LegoSR: A Unified Framework for Self-improving Agent-Guided Scientific Discovery

Abstract

Equation discovery solvers often use different data interfaces, equation representations and evaluation criteria, making their results hard to compare. We present LegoSR, a unified framework for algebraic symbolic regression and differential equation discovery. LegoSR integrates seven solvers through a common equation representation and evaluation process, and supports searches constrained by partially known equations. Researchers can run solvers directly or use LegoSR Agent, which selects solvers and adapts searches using solver knowledge, intermediate results and lessons from past tasks. On noisy ordinary and partial differential equation benchmarks, LegoSR Agent recovers nearly as many equations as the union of seven expert-tuned solvers and outperforms a generic agent with the same model, tools and budget by up to 29 percentage points. Three examples of increasing difficulty show the agent's role growing from running a solver to choosing one and then to building a partially known equation from failed searches.