Physics-augmented Multi-task Gaussian Process for Modeling Spatiotemporal Dynamics

• URL: http://arxiv.org/abs/2510.13601v1
• Date: Wed, 15 Oct 2025 14:33:10 GMT
• Title: Physics-augmented Multi-task Gaussian Process for Modeling Spatiotemporal Dynamics
• Authors: Xizhuo Zhang, Bing Yao,
• Abstract summary: This paper presents a physics-augmented multi-task Gaussian Process (P-M-GP) framework for dynamic systems.<n>We incorporate governing physical laws through a physics-based regularization scheme, thereby constraining predictions to be consistent with governing dynamical principles.<n> Numerical experiments demonstrate that our method significantly improves prediction accuracy over existing methods.
• Score: 4.282746516699566
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent advances in sensing and imaging technologies have enabled the collection of high-dimensional spatiotemporal data across complex geometric domains. However, effective modeling of such data remains challenging due to irregular spatial structures, rapid temporal dynamics, and the need to jointly predict multiple interrelated physical variables. This paper presents a physics-augmented multi-task Gaussian Process (P-M-GP) framework tailored for spatiotemporal dynamic systems. Specifically, we develop a geometry-aware, multi-task Gaussian Process (M-GP) model to effectively capture intrinsic spatiotemporal structure and inter-task dependencies. To further enhance the model fidelity and robustness, we incorporate governing physical laws through a physics-based regularization scheme, thereby constraining predictions to be consistent with governing dynamical principles. We validate the proposed P-M-GP framework on a 3D cardiac electrodynamics modeling task. Numerical experiments demonstrate that our method significantly improves prediction accuracy over existing methods by effectively incorporating domain-specific physical constraints and geometric prior.

Related papers

• i-PhysGaussian: Implicit Physical Simulation for 3D Gaussian Splatting [60.46736489360263]
  i-PhysGaussian is a framework that couples 3D Gaussian Splatting (3DGS) with an implicit Material Point Method (MPM) integrator.<n>Unlike explicit methods, our solution obtains an end-of-step state by minimizing a momentum-balance residual.<n>Results demonstrate that i-PhysGaussian maintains stability at up to 20x larger time steps than explicit baselines.
  arXiv  Detail & Related papers  (2026-02-19T06:38:35Z)
• Scalable Spatio-Temporal SE(3) Diffusion for Long-Horizon Protein Dynamics [51.85385061275941]
  Molecular dynamics (MD) simulations remain the gold standard for studying protein dynamics.<n>Recent generative models have shown promise in accelerating simulations, yet they struggle with long-horizon generation.<n>We present STAR-MD, a scalable diffusion model that generates physically plausible protein trajectories over micro-scale timescales.
  arXiv  Detail & Related papers  (2026-02-02T14:13:28Z)
• Physics-Inspired All-Pair Interaction Learning for 3D Dynamics Modeling [28.23126775948343]
  We propose PAINET, a principled SE(3)-equivariant neural architecture for learning all-pair interactions in multi-body systems.<n>We show that PAINET consistently outperforms recently proposed models, yielding 4.7% to 41.5% error reductions in 3D dynamics prediction with comparable computation costs in terms of time and memory.
  arXiv  Detail & Related papers  (2025-10-05T14:48:26Z)
• Geometry-aware Active Learning of Spatiotemporal Dynamic Systems [4.251030047034566]
  This paper proposes a geometry-aware active learning framework for modeling dynamic systems.<n>We develop an adaptive active learning strategy to strategically identify spatial locations for data collection and further maximize the prediction accuracy.
  arXiv  Detail & Related papers  (2025-04-26T19:56:38Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems.<n>Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics.<n>Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Geometric Trajectory Diffusion Models [58.853975433383326]
  Generative models have shown great promise in generating 3D geometric systems. Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
  arXiv  Detail & Related papers  (2024-10-16T20:36:41Z)
• PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems [31.006807854698376]
  We propose a new graph learning approach, namely, Physics-encoded Message Passing Graph Network (PhyMPGN)<n>We incorporate a GNN into a numerical integrator to approximate the temporal marching of partialtemporal dynamics for a given PDE system.<n>PhyMPGN is capable of accurately predicting various types of operatortemporal dynamics on coarse unstructured meshes.
  arXiv  Detail & Related papers  (2024-10-02T08:54:18Z)
• Equivariant Graph Neural Operator for Modeling 3D Dynamics [148.98826858078556]
  We propose Equivariant Graph Neural Operator (EGNO) to directly models dynamics as trajectories instead of just next-step prediction. EGNO explicitly learns the temporal evolution of 3D dynamics where we formulate the dynamics as a function over time and learn neural operators to approximate it. Comprehensive experiments in multiple domains, including particle simulations, human motion capture, and molecular dynamics, demonstrate the significantly superior performance of EGNO against existing methods.
  arXiv  Detail & Related papers  (2024-01-19T21:50:32Z)
• SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases [66.61789780666727]
  We show how the second-order continuity can be incorporated into GNNs while maintaining the equivariant property. We also offer theoretical insights into SEGNO, highlighting that it can learn a unique trajectory between adjacent states. Our model yields a significant improvement over the state-of-the-art baselines.
  arXiv  Detail & Related papers  (2023-08-25T07:15:58Z)
• Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling [86.9726984929758]
  We focus on the integration of incomplete physics models into deep generative models. We propose a VAE architecture in which a part of the latent space is grounded by physics. We demonstrate generative performance improvements over a set of synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2021-02-25T20:28:52Z)
• Prediction with Approximated Gaussian Process Dynamical Models [7.678864239473703]
  We present approximated GPDMs which are Markov and analyze their control theoretical properties. The outcomes are illustrated with numerical examples that show the power of the approximated models.
  arXiv  Detail & Related papers  (2020-06-25T16:51:17Z)

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.