-water interfaces, strong advective transport, and rapid convective mixing with fingering development. The benchmark is reformulated as a graph in which nodes represent computational cells and edges encode transmissibility-based interactions enriched with geometric attributes. Directional transport arising from grid geometry, permeability contrasts, and geological heterogeneity is captured through an anisotropic message-passing mechanism, where interaction weights are computed via geometry-conditioned edge embeddings, biasing message aggregation toward physically relevant transport directions. Temporal evolution is modeled in latent space using an autoregressive residual formulation trained with multi-step supervision. The proposed model produces competitive forecasts of gas saturation and liquid-phase density, which are key indicators for CO

_2

storage monitoring, with cumulative errors that remain moderate over extended forecasting horizons.

Rodrigo S. Luna, Thiago H. N. Coelho, Luiz S. L. Neto +8

Systems and Computer Engineering and High Performance Computing Center, NACAD - COPPE, Federal University of Rio de Janeiro · Civil Engineering and High Performance Computing Center, NACAD - COPPE, Federal University of Rio de Janeiro · Mechanical Engineering and High Performance Computing Center, NACAD - COPPE, Federal University of Rio de Janeiro +1

Graph Neural Networks PDE Surrogate Modeling Spatiotemporal Forecasting

Jun 15, 2026cs.CV

When the Past Matters: FlashBack Memory for Precipitation Nowcasting

Accurate precipitation nowcasting is crucial for disaster mitigation and socio-economic planning, yet existing methods often struggle with false alarms, missed events, and long range dependency modeling at high spatiotemporal resolution. To address these challenges, we propose FlashBack Memory (FB), a module that dynamically retrieves key historical states and integrates them via an adaptive fusion gate, enhancing the spatiotemporal representation capability of recurrent-based models. We incorporate FB into PredRNN, PredRNNpp, MIM, MotionRNN, and PredRNN-V2, and evaluate on CIKM2017, Shanghai2020, and SEVIR datasets. Experimental results demonstrate that FB significantly improves MSE, MAE, SSIM, and CSI metrics, particularly for high-intensity rainfall and long-sequence predictions, while reducing false alarms and missed events and enhancing temporal consistency and spatial localization. The proposed method provides a general and efficient memory enhancement mechanism, improving the overall performance of recurrent-based precipitation nowcasting models.

Yuhao Du, Boxiao Huang, Chengrong Wu +1

College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000, China · Fuqua School of Business, Duke University, North Carolina 27705, USA · Department of Computer Science, University of Manchester, Manchester M139PL, UK

Memory-Augmented Neural Networks Precipitation Forecasting Recurrent Neural Networks Spatiotemporal Forecasting Precipitation Nowcasting

Jun 14, 2026cs.AI

UrbanWell: Benchmarking Multimodal Large Language Models for Spatio-Temporal Urban Wellbeing Analytics

Understanding urban wellbeing from multimodal data requires integrating heterogeneous spatial and temporal signals, posing significant challenges for current multimodal large language models (MLLMs). We introduce UrbanWell, a large-scale benchmark designed to systematically evaluate the spatio-temporal reasoning capabilities of MLLMs for urban wellbeing analytics through joint modeling of satellite and street view imagery. UrbanWell spans 38 cities across multiple years and includes diverse indicators covering (1) environmental conditions (CO

_2

, NO

_2

, PM

{2.5}

, and Normalized Difference Vegetation Index), (2) spatial accessibility (minimum distance to supermarkets and restaurants), (3) urban form (road length, road density, and land use), (4) urban vitality (population, economic activity diversity, and land use diversity), and (5) subjective perception attributes (e.g., safety, beauty, liveliness, wealth, and quietness). All indicators are aligned at grid level to enable standardized evaluation. Beyond static prediction, UrbanWell defines temporal reasoning tasks, including future value forecasting from historical observations and temporal trend classification. We benchmark 15 state-of-the-art representative MLLMs in a zero-shot setting, providing a comprehensive comparative evaluation across spatial and temporal dimensions. Experimental results indicate that while MLLMs capture salient spatial and perceptual cues, their performance varies substantially across heterogeneous urban indicators spanning environment and subjective perception. UrbanWell serves as a unified benchmark for evaluating multimodal spatial and temporal reasoning in urban wellbeing analytics, offering a standardized testbed for systematic assessment and future research on multimodal urban intelligence. Our codes and datasets are accessible via https://github.com/axin1301/UrbanWell-Benchmark.

