Data-driven identification of parametric partial differential equations
For researchers in scientific machine learning, this method expands PDE identification to parametric cases that previously eluded automated discovery, though it is an incremental extension of prior constant-coefficient methods.
This work presents a data-driven method for discovering parametric PDEs, enabling identification of both evolution equations and their parametric dependencies. Group sparsity is used for parsimonious representations, and group sequentially thresholded ridge regression outperforms group LASSO in identifying minimal terms and parametric dependencies, demonstrated on four canonical models with and without noise.
In this work we present a data-driven method for the discovery of parametric partial differential equations (PDEs), thus allowing one to disambiguate between the underlying evolution equations and their parametric dependencies. Group sparsity is used to ensure parsimonious representations of observed dynamics in the form of a parametric PDE, while also allowing the coefficients to have arbitrary time series, or spatial dependence. This work builds on previous methods for the identification of constant coefficient PDEs, expanding the field to include a new class of equations which until now have eluded machine learning based identification methods. We show that group sequentially thresholded ridge regression outperforms group LASSO in identifying the fewest terms in the PDE along with their parametric dependency. The method is demonstrated on four canonical models with and without the introduction of noise.