Nonlocal Bayesian Modeling of Continuous Spatio-Temporal Dynamics

• URL: http://arxiv.org/abs/2606.14313v1
• Date: Fri, 12 Jun 2026 09:51:07 GMT
• Title: Nonlocal Bayesian Modeling of Continuous Spatio-Temporal Dynamics
• Abstract summary: We propose a principled NonLocal S-NL model (BST) for continuous-temporal fields that learns nonlocal coupling while retaining tractable inference.<n> NLBST represents the latent field via a coordinate-based spatial basis expansion and models the sequential process with a continuous-time ODE.<n>A linear-Gssianau observation model enables Kalmanssian-style sequential sparse updates under missing and irregular observations, while the spatial basis representation enables inductive prediction at unmeasured locations without retraining.
• Score: 9.926231893220061
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• DyG$^2$T: Modeling Object Dynamics with 3D Gaussian Temporal-Spatial Particle Graph Transformer [86.4618122245946]
  DyG$2$T is a dynamics modeling framework that infers object motion trajectories by spatially completing and temporally discriminating Key Point representations.<n>Experiments on both synthetic and real-world datasets demonstrate that DyG$2$T achieves accurate dynamics modeling and reasoning.
  arXiv  Detail & Related papers  (2026-08-19T03:44:28Z)
• Incremental Aggregation on the Grassmannian for Asynchronous Eigenspace Computation [37.26483427088676]
  We study asynchronous optimization for finite-sum eigenspace computation in heterogeneous distributed systems.<n>We propose a Grassmannian incremental aggregation method that refreshes only arriving components and reuses cached gradients.<n> Experiments on serial and distributed PCA demonstrate improved sample efficiency and wall-clock convergence over representative baselines.
  arXiv  Detail & Related papers  (2026-08-05T03:21:38Z)
• Learning Spatio-Temporal Foundation Models from Pure Synthetic Data [85.23980441738811]
  NeoST is a scalable synthetic-training corpus to real-world bias, a latent-space reasoning architecture that generates and iteratively refines multiple future trajectories, and latent-space objectives that emphasize structural dynamics and enable inference-time correction under distribution shifts.<n>Extensive experiments across diverse real-world benchmarks show that NeoST consistently outperforms existing STFMs in diverse real-worldtemporal systems.
  arXiv  Detail & Related papers  (2026-06-27T02:56:46Z)
• Not All Points Are Equal: Uncertainty-Aware 4D LiDAR Scene Synthesis [63.07333625429548]
  We present U4D, a new framework that explicitly leverages spatial uncertainty to guide LiDAR scene generation.<n>Experiments on nuScenes and Semantic KITTI demonstrate state-of-the-art scene fidelity, temporal consistency, and downstream performance.
  arXiv  Detail & Related papers  (2026-06-01T17:24:14Z)
• Towards Physically Consistent 4D Scene Reconstruction for Closed-loop Autonomous Driving Simulation [19.055975606481635]
  High-fidelity street scene reconstruction is pivotal for end-to-end autonomous driving simulation.<n>Existing 3DGS methods and their 4D extensions fail to simultaneously achieve both.<n>We propose Orthogonal Projected Gradient (OPG) to restore spatial identifiability.
  arXiv  Detail & Related papers  (2026-05-20T11:09:53Z)
• Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency [12.266189649117003]
  We replace local supervision with a global structural constraint.<n>We train a time-conditioned secant velocity field whose deviation from this property serves two purposes.<n>As a training regularizer, it confines the hypothesis space to flows that compose consistently across temporal scales.
  arXiv  Detail & Related papers  (2026-05-08T20:24:32Z)
• A Continuous-Time Ensemble Kalman-Bucy Smoother for Causal Inference and Model Discovery [6.75658113372928]
  This paper introduces an ensemble Kalman-Bucy smoother (EnKBS) for continuous-time DA of nonlinear dynamical systems.<n>The skill of the EnKBS is demonstrated in various important scientific problems.
  arXiv  Detail & Related papers  (2026-04-28T02:58:42Z)
• Beyond Attention: True Adaptive World Models via Spherical Kernel Operator [0.0]
  We introduce Spherical Kernel, a framework that replaces standard attention.<n>SKO mathematically decouples the true environmental transition dynamics from the biased observation frequency of the agent.<n> Empirical evaluations confirm that SKO significantly accelerates convergence and outperforms standard attention baselines in autoregressive language modeling.
  arXiv  Detail & Related papers  (2026-02-25T21:51:34Z)
• KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra [65.11254608352982]
  We introduce a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators.<n>By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation.
  arXiv  Detail & Related papers  (2026-02-15T06:32:23Z)
• Forecasting as Rendering: A 2D Gaussian Splatting Framework for Time Series Forecasting [79.37674445572462]
  Time series forecasting (TSF) remains a challenging problem due to the intricate entanglement of intraperiod-fluctuations and interperiod-trends.<n>Treating reshaped tensors as static images results in a topological mismatch.<n> relying on uniform fixed-size representations allocates modeling capacity inefficiently.<n>TimeGS is a novel framework that fundamentally shifts the forecasting paradigm from regression to 2D generative rendering.
  arXiv  Detail & Related papers  (2026-02-10T14:13:36Z)
• Generative System Dynamics in Recurrent Neural Networks [56.958984970518564]
  We investigate the continuous time dynamics of Recurrent Neural Networks (RNNs)<n>We show that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations.<n> Numerical simulations showcase how nonlinear activation functions not only maintain limit cycles, but also enhance the numerical stability of the system integration process.
  arXiv  Detail & Related papers  (2025-04-16T10:39:43Z)
• Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reduction [49.66486092259376]
  The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift. Recent works have shown that MFLD globally minimizes an entropy-regularized convex functional in the space of measures. We provide a framework to prove a uniform-in-time propagation of chaos for MFLD that takes into account the errors due to finite-particle approximation, time-discretization, and gradient approximation.
  arXiv  Detail & Related papers  (2023-06-12T16:28:11Z)
• STONet: A Neural-Operator-Driven Spatio-temporal Network [38.5696882090282]
  Graph-based graph-temporal neural networks are effective to model spatial dependency among discrete points sampled irregularly. We propose atemporal framework based on neural operators for PDEs, which learn the mechanisms governing the dynamics of spatially-continuous physical quantities. Experiments show our model's performance on forecasting spatially-continuous physic quantities, and its superior to unseen spatial points and ability to handle temporally-irregular data.
  arXiv  Detail & Related papers  (2022-04-18T17:20:12Z)
• The Connection between Discrete- and Continuous-Time Descriptions of Gaussian Continuous Processes [60.35125735474386]
  We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining' This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
  arXiv  Detail & Related papers  (2021-01-16T17:11:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.