ArticleSystems & control transactions2025
Selection of Fitness Criteria for Learning Interpretable PDE Solutions via Symbolic Regression.
Article in Systems & control transactions, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
Physics-Informed Symbolic Regression (PISR) offers a pathway to discover human-interpretable solutions to partial differential equations (PDEs). This work investigates three fitness metrics within a PISR framework: PDE fitness, Bayesian Information Criterion (BIC), and a fitness metric proportional to the probability of a model given the data. Through experiments with Laplace's equation, Burgers' equation, and a nonlinear wave equation, we demonstrate that incorporating information theoretic criteria like BIC can yield higher fidelity models while maintaining interpretability. Our results show that BIC-based PISR achieved the best performance, identifying an exact solution to Laplace's equation and finding solutions with
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