Robust Equation Structure Learning with Adaptive Refinement

Yunlun Li, Sinno Jialin Pan

Keywords: Symbolic Regression, Genetic Programming, Equation Discovery, Large Language Model, AI for Science

TL;DR: We introduce, RESTART, a symbolic regression framework combines LLM-based hypothesis generation with explicit structure refinement.

Abstract: Symbolic regression (SR) aims to automate scientific discovery, but often truncates the hypothetico–deductive cycle, focusing on hypothesis and experiment while lacking systematic analysis. We introduce RESTART, a framework that closes this loop by adding a principled analysis stage to diagnose and correct structural errors. RESTART features two core mechanisms: a short-term refinement process that uses boosting to identify unexplained signals and guide an LLM toward targeted corrections, and a long-term structure library that distills successful refinements into reusable code snippets for cumulative knowledge. On LLM-SRBench across Physics, Biology, and Materials Science, RESTART achieves lower error and higher accuracy than state-of-the-art baselines. It also generalizes robustly, recovering near-exact functional forms on out-of-distribution data, representing a significant advance toward fully automated scientific discovery.

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

Submission Number: 11291