An information-based model selection criterion for data-driven model discovery

Data-driven model discovery (DDMD) algorithms are powerful tools for extracting interpretable symbolic models from data. However, identifying the model that best balances goodness-of-fit and sparsity is often a laborious process requiring user fine-tuning, is prone to overfitting, and results may significantly vary depending on model initialization and specific training procedure. Here, we present a sparse regression algorithm that automatically and adaptively generates candidate models, and uses a novel sample-length-scaling logarithmic information criterion (SLIC) to identify the best model from these candidates. We demonstrate that SLIC greatly outperforms other popular information criteria in extracting the correct model from the data of several nonlinear ordinary and partial differential equations. Then, we demonstrate SLIC's ability to discover interpretable models from experimental datasets in fluid dynamics and nanotechnology that generate new testable predictions.