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版本更新 · v3arXiv:2610.33465

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

Hao Mao, Xu T. Liu, Hao Xu, Peng Zhao, Qian Li, Dongxiao Zhang, Jinyue Yan, Yuntian Chen

原文摘要

Discovering equations from data provides governing laws, constitutive relations and closure models for scientific understanding and prediction. Yet a method that succeeds on one system may fail on another or on noisy data, so discovery depends on expert trial and error. Unsuccessful searches can still reveal useful parts of an equation, but these clues must be recognized and combined. We present LegoSR, a unified framework for agent-guided equation discovery built on composable discovery and cumulative experience. Seven complementary equation discovery methods and shared computational modules form reusable building blocks, connected through a common equation representation. Researchers can launch discovery with one command and guide it with partially known equations. LegoSR Agent selects methods, revises searches using feedback and combines partial findings into new hypotheses. Its Experience Library consolidates graded outcomes into lessons that guide later tasks across equation families. Evaluation covers 134 algebraic regression problems, 40 ordinary differential equation targets and 17 partial differential equation problems at several noise levels, together with three case studies. On noisy differential equation benchmarks, LegoSR Agent nearly matches the recovery coverage of seven expert-tuned methods combined and exceeds a generic agent with the same model, tools and budget by up to 29.4 percentage points, with 51-61% shorter median wall-clock time.

cs.AI · cs.LG

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2610.18938

Beyond Equation Search: Conjecture-Guided Discovery with SCOPE and ClosureBench

Yuxiao Hu, Qian Li, Ding Wang, Siheng Chen, Linfeng Zhang, Jinyue Yan, Yuntian Chen

原文摘要

Most symbolic regression methods optimize candidate equations, but improving an equation's fit does not establish whether its underlying scientific conjecture should be retained, revised, or rejected. A conjecture may admit multiple mathematical realizations, and similarly accurate equations may imply different explanations. This motivates a shift from refining individual expressions to developing and testing the conjectures that guide them. We introduce SCOPE, a framework that sustains multiple conjecture-driven research trajectories. Multiple scientist agents independently pursue conjectures through equation modeling, question formulation, and active experimentation, then exchange evidence to revise their conjectures and research directions. Their findings are consolidated into a scientific report linking models, conclusions, and evidence. Existing equation-discovery benchmarks primarily assess recovered expressions, leaving the evidence and scientific conclusions established through the investigation underexamined. We therefore introduce ClosureBench, an interactive benchmark of 60 closure-discovery tasks across five scientific domains. ClosureBench focuses on closure-discovery tasks to give equation discovery a concrete scientific purpose. Each task embeds an unknown algebraic relation in a known PDE system, where agents control experimental conditions in OpenFOAM to acquire new data for equation discovery. Beyond equation accuracy, ClosureBench proposes three metrics to evaluate the discovery process: evidence faithfulness, mechanism insight, and experimental effectiveness. Compared with diverse baselines, SCOPE achieves higher equation accuracy on both ClosureBench and a real-world scientific discovery case, while producing more accurate, reliable, and effective scientific discoveries.

cs.AI · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.16812

DASS: A Solver-Adaptable Dynamic Auxiliary Search Strategy for Symbolic Regression

Yuxiao Hu, Qian Li, Ding Wang, Yekun Zheng, Jinyue Yan, Yuntian Chen

原文摘要

Symbolic regression (SR) aims to discover interpretable mathematical expressions from data and plays a key role in scientific discovery. However, existing methods face a common bottleneck: the enormous search space and severe combinatorial explosion make it difficult to achieve a favorable trade-off between accuracy and algorithmic efficiency. We argue that, in addition to designing increasingly complex solver-specific SR strategies, an equally promising direction is to equip them with a shareable auxiliary strategy that can provide reliable search guidance. To this end, we propose DASS, a solver-adaptable Dynamic Auxiliary Search Strategy that improves SR by constructing and refining a high-potential auxiliary search subspace. DASS represents the auxiliary search space as a functional subspace spanned by a set of high-potential basis function terms. It estimates term utility through multi-environment evaluation, filters unstable guidance, and updates term potential scores with a Gibbs posterior, thereby calibrating the subspace to provide more reliable guidance for downstream solvers. The high-quality solutions produced by the solver are used to update the set of basis terms. This forms a virtuous closed-loop optimization process: the subspace guides the downstream solver, and the solver feedback reshapes the subspace for subsequent exploration. DASS can be easily integrated with various types of SR solvers. Extensive experiments on LLM-SRBench show that DASS significantly improves the accuracy of original solvers with a manageable increase in runtime.

cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.16966

Learning to Design SR Solvers: Harness Optimization for Symbolic Regression

Qian Li, Yuxiao Hu, Qihao Duan, Jinyue Yan, Yuntian Chen

原文摘要

Symbolic regression (SR) seeks explicit equations that explain observed data, and recent methods increasingly employ large language models (LLMs) and agents for equation discovery. However, these systems typically rely on manually designed workflows and prompts. We argue that the SR agent harness should itself be an optimization target: its design shapes search priors and how numerical feedback guides subsequent equation refinement. We therefore propose HarnessSR, a framework for jointly optimizing prompts and workflows to construct reusable SR agents. During both harness optimization and agent execution, HarnessSR supports either PySR or an LLM-based equation generator through tool-specific interfaces, allowing the framework to optimize search guidance for different equation-discovery mechanisms. HarnessSR first optimizes role prompts through equation-discovery feedback in basic workflows, then jointly searches prompt assignments and workflows with brief adaptation to align the two. Finally, it refines role instructions through reflection on residual patterns, candidate equation structures, and search outcomes, improving how these signals guide subsequent equation search. On LSR-Synth in LLM-SRBench, HarnessSR achieves a mean ID $\mathrm{Acc}_{0.01}$ of 61.33% across three backbones, a 45.0% relative improvement over the next-best baseline.

cs.LG

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arXiv ↗PDF ↗