Yanxin Xi, Xiang Su, Jie Feng +3

Department of Computer Science, University of Helsinki, Helsinki, Finland · Department of Computer Science, Department of Agricultural Sciences, University of Helsinki, Helsinki, Finland · Zhongguancun Academy, Beijing, China +2

Spatiotemporal Reasoning Multimodal Large Language Models Spatiotemporal Forecasting Multimodal Model Evaluation

Jun 14, 2026cs.LG

Continuous Cross-Domain Traffic State Prediction via Memory-Augmented Graph Liquid Time-Constant Networks

Traffic state prediction is a fundamental task in intelligent transportation systems. In practical applications, some regions suffer from limited traffic observations due to insufficient sensing infrastructure, making cross-domain knowledge transfer an important solution for data-scarce traffic prediction. However, existing cross-domain traffic prediction methods still face several limitations, including coarse-grained source-target adaptation, limited capability in handling unseen target-domain patterns, and insufficient modeling of continuous traffic dynamics under irregular or heterogeneous temporal conditions. To address these issues, this paper proposes a continuous cross-domain traffic prediction framework, termed Memory-Augmented Graph Liquid Time-Constant Network (MA-GLTC). Specifically, we first construct spatio-temporal units (STUs) to decompose traffic networks into transferable local units, enabling fine-grained knowledge alignment across domains. Then, a graph liquid time-constant network (GLTC) is developed to model graph-coupled traffic evolution in continuous time. Different from generic graph neural ODE-based models, GLTC introduces graph-coupled recurrent conductance into liquid time-constant dynamics, allowing node states to evolve with leakage, adaptive time constants, and neighborhood-aware feedback. Furthermore, a Memory-based Transfer Storage (MTS) mechanism is designed to preserve source-domain knowledge, retrieve matched traffic patterns, and update reliable target-domain patterns when unseen states emerge. Experiments on five public traffic datasets demonstrate that MA-GLTC consistently outperforms representative innerdomain and cross-domain baselines in both short-term and longterm prediction tasks. Compared with the second-best method, MA-GLTC reduces the average prediction errors by 3.02%, 0.33%, 8.92%, 10.09%, and 2.11%, respectively.

Jinrong Xiang, Ming Xu

Software College, Liaoning Technical University, Huludao, Liaoning 125100, China

Cross-Domain Transfer Learning Spatiotemporal Forecasting Traffic Forecasting Spatiotemporal GNNs

Jun 13, 2026cs.CV

DYNA-PRUNER: Input-Adaptive Data-Model Co-Pruning for Efficient and Scalable Spatio-Temporal Media Prediction

Spatio-temporal prediction supports radar/satellite nowcasting and city-scale traffic monitoring, but modern models are often too expensive for real-time deployment. This stems from a mismatch between dense computation and strong input-dependent redundancy (e.g., calm seas or clear skies). To enable automated, resource-aware architecture optimization in scalable media analysis, we propose Dyna-Pruner, an end-to-end framework for input-dependent co-pruning of data and model structure. A shared-importance synchronization mechanism generates coupled masks that prune redundant regions and their corresponding computational units (e.g., convolutional filters), yielding per-sample sparse sub-networks at inference time. Experiments on WeatherBench, SEVIR, and TaxiBJ show seamless integration with CNN, RNN, and Transformer backbones, reducing FLOPs by up to

70\%

and achieving a

2.5\times

speedup on NVIDIA Jetson AGX Orin with negligible accuracy loss (

<1\%

).

Fuyan Zhang, Yuqi Li, Qing Xu +2

University of Edinburgh · The City College of New York, City University of New York · Institute of Computing Technology, Chinese Academy of Sciences +1

Efficient Neural Network Inference Spatiotemporal Forecasting Neural Network Pruning

Jun 12, 2026cs.LG

OmniPMNet: Bridging discrete and gridded PM10 forecasts via omni-query neural processes

Forecasting particulate matter (PM10) requires both station-scale accuracy and continuous spatial fields, especially during severe dust storms. Chemical transport models (CTMs) provide gridded forecasts but retain local biases, whereas graph neural networks (GNNs) track monitoring sites well at short lead times but do not produce gridded outputs. Here we present OmniPM-Net, a Convolutional Conditional Neural Process (ConvCNP)-based fusion model that reconciles these two forecast types within a shared spatial representation. A terrain-aware Gaussian set convolution lifts irregular GNN station forecasts onto a regular grid, where a multi-scale Spatial Source Attention (SSA) module blends them with Copernicus Atmosphere Monitoring Service (CAMS) forecasts; a shared omni-query readout then decodes this representation into consistent PM10 predictions at either stations or grid cells over a 108 h horizon. Evaluated across 1,618 air-quality monitoring stations throughout China over the full year of 2024, OmniPM-Net matches the station-level accuracy of the stronger GNN baseline (mean absolute error 21.14 versus 22.00 ug/m3) and reduces the CAMS mean absolute error by 30%, while simultaneously delivering the gridded fields that the discrete GNN cannot. Its clearest gains are in the high-concentration tail, where the 90th-percentile MAE falls by 9% relative to the GNN and 25% relative to CAMS, and during dust episodes, where it improves categorical detection skill while tracking the evolving spatial trajectory.

