Physically consistent and uncertainty-aware learning of spatiotemporal dynamics
This work addresses the problem of unreliable spatiotemporal predictions in scientific and engineering domains by ensuring physical consistency and uncertainty awareness, representing a novel method for a known bottleneck.
The paper tackles the challenge of accurate long-term forecasting of spatiotemporal dynamics by introducing a physics-consistent neural operator (PCNO) and its diffusion-enhanced version (DiffPCNO) to enforce physical laws and quantify uncertainties, achieving high-fidelity predictions across diverse systems like turbulent flow and flood forecasting.
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.