SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations
This work addresses the challenge of robustly discovering differential equations from noisy data, which is important for scientific modeling, but it appears incremental as it builds on threshold sparse Bayesian regression.
The authors tackled the problem of data-driven discovery of differential equations in the presence of high noise and outliers by proposing SubTSBR, a novel algorithm that improves accuracy over existing methods like TSBR, as demonstrated through numerical examples including predator-prey and shallow water equations.
Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm. It has two parameters: subsampling size and the number of subsamples. When the subsampling size increases with fixed total sample size, the accuracy of our algorithm goes up and then down. When the number of subsamples increases, the accuracy of our algorithm keeps going up. We demonstrate how to use our algorithm step by step and compare our algorithm with threshold sparse Bayesian regression (TSBR) for the discovery of differential equations. We show that our algorithm produces better results. We also discuss the merits of discovering differential equations from data and demonstrate how to discover models with random initial and boundary condition as well as models with bifurcations. The numerical examples are: (1) predator-prey model with noise, (2) shallow water equations with outliers, (3) heat diffusion with random initial and boundary condition, and (4) fish-harvesting problem with bifurcations.