Physically consistent and uncertainty-aware learning of spatiotemporal dynamics

TL;DR

This paper introduces a physics-informed neural operator framework that enforces physical laws and quantifies uncertainties, significantly improving long-term spatiotemporal forecasting accuracy across various systems.

Contribution

It presents a novel physics-consistent neural operator and an enhanced diffusion model that jointly ensure physical constraints and uncertainty quantification in spatiotemporal predictions.

Findings

Achieves high-fidelity, physically consistent forecasts across diverse systems.

Effectively quantifies and reduces uncertainties in long-term predictions.

Outperforms existing methods in accuracy and physical adherence.

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.