| Abstract Scope |
Equations are central to scientific discovery, translating data and trends into interpretable insights. In the era of data-driven, autonomous experimentation, equation learning (symbolic regression) uses machine learning architectures such as genetic algorithms, reinforcement learning, and LLMs to learn equations from data, with excellent benchmark performance. However, a fundamental question remains unanswered: is a learned equation interpretable and trustworthy for an unknown scientific problem? We introduce a comprehensive equation-learning toolkit that combines a neural network equation learner, nn-EQL, with diagnostics for scientific discovery workflows. nn-EQL uses custom activation functions (sin, cos, exp, log) to identify common scientific terms, and learns compact equations via pruning. We benchmark on AI-Feynman and SRBench, showing that equation learners can identify alternate equations with good generalization but incorrect functional forms. Our diagnostics address this, estimating term-wise sensitivities/uncertainties, and suggesting experiments that confirm/deny terms. We demonstrate our toolkit in AI-for-scientific-discovery workflows across atomistic and mesoscale experimental/simulation datasets |