Data-Driven Discovery of Interpretable Kalman Filter Variants through Large Language Models and Genetic Programming
This work addresses the challenge of algorithmic discovery in scientific computing, offering a data-driven approach that could reduce reliance on human experimentation, though it appears incremental as it builds on existing evolutionary and generative methods.
The researchers tackled the problem of automating the discovery of Kalman Filter variants using a combination of Cartesian Genetic Programming and Large Language Models, resulting in a framework that converges to near-optimal solutions under standard assumptions and evolves interpretable alternatives that outperform the Kalman Filter when assumptions are violated.
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.