Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluation
Sum Kyun Song, Bong Gyun Shin, Jae Yong Lee
TLDR
DoLQ uses an LLM-based multi-agent system to discover ordinary differential equations from data, incorporating both qualitative and quantitative evaluation.
Key contributions
- Introduces DoLQ, a novel method for discovering ODEs from observational data using LLM-based evaluation.
- Employs a multi-agent architecture with Sampler, Optimizer, and an LLM-powered Scientist Agent.
- Scientist Agent performs qualitative (plausibility) and quantitative (accuracy) evaluation to guide the search.
- Achieves superior performance on ODE benchmarks, recovering correct symbolic terms more accurately.
Why it matters
This paper addresses a key limitation in scientific machine learning by integrating domain knowledge into differential equation discovery. By leveraging LLMs for qualitative evaluation, DoLQ ensures physically plausible models, leading to more robust and interpretable scientific insights.
Original Abstract
Discovering governing differential equations from observational data is a fundamental challenge in scientific machine learning. Existing symbolic regression approaches rely primarily on quantitative metrics; however, real-world differential equation modeling also requires incorporating domain knowledge to ensure physical plausibility. To address this gap, we propose DoLQ, a method for discovering ordinary differential equations with LLM-based qualitative and quantitative evaluation. DoLQ employs a multi-agent architecture: a Sampler Agent proposes dynamic system candidates, a Parameter Optimizer refines equations for accuracy, and a Scientist Agent leverages an LLM to conduct both qualitative and quantitative evaluations and synthesize their results to iteratively guide the search. Experiments on multi-dimensional ordinary differential equation benchmarks demonstrate that DoLQ achieves superior performance compared to existing methods, not only attaining higher success rates but also more accurately recovering the correct symbolic terms of ground truth equations. Our code is available at https://github.com/Bon99yun/DoLQ.
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