Breaking the Discretization Barrier of Continuous Physics Simulation Learning

2025-09-22

AI Summary

Modeling continuous spatiotemporal physical dynamics under sparse, unstructured, and partially observed conditions remains challenging, as existing methods rely on fixed spatial grids and discrete time stepping. This paper proposes CoPS—a novel framework for fully mesh-free and step-size-agnostic continuous spatiotemporal modeling. CoPS employs multi-scale graph ordinary differential equations to model temporal evolution, integrates a Markovian neural self-correction module for robustness against observation noise and sparsity, and leverages multiplicative filtering networks coupled with geometry-aware graph message passing to enable continuous spatial feature mapping. Evaluated on complex physical fields—including turbulence, reaction-diffusion systems, and elastic deformation—CoPS consistently outperforms state-of-the-art methods, achieving superior long-term predictive accuracy and high-fidelity field reconstruction from sparse observations. These results demonstrate CoPS’s fundamental advantages in learning continuous spatiotemporal dynamics.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

The modeling of complicated time-evolving physical dynamics from partial observations is a long-standing challenge. Particularly, observations can be sparsely distributed in a seemingly random or unstructured manner, making it difficult to capture highly nonlinear features in a variety of scientific and engineering problems. However, existing data-driven approaches are often constrained by fixed spatial and temporal discretization. While some researchers attempt to achieve spatio-temporal continuity by designing novel strategies, they either overly rely on traditional numerical methods or fail to truly overcome the limitations imposed by discretization. To address these, we propose CoPS, a purely data-driven methods, to effectively model continuous physics simulation from partial observations. Specifically, we employ multiplicative filter network to fuse and encode spatial information with the corresponding observations. Then we customize geometric grids and use message-passing mechanism to map features from original spatial domain to the customized grids. Subsequently, CoPS models continuous-time dynamics by designing multi-scale graph ODEs, while introducing a Markov-based neural auto-correction module to assist and constrain the continuous extrapolations. Comprehensive experiments demonstrate that CoPS advances the state-of-the-art methods in space-time continuous modeling across various scenarios.

Problem

• Modeling continuous physics from sparse partial observations
• Overcoming fixed discretization limits in simulation learning
• Capturing nonlinear spatio-temporal dynamics in scientific problems

Innovation

• Multiplicative filter network encodes spatial observations
• Message-passing maps features to customized geometric grids
• Multi-scale graph ODEs with neural auto-correction module