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

Vasileios Saketos, Sebastian Kaltenbach, Sergey Litvinov, Petros Koumoutsakos

Abstract:

Algorithmic discovery has traditionally relied on human in
genuity 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 condi
tions. Our results demonstrate that our framework of CGP and
LLM-assisted evolution converges to near-optimal solutions
when Kalman optimality assumptions hold. When these as
sumptions are violated, our framework evolves interpretable
alternatives that outperform the Kalman filter. These results
demonstrate that combining evolutionary algorithms and gen
erative models for interpretable, data-driven synthesis of sim
ple computational modules is a potent approach for algorith
mic discovery in scientific computing.