Multi-scale fusion network: A new deep learning structure for elliptic interface problems

Abstract

In this paper, we construct a novel multi-scale fusion network as a new deep learning structure to solve the elliptic interface problem. Compared with the results of the fully connected neural network and ResNet, the new multi-scale fusion network is shown to be able to better capture “sharp turns”, leading to the improved accuracy. Furthermore, its numerical solutions can preserve the C0 continuity of the solution while keeping the flux jumps passing through different interfaces, thus maintaining the physics of the differential equation. Then, as an application, the new method is applied to solve the three-dimensional Poisson-Boltzmann equations to calculate the electrostatic potential of immersed biomolecules. Numerical experiments demonstrate the effectiveness of our new method compared to the results obtained by the finite element method.