Learning physically consistent mathematical models from data using group sparsity

Understand

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 learning or inferring differential-equation models from measurement data.

• Directly learning $\textit{interpretable}$ mathematical models from data has emerged as a valuable modeling approach.
• However, in areas like biology, high noise levels, sensor-induced correlations, and strong inter-system variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure.
• Hence, it is important to leverage $\textit{prior}$ knowledge from physical principles to learn "biologically plausible and physically consistent" models rather than models that simply fit the data best.