# Data-driven PDE discovery with evolutionary approach

## TL;DR

This paper introduces an evolutionary symbolic regression approach for discovering partial differential equations from data, overcoming limitations of sparse regression and tested on canonical PDEs with noise robustness analysis.

## Contribution

It presents the EPDE method, a novel evolutionary approach for PDE discovery that offers greater flexibility in model form compared to traditional sparse regression techniques.

## Key findings

- EPDE successfully discovers canonical PDEs from data.
- The method demonstrates robustness to noisy data.
- Fewer restrictions on PDE form compared to existing methods.

## Abstract

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.