DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm
This addresses a limitation in data-driven PDE discovery for researchers in physics and engineering, though it appears incremental as it builds on existing methods by handling incomplete libraries.
The authors tackled the problem of discovering partial differential equations (PDEs) from data when a complete candidate library of terms is unavailable, by proposing DLGA-PDE, a framework combining deep learning and genetic algorithms, which successfully discovered several PDEs like the KdV and Burgers equations even with noisy and limited data.
Data-driven methods have recently been developed to discover underlying partial differential equations (PDEs) of physical problems. However, for these methods, a complete candidate library of potential terms in a PDE are usually required. To overcome this limitation, we propose a novel framework combining deep learning and genetic algorithm, called DLGA-PDE, for discovering PDEs. In the proposed framework, a deep neural network that is trained with available data of a physical problem is utilized to generate meta-data and calculate derivatives, and the genetic algorithm is then employed to discover the underlying PDE. Owing to the merits of the genetic algorithm, such as mutation and crossover, DLGA-PDE can work with an incomplete candidate library. The proposed DLGA-PDE is tested for discovery of the Korteweg-de Vries (KdV) equation, the Burgers equation, the wave equation, and the Chaffee-Infante equation, respectively, for proof-of-concept. Satisfactory results are obtained without the need for a complete candidate library, even in the presence of noisy and limited data.