Data-driven partial differential equations discovery approach for the noised multi-dimensional 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, which can be helpful both for process simulation and studying. The paper describes the progress made within the PDE discovery framework. The framework involves a combination of evolutionary algorithms and sparse regression. Such an approach gives more versatility in comparison with other commonly used methods of data-driven partial differential derivation by making fewer restrictions on the resulting equation. This paper highlights the algorithm features which allow the processing of data with noise, which is more similar to the real-world applications of the algorithm.