Data-driven PDE discovery with evolutionary approach
This work addresses the need for more flexible PDE discovery in physics and engineering, though it appears incremental as it builds on existing symbolic regression techniques.
The authors tackled the problem of discovering partial differential equations (PDEs) from data by introducing an evolutionary approach (EPDE) that uses symbolic regression to overcome restrictions of sparse regression methods, and they tested it on canonical PDEs and noisy data.
The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation discovery techniques. The existing methods of PDE (partial derivative equations) discovery are bound with the sparse regression. However, sparse regression is restricting the resulting model form, since the terms for PDE are defined before regression. The evolutionary approach described in the article has a symbolic regression as the background instead and thus has fewer restrictions on the PDE form. The evolutionary method of PDE discovery (EPDE) is described and tested on several canonical PDEs. The question of robustness is examined on a noised data example.