Equation discovery solvers often rely on heterogeneous data interfaces, equation representations, and evaluation criteria, making cross‑method comparison difficult. LegoSR addresses this by providing a unified framework for algebraic symbolic regression and differential equation discovery.
LegoSR integrates seven state‑of‑the‑art solvers through a common equation representation and evaluation pipeline, and it supports searches constrained by partially known equations. Users can either invoke a specific solver directly or employ the LegoSR Agent—a self‑improving agent that selects solvers and adapts the search based on each solver's prior knowledge, intermediate results, and lessons learned from previous tasks.
On noisy ordinary and partial differential equation benchmarks, the LegoSR Agent recovers nearly as many correct equations as the union of the seven expert‑tuned solvers. Compared with a generic agent using the same model, tools, and budget, it achieves up to a 29 percentage‑point improvement.
Three illustrative examples are provided:
- Basic usage: directly run a chosen solver for equation discovery.
- Adaptive solver selection: let the LegoSR Agent switch solvers dynamically according to real‑time feedback.
- Discovery guided by partial physical knowledge: constrain the search with known parts of the target equation.
These cases demonstrate LegoSR’s ability to boost discovery efficiency while reducing manual tuning effort.
Review