Over the years, mathematicians and engineers have invested significant analytical effort to derive algorithms customized for modeling dynamic processes. However, such methods are often costly to develop and difficult to generalize. This thesis investigates whether these algorithms can instead be discovered automatically, without access to privileged information about the underlying system dynamics. To that end, we employ two genetic programming techniques: Cartesian Genetic Programming (CGP) and a Large Language Model (LLM)-assisted approach. Both methods operate without knowledge of the underlying model: they observe only raw input–output trajectories and are optimized solely via a black-box loss. We evaluate their ability to replicate the Kalman filter’s performance. Both CGP and the LLM-assisted approach reliably evolve compact, interpretable estimation algorithms with meansquared error comparable to that of the Kalman baseline. CGP performs well within modest compute limits, while the LLM-based method converges more slowly but ultimately reaches baseline performance in simpler cases. These results highlight the potential of fully automated, domain-agnostic algorithm discovery through evolutionary search and LLM-guided code generation.
Vasileios Saketos (Wed,) studied this question.