General Explicit Network (GEN): A novel deep learning architecture for solving partial differential equations

TL;DR

This paper introduces the General Explicit Network (GEN), a new deep learning architecture for solving PDEs that improves robustness and extensibility over existing methods like PINNs.

Contribution

The paper proposes GEN, a novel neural network architecture that incorporates prior knowledge of PDEs through basis functions for more robust and extensible solutions.

Findings

GEN achieves high robustness in PDE solutions.

GEN demonstrates strong extensibility in various PDE problems.

Experimental results outperform traditional PINNs.

Abstract

Machine learning, especially physics-informed neural networks (PINNs) and their neural network variants, has been widely used to solve problems involving partial differential equations (PDEs). The successful deployment of such methods beyond academic research remains limited. For example, PINN methods primarily consider discrete point-to-point fitting and fail to account for the potential properties of real solutions. The adoption of continuous activation functions in these approaches leads to local characteristics that align with the equation solutions while resulting in poor extensibility and robustness. A general explicit network (GEN) that implements point-to-function PDE solving is proposed in this paper. The "function" component can be constructed based on our prior knowledge of the original PDEs through corresponding basis functions for fitting. The experimental results demonstrate that this approach enables solutions with high robustness and strong extensibility to be obtained.