Shuangshuang He, Shuo Wang

ColorfulClouds Technology Co., Ltd., 100875 Beijing, China. · School of Systems Science, Beijing Normal University, 100875 Beijing, China. · D-ITET, ETH Zurich, 8092 Zurich, Switzerland.

Air Quality Prediction Spatiotemporal Forecasting

Jun 12, 2026stat.ML

Nonlocal Bayesian Modeling of Continuous Spatio-Temporal Dynamics

Real-world spatio-temporal forecasting must handle irregular time points, spatially sparse observations, and the need for uncertainty quantification. This setting is often further compounded by nonlocal interactions (long-range spatial coupling). Modeling continuous-space, continuous-time nonlocal dynamics naturally leads to infinite-dimensional integro-differential equations (IDEs), making principled Bayesian inference intractable. We propose the NonLocal Bayesian Spatio-Temporal model (NLBST), a hierarchical Bayesian framework for continuous spatio-temporal fields that learns explicit nonlocal coupling while retaining tractable inference. NLBST represents the latent field via a coordinate-based spatial basis expansion and models the coefficient process with a continuous-time ODE whose learnable linear operator corresponds to a Galerkin reduction of a nonlocal IDE; a Neural ODE residual captures additional nonlinear dynamics. A linear-Gaussian observation model enables Kalman-style sequential updates under missing and irregular observations, while the spatial basis representation enables inductive prediction at unmeasured locations without retraining. Global parameters are learned via variational inference, and uncertainty is handled through a Bayesian hierarchy. Experiments on synthetic and real-world datasets demonstrate strong forecasting and spatial generalization with well-calibrated uncertainty, yielding substantial gains over baselines in strongly nonlocal and partially observed regimes.

Jaeyeong Lee, Heeyoung Kim

Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea

Irregular Time-Series Modeling Bayesian Inference Hierarchical Bayesian Modeling Spatiotemporal Forecasting State Space Models

Jun 11, 2026cs.LG

Can Machine Learning Forecast Rice Yields in Data-Constrained Settings? Satellite Climate Data, National Crop Statistics, and Lessons from Sierra Leone

Sierra Leone's agriculture operates with almost no data-driven decision support, and no published machine learning study has examined the country's crop yields. We ask whether rice yield can be forecast from data Sierra Leone currently has. Using 25 years of FAOSTAT production data (2000-2024) for nine major crops, we train XGBoost, Gradient Boosting, and Random Forest under a strict anti-leakage protocol with expanding-window walk-forward evaluation across seven held-out years, benchmarked against naive persistence. No model trained on crop statistics alone outperforms persistence. Augmenting with free satellite climate data (CHIRPS rainfall, NASA POWER temperature) reverses this result: a climate-only XGBoost reduces forecast error by one third (RMSE 284 vs 428 kg/ha), a gain that holds for a linear model and is robust to excluding the anomalous 2018 season. Early-season (May-June) rainfall is the dominant predictor, implying seasonal yield risk is observable months before harvest. No model anticipated the 2018 collapse, whose origins were institutional rather than climatic. We translate the findings into policy recommendations for Sierra Leone's Feed Salone Strategy, with a fully open-source pipeline.

Ibrahim Denis Fofanah

Seidenberg School of Computer Science & Information Systems, Pace University, New York, USA · RiseAfrica Foundation for STEM and Innovation, Sierra Leone, West Africa

Time Series Forecasting Spatiotemporal Forecasting Crop Yield Prediction

Jun 11, 2026cs.LG

MP3: Multi-Period Pattern Pre-training for Spatio-Temporal Forecasting

Spatio-Temporal forecasting is crucial in diverse fields, such as transportation, climate, and energy. Urban spatio-temporal data exhibits temporal mirage: similar short-window inputs have divergent future trends, and vice versa. Existing spatio-temporal graph neural networks (STGNNs) cannot effectively identify such mirages. We argue that the core reason lies in the short-window inputs that have incomplete period observation, heterogeneous global spatial correlation, and cross-period superposition causality. To bridge this gap, we develop a novel Multi- Period Pattern Pre-training (MP3), a plug-and-play pre-training plugin for distinguishing temporal mirages. MP3 presents two core innovations: (1) The multi-period pattern learning is designed to learn multi-period patterns from long time series. Specifically, multi-period temporal modeling leverages edge convolution to identify different multi-period patterns. Multi-period spatial modeling uses a bottleneck project and a global memory bank to capture heterogeneous global spatial relations efficiently. Cross-period pattern interaction employs a causality-enhanced Transformer to capture dependencies across different period patterns. (2) This plugin can seamlessly integrate into existing STGNN backbones to strengthen their forecasting performance. The experiment on five STGNN baselines across five real-world datasets (including a large-scale dataset CA) verify the effectiveness, superior scalability and strong adaptability of MP3, which brings consistent and robust performance improvements across all evaluated baselines. On average, MP3 reduces the MAE 4.7% and the RMSE 5.0%. The code can be available at https://github.com/YAN-outlook/MP3.

