EvoTrace: Learning to Evolve Scientific Hypotheses from Trajectories of Agentic Symbolic Regression

Discovering concise and interpretable mathematical laws from observational data has conventionally been addressed through symbolic regression (SR). Recent advances in large language models (LLMs) have enabled this task to be formulated as an agentic search process that iteratively proposes, evaluates, and refines candidate formulas, often achieving superior performance. However, existing LLM-based approaches often fail to learn effectively from accumulated search experience: unsuccessful hypotheses are seldom reused, scalar feedback provides little guidance for structural revision, and exploration repeatedly revisits unproductive regions of the search space. This paper proposes EvoTrace, an agentic SR framework that distills actionable knowledge from search trajectories to drive mechanism-guided hypothesis evolution. By contrasting successful and unsuccessful trajectories, EvoTrace identifies structural modifications associated with performance improvements and uses them to guide subsequent hypothesis generation. It further integrates mechanism-anchored constraints with evaluation feedback to determine whether candidate hypotheses should be retained, revised, or rejected. Experiments across five key space-physics applications, including sunspot activity, plasma pressure, and lunar-tide signals, demonstrate that EvoTrace achieves stronger overall performance than existing LLM-based and non-LLM symbolic regression methods across evaluations of predictive accuracy, formula simplicity, extrapolation capability, and physical interpretability.