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

arXiv cs.LG / 4/7/2026

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Key Points

The paper proposes a new deep learning architecture called the General Explicit Network (GEN) aimed at solving partial differential equations (PDEs) more reliably than prior physics-informed neural network (PINN) approaches.
It argues that many existing PINN variants, which rely on discrete point-to-point fitting and continuous activations, can capture local solution characteristics but struggle with robustness and extensibility.
GEN is designed as a point-to-function solver, where the function component is built using basis functions derived from prior knowledge of the underlying PDEs.
Experiments reported in the paper suggest that this formulation improves robustness of the learned solutions and enhances their ability to generalize across problem settings.

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.