GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications

TL;DR

This paper introduces a novel graph feedforward neural network for resolution-invariant model order reduction in multifidelity applications, demonstrating superior flexibility and generalization on complex PDE benchmarks.

Contribution

The work develops a new neural network layer, the graph feedforward network, that links mesh nodes to network weights, enabling resolution-invariant learning with provable error guarantees.

Findings

Effective on advection-dominated problems

Handles high-dimensional parameter spaces

Outperforms state-of-the-art models in flexibility

Abstract

This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in this work, the graph feedforward network, which extends the concept of feedforward networks to graph-structured data by creating a direct link between the weights of a neural network and the nodes of a mesh, enhancing the interpretability of the network. We exploit the method's capability of training and testing on different mesh sizes in an autoencoder-based reduction strategy for parametrised partial differential equations. We show that this extension comes with provable guarantees on the performance via error bounds. The capabilities of the proposed methodology are tested on three challenging benchmarks, including advection-dominated phenomena and problems with a high-dimensional parameter space. The method results in a more lightweight and highly flexible strategy when compared to state-of-the-art models, while showing excellent generalisation performance in both single fidelity and multifidelity scenarios.