Partial differential equations discovery with EPDE framework: Application for real and synthetic data

Abstract

Data-driven methods provide model creation tools for systems where the application of conventional analytical methods is restrained. The proposed method involves the data-driven derivation of a partial differential equation (PDE) for process dynamics, helping process simulation and study. The paper describes the methods that are used within the EPDE (Evolutionary Partial Differential Equations) partial differential equation discovery framework [1]. The framework involves a combination of evolutionary algorithms and sparse regression. Such an approach is versatile compared to other commonly used data-driven partial differential derivation methods by making fewer assumptions about the resulting equation. This paper highlights the algorithm features that allow data processing with noise, which is similar to the algorithm's real-world applications. This paper is an extended version of the ICCS-2020 conference paper [2].