Learning physically consistent differential equation models from data using group sparsity

We propose a statistical learning framework based on group-sparse regression that can be used to 1) enforce conservation laws, 2) ensure model equivalence, and 3) guarantee symmetries when or inferring differential-equation models from measurement data. Directly $\textit{interpretable}$ mathematical data has emerged as valuable modeling approach. However, in areas like biology, high noise levels, sensor-induced correlations, strong inter-system variability render data-driven nonsensical physically inconsistent without additional constraints the structure. Hence, it is important leverage $\textit{prior}$ knowledge physical principles learn "biologically plausible consistent" rather than simply fit best. present novel group Iterative Hard Thresholding (gIHT) algorithm use stability selection infer consistent with minimal parameter tuning. show several applications systems biology demonstrate benefits of enforcing $\textit{priors}$ modeling.