STRIDE: A Self-Reflective Agent Framework for Reliable Automatic Equation Discovery

LLM-based equation discovery offers a promising route to recovering symbolic laws from data, but many systems still rely on generation-centered loops that propose candidates, fit parameters, score results, and reuse selected examples. Such loops can misjudge useful skeletons under unreliable fitting, discard near-correct equations that require repair, and accumulate redundant memories that provide limited guidance. We propose STRIDE, a self-reflective agent framework that improves reliability by coordinating data-aware generation, mixed-fitting evaluation, critic–executor repair, and diversity-preserving semantic memory. STRIDE turns fitting scores and candidate behavior into shared feedback to guide targeted structural repair, while retaining diverse, high-quality equations to inform subsequent generation, thereby closing the loop between evaluation, refinement, and sampling. Experiments on representative symbolic-regression benchmarks and LSR-Synth suites show that STRIDE improves accuracy, OOD robustness, and structural recovery across multiple LLM backbones, with ablations and analyses confirming the contribution of its core components.