Seven equation-discovery solvers behind one interface let an agent pick the right one and beat a generic agent by up to 29 points on noisy PDE benchmarks
AspireAI community · arXiv
Equation-discovery solvers use different data interfaces, equation representations and evaluation criteria, which makes their results hard to compare. LegoSR is a unified framework for algebraic symbolic regression and differential equation discovery that 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 worked examples demonstrate basic use, adaptive solver selection, and discovery guided by partial physical knowledge.
The honest limit: the comparison baseline is a generic agent given the same tools, not the expert-tuned solvers themselves - which LegoSR nearly matches but does not beat. The evidence is confined to symbolic regression and differential equation discovery on synthetic and noisy benchmarks, and the 29-point gap is an upper bound across the reported settings rather than a uniform margin.
https://arxiv.org/abs/2610.33465
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