Discovering physical laws with parallel symbolic enumeration

Symbolic regression has a crucial role in modern scientific research owing to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and generalizable mathematical formulas, in an infinite search space, while intending to fit the training data. Existing algorithms have faced a critical bottleneck of accuracy and efficiency over a decade when handling problems of complexity, which essentially hinders the pace of applying symbolic regression for scientific exploration across interdisciplinary domains. Here, to this end, we introduce parallel symbolic enumeration (PSE) to efficiently distill generic mathematical expressions from limited data. Experiments show that PSE achieves higher accuracy and faster computation compared with the state-of-the-art baseline algorithms across over 200 synthetic and experimental problem sets (for example, improving the recovery accuracy by up to 99% and reducing runtime by an order of magnitude). PSE represents an advance in accurate and efficient data-driven discovery of symbolic, interpretable models (for example, underlying physical laws), and improves the scalability of symbolic learning.