Structure informed neural networks for boundary observation problems
File(s)
Published version
Author(s)
Horsky, Jakub
Wynn, Andrew
Type
Journal Article
Abstract
We introduce a new machine learning architecture called Structure Informed Neural Networks (SINNs) for inferring the interior behaviour of a system using measurements taken only at its domain boundary. The key novelty is to model the transfer of information from boundary
to-interior by embedding elliptic systems of Partial Differential Equations (PDEs), via a finite element solver, into an encoder–decoder architecture. This gives the SINN architecture physics inspired structural priors which allow it to both achieve high data efficiency and to naturally
generalise across variable domain geometries. Since elliptic systems are agnostic to domain geometry, we are able to introduce that notion of training patches which allow SINN models to be efficiently trained on only small subdomains of the training data, enabling significant data
efficiency in model training. We demonstrate the effectiveness of the proposed architecture with three challenging boundary observation problems: predicting the steady flow of fluid past bodies of variable geometries; reconstructing an unsteady flow field from a history of
boundary measurements; and reconstructing the unsteady, separated flow over a stalled airfoil from compressible-Euler simulations. We show that the proposed methodology outperforms fine tuned U-Net, GNN and LP-FNO models, achieving at least 1.8× lower relative 𝐿2 error (and more than 3× lower than LP-FNO) on the validation dataset compared to these existing state-of-the
art architectures.
to-interior by embedding elliptic systems of Partial Differential Equations (PDEs), via a finite element solver, into an encoder–decoder architecture. This gives the SINN architecture physics inspired structural priors which allow it to both achieve high data efficiency and to naturally
generalise across variable domain geometries. Since elliptic systems are agnostic to domain geometry, we are able to introduce that notion of training patches which allow SINN models to be efficiently trained on only small subdomains of the training data, enabling significant data
efficiency in model training. We demonstrate the effectiveness of the proposed architecture with three challenging boundary observation problems: predicting the steady flow of fluid past bodies of variable geometries; reconstructing an unsteady flow field from a history of
boundary measurements; and reconstructing the unsteady, separated flow over a stalled airfoil from compressible-Euler simulations. We show that the proposed methodology outperforms fine tuned U-Net, GNN and LP-FNO models, achieving at least 1.8× lower relative 𝐿2 error (and more than 3× lower than LP-FNO) on the validation dataset compared to these existing state-of-the
art architectures.
Date Issued
2026-11-01
Date Acceptance
2026-07-05
Citation
Computer Methods in Applied Mechanics and Engineering, 2026, 461, Part B
ISSN
0045-7825
Publisher
Elsevier BV
Journal / Book Title
Computer Methods in Applied Mechanics and Engineering
Volume
461, Part B
Copyright Statement
© 2026 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Publication Status
Published
Article Number
119226
Date Publish Online
2026-07-20