General Explicit Network (GEN): A novel deep learning architecture for solving partial differential equations
For researchers using neural networks to solve PDEs, this work addresses limitations of PINNs in robustness and extensibility, though the improvements are not quantified.
The paper proposes a General Explicit Network (GEN) that implements point-to-function PDE solving, using basis functions based on prior knowledge of the PDEs. Experiments show the approach yields solutions with high robustness and strong extensibility.
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.