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

Authors: Hao Mao , Xu T. Liu , Peng Zhao , Shuai Lu , Yuntian Chen

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Abstract: Equation discovery solvers often use different data interfaces, equation representations and evaluation criteria, making their results difficult 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 based on solver knowledge, intermediate results and lessons from earlier 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 demonstrate basic use, adaptive solver selection and discovery guided by partial physical knowledge.

Comments:

36 pages, 6 figures. Code is available at this https URL

Subjects:

Artificial Intelligence (cs.AI) ; Machine Learning (cs.LG)

Cite as:

arXiv:2610.33465 [cs.AI]

(or

arXiv:2610.33465v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.33465

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arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Hao Mao [ view email ]

[v1]

Sat, 24 Oct 2026 05:36:55 UTC (437 KB)

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