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Learning finite element convergence with the Multi-fidelity Graph Neural Network
Journal article   Open access   Peer reviewed

Learning finite element convergence with the Multi-fidelity Graph Neural Network

Nolan Black and Ahmad R. Najafi
Computer methods in applied mechanics and engineering, v 397, 115120
01 Jul 2022
DOI: https://doi.org/10.1016/j.cma.2022.115120
url
https://doi.org/10.1016/j.cma.2022.115120View
Accepted (AM)Open Access (Publisher-Specific),  Open

Abstract

Graph Neural Networks Multi-fidelity analysis Surrogate modeling Machine Learning
Machine learning techniques have emerged as potential alternatives to traditional physics-based modeling and partial differential equation solvers. Among these machine learning techniques, Graph Neural Networks (GNNs) simulate physics via graph models; GNNs embed relevant physical features into graph data structures, perform message passing within the graphs, and produce new attributes based on the system’s relationships. Like many machine learning frameworks, GNNs are limited by excessive data generation costs and limited generalizability outside of a narrow training domain. To address these limitations, we introduce the Multi-Fidelity Graph Neural Network (MFGNN), a supervised machine learning framework that uses low-fidelity projections to inform high-fidelity modeling across arbitrary subdomains represented by subgraphs. We implement the MFGNN for two-dimensional elastostatic problems with finite element training data. The MFGNN is trained to produce accurate analysis given low-fidelity evaluations and emulate the convergence behavior of traditional finite element analysis (FEA). Through subdomain abstraction, we also extend the MFGNN as a general model for new boundary conditions and material domains outside of the training domain. • A machine learning model is developed to learn FEA convergence. • Graph-based modeling is informed by multi-fidelity data. • A single model is stable and accurate across multiple meshes. • Abstraction through subgraph analysis improves generalizability.

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30 citations in Web of Science
27 citations in Scopus

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Web of Science research areas
Engineering, Multidisciplinary
Mathematics, Interdisciplinary Applications
Mechanics
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