用动态提示优化让大模型更准发现微分方程。
Dynamic Bayesian Optimization Framework for Instruction Tuning in Partial Differential Equation Discovery
- 将提示工程转为逐步决策，根据反馈选最优指令。
- 在偏微分方程发现任务中，解的准确率显著提升。
- 适合想提升大模型科学推理能力的研究者。
大型语言模型（LLMs）在方程发现中展现潜力，但其输出对提示措辞极为敏感，这种现象称为指令脆弱性。静态提示无法适应多步生成过程中的动态变化，导致模型陷入次优解。为此，我们提出NeuroSymBO，将提示工程重构为序列决策问题。该方法维护一个离散的推理策略库，并利用贝叶斯优化根据数值反馈，在每一步选择最优指令。在偏微分方程发现基准测试中，自适应指令选择显著优于固定提示，不仅恢复率更高，且解更简洁。
原文摘要 · Abstract (English)
Large Language Models (LLMs) show promise for equation discovery, yet their outputs are highly sensitive to prompt phrasing, a phenomenon we term instruction brittleness. Static prompts cannot adapt to the evolving state of a multi-step generation process, causing models to plateau at suboptimal solutions. To address this, we propose NeuroSymBO, which reframes prompt engineering as a sequential decision problem. Our method maintains a discrete library of reasoning strategies and uses Bayesian Optimization to select the optimal instruction at each step based on numerical feedback. Experiments on PDE discovery benchmarks show that adaptive instruction selection significantly outperforms fixed prompts, achieving higher recovery rates with more parsimonious solutions.
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