PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems

TL;DR

PeSANet is a novel neural network that combines physics-based constraints and spectral attention to improve the simulation and forecasting of complex PDE-governed systems, especially with limited data.

Contribution

The paper introduces PeSANet, integrating physics-encoded local operators and spectral global dependencies, advancing modeling of complex systems with scarce data and incomplete physical knowledge.

Findings

Outperforms existing methods in accuracy

Effective in long-term forecasting

Handles limited data and incomplete physics

Abstract

Accurately modeling and forecasting complex systems governed by partial differential equations (PDEs) is crucial in various scientific and engineering domains. However, traditional numerical methods struggle in real-world scenarios due to incomplete or unknown physical laws. Meanwhile, machine learning approaches often fail to generalize effectively when faced with scarce observational data and the challenge of capturing local and global features. To this end, we propose the Physics-encoded Spectral Attention Network (PeSANet), which integrates local and global information to forecast complex systems with limited data and incomplete physical priors. The model consists of two key components: a physics-encoded block that uses hard constraints to approximate local differential operators from limited data, and a spectral-enhanced block that captures long-range global dependencies in the frequency domain. Specifically, we introduce a novel spectral attention mechanism to model inter-spectrum relationships and learn long-range spatial features. Experimental results demonstrate that PeSANet outperforms existing methods across all metrics, particularly in long-term forecasting accuracy, providing a promising solution for simulating complex systems with limited data and incomplete physics.