Data-Driven Discovery of Interpretable Kalman Filter Variants through Large Language Models and Genetic Programming

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.