WEAK SINDy: GALERKIN-BASED DATA-DRIVEN MODEL SELECTION

We present a novel weak formulation and discretization for discovering governing equations from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative approximations with linear transformations and variance reduction techniques. Compared to the standard SINDy algorithm presented in [S. L. Brunton, J. L. Proctor, and J. N. Kutz, Proc. Natl. Acad. Sci. USA, 113 (2016), pp. 3932-3937], our so-called weak SINDy (WSINDy) algorithm allows for reliable model identification from data with large noise (often with ratios greater than 0.1) and reduces the error in the recovered coefficients to enable accurate prediction. Moreover, the co-efficient error scales linearly with the noise level, leading to high-accuracy recovery in the low-noise regime. Altogether, WSINDy combines the simplicity and efficiency of the SINDy algorithm with the natural noise reduction of integration, as demonstrated in [H. Schaeffer and S. G. McCalla, Phys. Rev. E, 96 (2017), 023302], to arrive at a robust and accurate method of sparse recovery.

Automated summary

A novel weak formulation and discretization method, called WSINDy, is proposed to discover governing equations from noisy measurement data. Compared to the standard SINDy algorithm, WSINDy allows for reliable model identification and reduces errors in data with large noise levels.