用智能算法自动发现可解释的卡尔曼滤波替代方案。
Data-Driven Discovery of Interpretable Kalman Filter Variants through Large Language Models and Genetic Programming
- 结合遗传编程与大模型，自动化演化滤波算法。
- 在理想条件下逼近最优，偏离时性能更优。
- 适合需要可解释性算法的科研与工程场景。
传统算法发现依赖人工直觉与大量实验。本文探究能否通过数据驱动、基于进化的方法自动发现一种重要的科学计算算法——卡尔曼滤波。方法结合笛卡尔遗传编程（CGP）与大语言模型（LLM），评估二者在不同条件下的贡献。结果表明，当卡尔曼最优性假设成立时，该框架能收敛至近优解；当假设被违反时，可演化出可解释的替代方案，其性能优于标准卡尔曼滤波。这证明，将进化算法与生成模型结合，用于可解释的简单计算模块的数据驱动合成，是科学计算中算法发现的强大策略。
原文摘要 · Abstract (English)
Algorithmic discovery has traditionally relied on human ingenuity and extensive experimentation. Here we investigate whether a prominent scientific computing algorithm, the Kalman Filter, can be discovered through an automated, data-driven, evolutionary process that relies on Cartesian Genetic Programming (CGP) and Large Language Models (LLM). We evaluate the contributions of both modalities (CGP and LLM) in discovering the Kalman filter under varying conditions. Our results demonstrate that our framework of CGP and LLM-assisted evolution converges to near-optimal solutions when Kalman optimality assumptions hold. When these assumptions are violated, our framework evolves interpretable alternatives that outperform the Kalman filter. These results demonstrate that combining evolutionary algorithms and generative models for interpretable, data-driven synthesis of simple computational modules is a potent approach for algorithmic discovery in scientific computing.
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