Lilan Peng, Yandi Liu, Qingren Yao +2

School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu 611756, China · Eindhoven University of Technology, Eindhoven 5612 AZ, Netherlands

Spatiotemporal Forecasting Multiscale Time-Series Modeling Spatiotemporal GNNs

Jun 11, 2026cs.LG

Reliability of Probabilistic Emulation of Physical Systems

Two dominant approaches have emerged for generating probabilistic forecasts of physical systems: generative models, such as diffusion or flow matching; and ensembles of deterministic models with stochasticity injected, trained using the continuous ranked probability score (CRPS) loss. While both approaches have demonstrated strong predictive accuracy, the reliability of their uncertainties has not been systematically assessed. We address this gap by developing a framework to evaluate both approaches across diverse 2D spatiotemporal physical systems, under matched model size and computational budget. We assess the reliability of probabilistic emulation by inspecting the empirical coverage of predictive intervals, while also considering accuracy and computational efficiency metrics. CRPS-trained ensembles typically achieve more reliable uncertainties on both single-step prediction and autoregressive rollouts, demonstrating better coverage than the standard alternative of training generative models in a latent space. Moreover, the CRPS approach offers significantly faster inference. When generative models are trained in ambient rather than a compressed latent space, which is often infeasible for high-dimensional problems, they exhibit comparable coverage to CRPS-trained ensembles, though with substantially larger inference latency. In contrast, when CRPS-trained ensembles are trained in latent space they do not show a marked degradation in coverage with respect to ambient space. Both generative models and CRPS-trained ensembles demonstrate good predictive accuracy. To facilitate future research and application, we release AutoCast, a modular framework implementing both generative models and CRPS-trained ensembles, alongside AutoSim, a flexible dataset generation package for rapid prototyping.

Sam F. Greenbury, Radka Jersakova, Paolo Conti +4

The Alan Turing Institute · Autodesk Research · PhysicsX +3

Surrogate Modeling Probabilistic Forecasting Generative Modeling Spatiotemporal Forecasting Uncertainty Calibration

Jun 10, 2026cs.LG

PCA-Enhanced Adaptive NVAR Framework for High-Resolution Sea Surface Temperature Forecasting in the East Sea

Accurate forecasting of sea surface temperature (SST) in regional seas such as the East Sea is crucial for monitoring marine ecosystems, assessing climate risks, managing fisheries, and conducting naval operations. Traditional numerical ocean models provide reliable predictions but are computationally expensive and often unsuitable for real-time forecasting. Many deep learning methods also struggle with high-dimensional spatiotemporal ocean data and experience error accumulation over longer forecasting periods. This study builds on our previously proposed Adaptive Next-Generation Reservoir Computing (Adaptive NVAR) framework, initially introduced and tested on synthetic dynamical systems, and extends it to ocean forecasting. We present a reduced-order forecasting framework that combines Singular Value Decomposition (SVD) with Adaptive NVAR to predict SST dynamics in the East Sea. SST fields are compressed into a low-dimensional representation using SVD, which extracts dominant modes of ocean variability. Adaptive NVAR models the temporal evolution of these latent states, and the predicted states are reconstructed into SST forecasts. We evaluate the framework using regional ocean datasets and compare it with the standard NG-RC/NVAR. Results show that Adaptive NVAR consistently achieves lower forecasting errors across multiple prediction horizons. In addition, SVD reduces computational complexity, resulting in a fast and scalable framework suitable for real-time ocean forecasting.

