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

2025-08-13

AI Summary

This work addresses the heavy reliance on human expertise in algorithm discovery for scientific computing. We propose an LLM-guided Cartesian Genetic Programming (CGP) co-evolutionary framework for data-driven automatic discovery of Kalman filters. Methodologically, the LLM injects semantic priors and structural constraints, while CGP evolves interpretable computational graphs of filters under data-driven feedback; the two components jointly optimize both algorithmic structure and parameters. Our contributions are threefold: (1) the first deep integration of LLMs and CGP for automated reconstruction of classical estimation algorithms; (2) guaranteed convergence to near-optimal solutions when the Kalman optimality assumptions hold, and—when they fail—evolution of novel, high-performing, and structurally transparent filter variants; and (3) generation of algorithms that are simultaneously interpretable, robust, and amenable to scientific validation, thereby establishing a new paradigm for “algorithm discovery” in scientific computing.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Evolutionary Computation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

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.

Problem

• Automated discovery of Kalman Filter variants using evolutionary algorithms
• Evaluating performance when Kalman assumptions are violated
• Combining genetic programming and LLMs for interpretable algorithmic synthesis

Innovation

• Combining genetic programming with large language models
• Automated discovery of Kalman filter variants
• Evolving interpretable alternatives outperforming standard filter