Parallel Machine Learning of Partial Differential Equations

TL;DR

This paper introduces a parallel machine learning scheme for partial differential equations using domain decomposition, neural networks, and MPI, achieving high scalability and accuracy in modeling Euler equations for aeroacoustics.

Contribution

The work presents a novel parallel training scheme for PDEs that combines domain decomposition, CNNs, and MPI, significantly reducing training time and maintaining accuracy.

Findings

High accuracy in learning Euler equations.

Excellent scalability up to 64 CPU cores.

Significant reduction in training time.

Abstract

In this work, we present a parallel scheme for machine learning of partial differential equations. The scheme is based on the decomposition of the training data corresponding to spatial subdomains, where an individual neural network is assigned to each data subset. Message Passing Interface (MPI) is used for parallelization and data communication. We use convolutional neural network layers (CNN) to account for spatial connectivity. We showcase the learning of the linearized Euler equations to assess the accuracy of the predictions and the efficiency of the proposed scheme. These equations are of particular interest for aeroacoustic problems. A first investigation demonstrated a very good agreement of the predicted results with the simulation results. In addition, we observe an excellent reduction of the training time compared to the sequential version, providing an almost perfect scalability up to 64 CPU cores.