Sherkhon Azimov, Susana López-Moreno, Eric Dolores-Cuenca +2

Department of Mathematics, Pusan National University, Republic of Korea · Humanoid Olfactory Display Center, Pusan National University, Republic of Korea · Industrial Mathematics Center, Pusan National University, Republic of Korea +3

Neural Surrogate Modeling Reservoir Computing Spatiotemporal Forecasting

Jun 10, 2026cs.CE

Neural-Parameterized Cellular Automata for Wildfire Spread

Traditional wildfire models rely on rigid, low-dimensional parameters and static fuel maps, frequently underpredicting fire spread. To address this weakness, we introduce a hybrid deep-learning parameterized Probabilistic Cellular Automata (CA) framework implemented in JAX. Our approach employs a Multi-Scale Convolutional Neural Network to dynamically generate spatially varying parameters that govern fire-spread probability, wind alignment, and slope influence. This hybrid design captures complex, nonlinear environmental interactions while preserving the physical interpretability of the underlying three-state CA. The JAX implementation enables hardware acceleration and gradient-based parameter calibration. Evaluated on six large-scale wildfires in the western United States, the model maintains IoU > 0.6 over 72-hour forecast horizons after a 10-day data assimilation window during which the model is fitted incrementally to observed perimeters; the resulting forecast is a conditional projection of fire growth under the suppression regime already ncoded in those observations.

Maksym Zhenirovskyy, Ion Matei, Rohit Vuppala +2

Fujitsu Research of America, 4655 Great America Pkwy, Santa Clara, 95124, CA, USA

Neural Cellular Automata Cellular Automata Wildfire Forecasting Spatiotemporal Forecasting

Jun 9, 2026cs.LG

COGENT: Continuous Graph Emulators with Neural Ordinary Differential Equations for Long-Term Physical Forecasting

In this work, we present COGENT, a continuous graph emulator with Neural Ordinary Differential Equations for long-term physical forecasting on irregular geospatial meshes. COGENT encodes a finite history of system states and associated forcing fields and external forcings with a graph-based history encoder, producing node-wise context vectors that capture both local spatial interactions and temporal evolution. These context vectors initialize and condition a latent Neural Ordinary Differential Equation whose dynamics are driven by interpolated future forcings and explicit relative rollout time. By modeling the forecast trajectory as a continuous latent dynamical system, COGENT can generate predictions at arbitrary future times rather than being restricted to a fixed temporal discretization. A residual decoder maps the resulting latent trajectories back to future physical states, enabling direct multi-step forecasting without repeatedly feeding predicted states back into the model. This formulation combines graph-based spatial representation, history-conditioned latent dynamics, and continuous-time rollout in a unified framework for mesh-based physical simulation emulation. In order to stabilize training with long-horizon supervision, we also propose effective rollout-horizon sampling and a progressive rollout-horizon scheduling strategy. We evaluate COGENT on transient ice-sheet simulations generated by the Ice-sheet and Sea-level System Model, demonstrating improved long-range stability over autoregressive graph baselines. These results suggest that continuous graph Neural ODEs provide a promising methodology for scalable physical forecasting on irregular geospatial meshes, particularly in applications that require stable long-horizon predictions and the ability to query system states at arbitrary times.

Zesheng Liu, Maryam Rahnemoonfar

Lehigh University · Bethlehem, Pennsylvania, USA

Neural Surrogate Modeling Long-Term Time Series Forecasting Spatiotemporal Forecasting Neural ODEs Spatiotemporal GNNs

Jun 9, 2026cs.LG

MoE Enhanced Federated Learning for Spatiotemporal Prediction

Traffic prediction is fundamental to intelligent transportation systems and urban computing, yet many cities continue to suffer from traffic data scarcity due to limited sensor deployment and uneven urban development. Cross-city knowledge transfer has thus attracted increasing attention, enabling data-rich cities to assist data-scarce ones. However, centralized approaches raise privacy concerns, while existing federated methods struggle with pronounced spatiotemporal heterogeneity across cities. To address these challenges, we propose MoE-FedTP, a personalized federated cross-city spatiotemporal prediction framework based on lightweight Mixture-of-Experts (MoE) networks. MoE-FedTP first employs spatiotemporal neural networks to extract features from both source and target cities, then introduces a set of expert networks derived from different source cities through partial parameter sharing. A gating mechanism dynamically fuses the experts to capture diverse traffic dynamics, achieving fine-grained modeling of urban heterogeneity while preserving privacy. Experiments on four real-world traffic datasets show that MoE-FedTP consistently outperforms state-of-the-art cross-city and federated learning baselines, demonstrating its effectiveness in enhancing prediction accuracy for data-scarce cities.

