Scalar Field Prediction on Meshes Using Interpolated Multi-Resolution Convolutional Neural Networks

TL;DR

This paper introduces a neural network method for predicting scalar fields directly on arbitrary mesh structures, enabling faster analysis in engineering design without fixed grid constraints.

Contribution

The work presents a novel multi-resolution convolutional neural network that interpolates features on meshes for scalar field prediction, extending data-driven methods beyond fixed grids.

Findings

Median R-squared of 0.91 for stress fields on shape datasets

Median R-squared of 0.99 for temperature field in heat conduction

Model performs well on complex, arbitrary mesh structures

Abstract

Scalar fields, such as stress or temperature fields, are often calculated in shape optimization and design problems in engineering. For complex problems where shapes have varying topology and cannot be parametrized, data-driven scalar field prediction can be faster than traditional finite element methods. However, current data-driven techniques to predict scalar fields are limited to a fixed grid domain, instead of arbitrary mesh structures. In this work, we propose a method to predict scalar fields on arbitrary meshes. It uses a convolutional neural network whose feature maps at multiple resolutions are interpolated to node positions before being fed into a multilayer perceptron to predict solutions to partial differential equations at mesh nodes. The model is trained on finite element von Mises stress fields, and once trained it can estimate stress values at each node on any input mesh. Two shape datasets are investigated, and the model has strong performance on both, with a median R-squared value of 0.91. We also demonstrate the model on a temperature field in a heat conduction problem, where its predictions have a median R-squared value of 0.99. Our method provides a potential flexible alternative to finite element analysis in engineering design contexts. Code and datasets are available online.