Model selection via reweighted partial sparse recovery

Abstract

In this work, we propose an iterative reweighted algorithm for model selection with a-priori information on some possible terms present in the unknown dynamics, which is able to recover the governing equations from noisy time-series data and has strong adaptability. In addition, we prove that the algorithm converges to a local minimizer with in a few steps. Through several examples, we show that the proposed algorithm is more robust to noise and less dependent on hyperparameters, compared to its non-reweighted counterpart. We also apply the algorithm to the model selection problems.