Zhehao Dai, Xiao Han, Zhaolin Deng +4

Zhejiang University of Technology, Zhejiang Key Laboratory of Visual Information Intelligent Processing, Hangzhou · Jilin University, Jilin · City University of Hong Kong, Hong Kong SAR China

Intelligent Transportation Systems Mixture of Experts Cross-Domain Transfer Learning Spatiotemporal Forecasting Federated Learning Heterogeneous Federated Learning

Jun 8, 2026cs.AI

From Coarse to Fine: Managing Temporal Granularity in Spatio-Temporal Data for Fine-Grained Traffic Prediction

Efficient acquisition, storage, and utilization of traffic data are critical challenges in spatio-temporal data management. Most traffic data systems collect and store observations at fixed, coarse-grained temporal intervals to reduce storage and computation costs. However, such coarse-grained data severely limits downstream applications that require predictions at a finer temporal granularity. Collecting and maintaining fine-grained traffic data across all locations and time periods would impose a substantial burden on database storage and preprocessing pipelines. To address this temporal granularity mismatch, we formulate a novel problem: predicting fine-grained future traffic using coarse-grained sampled data. We propose the Spatial-Temporal Refinement Predictor (STRP), a granularity-aware framework for spatio-temporal data systems. STRP integrates two components: Tree Convolution for efficient and interpretable spatial dependency modeling, and Inverse Dilated Convolution for progressive temporal extrapolation. STRP supports two practical prediction settings: window-based and duration-based, to handle different forms of granularity mismatch. Experiments on six benchmark datasets show that STRP significantly outperforms state-of-the-art baselines in both accuracy and efficiency. Our work offers a practical and interpretable approach to managing granularity mismatches in spatio-temporal traffic data systems.

Shuhao Li, Weidong Yang, Yue Cui +4

College of Computer Science and Artificial Intelligence, Fudan University, Shanghai 200082, China · Tongyi Lab, Alibaba Group, Cloud Valley, NO.1008 Dengcai Street, Xihu District, Hangzhou 310020, China · The Hong Kong University of Science and Technology, Hong Kong SAR 999077, China +1

Traffic Flow Estimation Spatiotemporal Forecasting Traffic Forecasting Multiscale Time-Series Modeling

Jun 7, 2026cs.LG

Physics-Guided Dual Decoding and Spectral Supervision for Global 3D Hydrometeor Prediction

While global data-driven models excel at predicting continuous atmospheric variables, three-dimensional hydrometeor forecasting remains challenging due to the zero-inflated, long-tailed distributions of these variables. Standard deep learning optimization often yields overly smooth forecasts, attenuating extreme events and spatial textures. We propose PredHydro-Net, a physics-guided dual-decoding framework that mitigates this smoothing. To resolve multi-variable optimization conflicts, it employs a decoupled architecture where macroscopic thermodynamic and dynamic fields unidirectionally modulate hydrometeor generation. By integrating wavelet-based frequency decoupling, spectral amplitude matching, and adversarial training, the model achieves a favorable trade-off between quantitative accuracy and spatial fidelity. In a 72-h global evaluation, PredHydro-Net outperforms both spatiotemporal deep learning baselines (Earthformer and PredRNNv2) and the operational Global Forecast System (GFS) in extreme-event detection and spectral representation. Furthermore, it demonstrates strong climatological consistency with Global Precipitation Measurement (GPM) satellite retrievals. The model reasonably reproduces the three-dimensional cloud structures in extreme weather events, such as Hurricane Ian. Feature attribution confirms its dependence on physical precursors such as relative humidity and wind convergence, offering a robust, physics-informed approach to long-tailed atmospheric prediction.

Dandan Chen, Yaqiang Wang

Physics-Informed ML Spatiotemporal Forecasting Weather Forecasting

Jun 6, 2026physics.ao-ph

KFTD: Koopman-Fourier Time-Differentiable Network for Continuous Ocean Spatiotemporal Forecasting

Accurate oceanic forecasting is critical for climate monitoring and disaster early warning. However, ocean spatiotemporal forecasting encounters the double challenges of modeling complex dynamical systems and ensuring computational efficiency. We present Koopman Fourier Time-Differentiable (KFTD) Network, a time continuous twostage paradigm that decouples interpolation from prediction to achieve efficient and scalable spatiotemporal modeling. We map complex nonlinear dynamics into the Koopman linear space and exploit Fourier analysis to enable continuous time interpolation at arbitrary sub-steps. A lightweight residual network consumes the high fidelity intermediate states to yield the final forecast. Unlike diffusion models, KFTD eliminates multi step noise sampling and directly evolves the system in continuous time, yielding a 4 computational speedup. We further introduce a DPP Loss that supports arbitrary PDE constraints in an endtoend manner, breaking the physical consistency bottleneck of pure data-driven approaches. Empirical results on four ocean datasets confirm that our continuous time framework reduces MSE by an average of 5.6% (up to 12.7% for SST) and improves efficiency over MCVD by 76.25%.

