Physically consistent and uncertainty-aware learning of spatiotemporal dynamics

2025-10-23

AI Summary

Accurately forecasting the long-term evolution of complex spatiotemporal dynamics—such as turbulence, flood propagation, and atmospheric flows—faces two fundamental challenges: (1) prevalent machine learning methods often violate physical conservation laws, and (2) they lack reliable uncertainty quantification. To address these, we propose the Physics-Consistent Neural Operator (PCNO) and its diffusion-enhanced extension, DiffPCNO. PCNO is the first neural operator framework to explicitly embed hard physical constraints—namely mass and momentum conservation—via a differentiable, Fourier-domain physical projection layer. DiffPCNO further integrates a consistency-model-based diffusion mechanism to enable physics-aware uncertainty estimation. Evaluated on multiscale real-world systems, our approach achieves significant improvements in long-horizon prediction accuracy and uncertainty calibration, while ensuring both high fidelity and reliability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Computer Vision: Diffusion Models for Vision

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent uncertainties in spatiotemporal predictions. To address these challenges, we introduce a physics-consistent neural operator (PCNO) that enforces physical constraints by projecting surrogate model outputs onto function spaces satisfying predefined laws. A physics-consistent projection layer within PCNO efficiently computes mass and momentum conservation in Fourier space. Building upon deterministic predictions, we further propose a diffusion model-enhanced PCNO (DiffPCNO), which leverages a consistency model to quantify and mitigate uncertainties, thereby improving the accuracy and reliability of forecasts. PCNO and DiffPCNO achieve high-fidelity spatiotemporal predictions while preserving physical consistency and uncertainty across diverse systems and spatial resolutions, ranging from turbulent flow modeling to real-world flood/atmospheric forecasting. Our two-stage framework provides a robust and versatile approach for accurate, physically grounded, and uncertainty-aware spatiotemporal forecasting.

Problem

• Enforcing physical laws in spatiotemporal dynamics learning
• Quantifying inherent uncertainties in long-term spatiotemporal predictions
• Achieving high-fidelity forecasts across diverse scientific systems

Innovation

• Physics-consistent neural operator enforces physical constraints
• Diffusion model-enhanced framework quantifies prediction uncertainties
• Two-stage approach preserves physical consistency across resolutions