AMS-Net: Adaptive Multiscale Sparse Neural Network with Interpretable Basis Expansion for Multiphase Flow Problems

Abstract

In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of precomputed basis functions that can be used to approximate the quantity of interest. For instance, in the simulation of multiscale flow system, one can adopt mixed multiscale methods to compute velocity bases from local problems and apply the proper orthogonal decomposition (POD) method to construct bases for the saturation equation. We then design a neural network architecture to learn the coefficients of solutions in the spaces which are spanned by these basis functions. The information of the basis functions are incorporated in the loss function, which minimizes the differences between the downscaled reduced order solutions and reference solutions at multiple time steps. The network contains multiple submodules and the solutions at different time steps can be learned simultaneously. We propose some strategies in the learning framework to identify important degrees of freedom. To find a sparse solution representation, a soft thresholding operator is applied to enforce the