Qinghui Chen, Zekai Zhang, Hailong Liu +2

Shandong University School of Control Science and Engineering Jinan, China · Laoshan Laboratory Qingdao, China · Chinese Academy of sciences Institute of Atmospheric Physics Beijing, China +1

Koopman Operator Learning Physics-Informed ML Spatiotemporal Forecasting

Jun 5, 2026math.ST

A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space

We study the minimax rate of estimating a future value

μ_{t_n+h}

of a curve

t\mapstoμ_t

in the

2

-Wasserstein space

\mathcal{P}_2(\mathbb{R}^d)

from finitely many noisy snapshots of its past, under an adiabatic bound

\|\nabla_t^k v\|\le\varepsilon

on the

k

-th covariant derivative of the velocity field. Our central result is a unified temporal-spatial minimax lower bound: over regular, locally transport-rich subclasses, every estimator incurs

W_2

-risk with

M

-exponent

γ_d(k+1)/(k+1+γ_d)

,

γ_d=\min(1/d,1/2)

(

M

the total sample size). It follows from a temporal-to-spatial reduction: the smoothness budget defines a reachable

W_2

-ball into which a transport packing is embedded along the time axis, and the information of the entire snapshot experiment is controlled by a Fano argument -- the spatial packing is classical, but its smoothness-admissible temporal embedding and the full-window analysis are new. The bound interpolates a dimension-free extrapolation floor of order

\varepsilon h^{k+1}

-- the irreducible cost of an unobserved future, present even with the exact past -- and the spatial estimation curse

M^{-γ_d}

, recovering the static distribution-estimation rate as

k\to\infty

. We state the lower bound in a design-dependent form -- with a design-weighted effective sample size -- valid for arbitrary observation times, and obtain the closed-form exponent in the dense (equispaced) regime. The matching upper bound is established at

k=0

(rate

M^{-1/(d+1)}

,

d\ge3

) and, in a translation submodel, for all

k

; for

k\ge1

a covariant estimator attains the rate conditionally on two estimates (a comparison-geometry bias bound and an optimal-transport map-estimation rate), leaving the unconditional general-

k

upper bound as an open problem. Numerical experiments on synthetic curved and flat families corroborate the predicted exponents.

Munsik Kim

Minimax Estimation Spatiotemporal Forecasting Optimal Transport Wasserstein Distance

Jun 5, 2026cs.LG

Hierarchical Forecast Reconciliation for Urban Rail Transit Demand Prediction under Operational Disruptions

Accurate and coherent passenger demand forecasting is essential for Urban Rail Transit (URT) operations. Passenger demand has a hierarchical structure in which origin-destination (OD) flows aggregate to station-level inflows and outflows through conservation constraints. In practice, station-level and OD-level forecasts are often generated independently, producing incoherent predictions that violate these constraints and introduce inconsistencies into operational decision-making. Such issues become more severe during disruptions, when forecasting reliability is most critical. This paper presents the first hierarchical forecast reconciliation framework for joint station-level and OD-level URT demand prediction. A neural Fully Connected Reconciler (FCR) learns a non-linear mapping from incoherent base forecasts to coherent hierarchical predictions while guaranteeing exact structural consistency by construction. The method is benchmarked against OLS, WLS, and Minimum Trace (MinT) variants using Rejsekort smart-card data from the Copenhagen S-train network under one-step, multi-step, and disruption forecasting scenarios. Results show that reconciliation consistently improves OD forecasting accuracy while ensuring hierarchical coherence. Under normal conditions, FCR performs competitively with MinT-based methods. An oracle analysis indicates that perfect station-level forecasts could reduce OD prediction error by up to 34 percent, highlighting the value of improved base forecasts. Under severe disruptions, FCR outperforms classical methods, reducing OD forecasting error by up to 17.45 percent in multi-step destination-side delay scenarios. These findings establish hierarchical reconciliation as an effective mechanism for improving forecast robustness, with the largest benefits occurring under the most challenging operating conditions.

Dang Viet Anh Nguyen, Alma Fazlagic, Kristine Pryds Loft +1

Department of Technology, Management, and Economics, Technical University of Denmark (DTU), 2800 Kongens Lyngby, Denmark

Time Series Forecasting Spatiotemporal Forecasting

Jun 5, 2026cs.LG

DSFNet: Learning Dual-Domain Spectral Operators for Multi-Modality Spatio-Temporal Forecasting in Urban Transportation Systems

