Does LLM dream of differential equation discovery?

Timur Bavshin, Elizaveta Ivanchik, Alexander Hvatov

Keywords: equation discovery, differential equation, LLM, EPDE

TL;DR: LLM are decent on differential equation discovery but require function calling to be better

Abstract: Large Language Models (LLMs) show promise in symbolic regression tasks. However, applying them to partial differential equation (PDE) discovery presents significant challenges. Unlike traditional symbolic regression, which allows for quick feedback by directly generating data, PDE discovery involves solving implicit equations and deriving data from physical fields, capabilities LLMs currently lack. Our method bridges the gap between LLMs' theoretical understanding of differential equations from textbooks and the practical needs of scientific discovery, where textbooks are less helpful. We show that when physical field data are appropriately formatted and coupled with code generation prompts, general-purpose LLMs can effectively engage in the equation discovery process, even without specific training for this task. This research lays the groundwork for utilizing pre-trained LLMs in automated scientific discovery, while recognizing current limitations and the necessity of hybrid human-AI validation.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Submission Number: 7676