Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Models
TLDR
LLMs integrate domain knowledge into symbolic regression loss function, improving equation discovery from physical dynamics data.
Reasoning
The paper presents a novel method using LLMs to automate knowledge integration in physics-informed symbolic regression, with empirical validation across multiple algorithms and dynamics. Strengths include clear methodology and consistent improvements; weaknesses include limited scope of dynamics and potential lack of generalizability.
Read-first score
Read-first score 48.6, weighted from topical fit, citation, graph, method, reproducibility, and recency signals. Original total remains 47.
Field roles
Rank sensitivity
Stability: volatile; rank range: 16.
Keyword Scores
Deep Analysis
Innovations
- Automated domain knowledge integration in physics-informed symbolic regression using pre-trained large language models
- Incorporation of LLM evaluation as an additional term in the symbolic regression loss function
- Prompt engineering to improve LLM guidance for equation discovery
Methodology
The LLM is integrated into the symbolic regression loss function by adding a term that evaluates the produced equation. The method is tested with three SR algorithms (DEAP, gplearn, PySR) and three pre-trained LLMs (Falcon, Mistral, LLama 2) on three physical dynamics (dropping ball, simple harmonic motion, electromagnetic wave).
Key Results
LLM integration consistently improved the reconstruction of physical dynamics from data, enhancing robustness to noise and complexity. More informative prompts significantly improved performance.