Generative Discovery of Partial Differential Equations by Learning from Math Handbooks
Hao Xu, Yuntian Chen, Rui Cao, Tianning Tang, Mengge Du, Jian Li, Adrian H. Callaghan, Dongxiao Zhang

TL;DR
This paper presents EqGPT, a knowledge-guided generative model that leverages mathematical handbooks to efficiently discover complex PDEs from data, including real-world nonlinear wave equations.
Contribution
It introduces a novel approach that encodes existing PDEs into a generative model to improve discovery accuracy and efficiency in complex systems.
Findings
Successfully recovers various PDE forms with high accuracy
Demonstrates effectiveness on complex temporal and spatial derivatives
Discovers a new PDE for nonlinear surface gravity waves
Abstract
Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with optimization efficiency. This study introduces a knowledge guided approach that incorporates existing PDEs documented in a mathematical handbook to facilitate the discovery process. These PDEs are encoded as sentence like structures composed of operators and basic terms, and used to train a generative model, called EqGPT, which enables the generation of free form PDEs. A loop of generation evaluation optimization is constructed to autonomously identify the most suitable PDE. Experimental results demonstrate that this framework can recover a variety of PDE forms with high accuracy and computational efficiency, particularly in cases involving complex…
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Taxonomy
TopicsModel Reduction and Neural Networks · Numerical methods for differential equations · Machine Learning in Materials Science
MethodsGravity