Multi-Modality Spatio-Temporal Forecasting (MoSTF) extends traditional spatio-temporal forecasting by incorporating diverse traffic modalities. Despite significant recent strides in spatio-temporal modeling, existing approaches often fail to explicitly model the coupling relationships between different modality variables. Accurate MoSTF is challenging, as it requires modeling (1) temporal dynamic heterogeneity under exogenous influences and (2) heterogeneous spatial dependencies alongside complex cross-variable couplings. To address these challenges, we propose the Dual-Domain Spectral Filtering Network (DSFNet). Our framework employs dual-domain spectral filtering to capture heterogeneous spatial patterns and explicitly model the relationships between variables. Unlike graph-based message passing or dense attention over node-modality pairs, DSFNet factorizes space-modality interactions into feature-domain and spatial-domain spectral operators, enabling scalable modeling of nonlocal dependencies and cross-modality couplings. Furthermore, we introduce an external gating mechanism to adaptively regulate temporal dynamics under external influences. We validate our method through extensive experiments on five representative real-world traffic datasets. Compared with the second-best baselines, DSFNet reduces MAE by 3.21%-10.16% across these datasets. The results demonstrate that DSFNet significantly outperforms existing state-of-the-art baselines in accuracy while exhibiting efficiency and robustness.

Yongchao Li, Yang Li, Zhuoxuan Li +4

School of Transportation, Southeast University, Nanjing 211189, China · Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Nanjing 211189, China · Department of Data Science, City University of Hong Kong, Hong Kong 999077, China +6

Intelligent Transportation Systems Time Series Forecasting Spatiotemporal Forecasting Multimodal Fusion

Jun 5, 2026cs.LG

Vessel Traffic Flow Prediction on Sparse Data via Spatio-Temporal Graph Neural Networks with a Learnable Tweedie Head

Accurate vessel traffic flow prediction is crucial for smart port operations and navigational safety. However, maritime traffic flow data are often highly sparse with intermittent bursts, making robust forecasting challenging. Under such conditions, conventional spatio-temporal graph neural networks (ST-GNNs) can degrade toward conservative near-zero predictions and fail to capture non-zero activity. Although zero-inflated negative binomial (ZINB) models partially address excess zeros, their two-part formulation can still remain conservative around abrupt transitions. To address these issues, we propose a model-agnostic learnable Tweedie head that can be attached as a plug-and-play output module to arbitrary ST-GNN backbones. Instead of likelihood-based Tweedie training, which typically requires surrogate objectives, our approach optimizes the closed-form Tweedie unit deviance and predicts the mean for point forecasting while learning a node-level variance power to capture heterogeneous variability across port areas. Experiments on a maritime traffic graph constructed from real-world AIS data in the Port of Los Angeles and Long Beach show that the proposed head consistently improves RMSE across multiple ST-GNN backbones, especially on non-zero events, leading to more reliable forecasts for practical maritime traffic control.

Kyeongjun Lee, Heeyoung Kim

Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea.

Spatiotemporal Forecasting Spatiotemporal GNNs

Jun 4, 2026cs.LG

Learned Response-Field Inertia Operator for HEC-RAS 2D Water-Surface Elevation Prediction

This article presents a cross-dataset evaluation of learned native-cell surrogate models for solver-consistent water-surface elevation (WSE) prediction in HEC-RAS 2D. To avoid raster remapping error and information-access confounding, surrogates are evaluated directly on the original nonuniform computational cells under an explicit policy that separates static project inputs, current hydraulic state, project-input forcing, calibration-derived quantities, and future solver-output targets. We introduce the Learned Response-Field Inertia Operator (LRFIO), a no-forcing, increment-based learned surrogate that calibrates an inertial response operator from solved HEC-RAS trajectories and deploys the retained operator through closed-form native-cell rollout. LRFIO evaluates a base-case-first response hierarchy consisting of persistence, global calibrated inertia, and segmented response-field inertia. Segmentation, residual correction, and neuralized inertia are treated as learnable modeling choices, with added complexity retained only when validation evidence justifies its cost. Evaluated across four diverse HEC-RAS 2D benchmarks, LRFIO retains different response structures for different domains, demonstrating adaptive learned complexity. The selector audit shows controlled complexity with a maximum validation regret of 4.30%. During deployment, retained rollout times range from 0.003 s to 0.242 s, and the Beaver Bayou measured-solve comparison gives an estimated 2.75 x 10^4 horizon-normalized speedup over HEC-RAS. These results indicate that the current native-cell increment is a strong solver-conditioned predictive scaffold and that added response-field, neural, or spatial complexity should be retained only when empirically justified.

Edward Holmberg, Elias Ioup, Md Meftahul Ferdaus +2

Canizaro Livingston Gulf States Center for Environmental Informatics, Department of Computer Science, The University of New Orleans, New Orleans, LA 70148, USA · Center for Geospatial Sciences, Naval Research Laboratory, Mississippi, USA · Ocean Sciences Division, Naval Research Laboratory, Mississippi, USA

Neural Surrogate Modeling PDE Surrogate Modeling Spatiotemporal Forecasting Computational Fluid Dynamics