# Graph-Based Nonlinear Reduced-Order Modeling for Time-Domain Electromagnetics

Carlotta Filippin, Stephane Lanteri, Claire Scheid, F Pichi, M Strazzullo

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Carlotta Filippin, Stephane Lanteri, Claire Scheid, F Pichi, M Strazzullo. Graph-Based Nonlinear Reduced-Order Modeling for Time-Domain Electromagnetics. MORTech 2025 - 7th International Workshop on Model Order Reduction Techniques, Nov 2025, Zaragoza, Spain. hal-05286533

HAL Id: hal-05286533

https://inria.hal.science/hal-05286533v1

Submitted on 27 Sep 2025

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# Graph-Based Nonlinear Reduced-Order Modeling for Time-Domain Electromagnetics

C. Filippin<fnref n="1" />, S. Lanteri<fnref n="1" />, C. Scheid<fnref n="1" />, F. Pichi<fnref n="2" />, M. Strazzullo<fnref n="3" />

## ABSTRACT

Numerical modelling plays a crucial role in revealing the behaviour of light and matter interactions at the nanoscale, exploiting computational schemes such as the Discontinuous Galerkin Time-Domain (DGTD) method. Given the computational complexity associated to this task, we study reduced-order modelling (ROM) due to the pressing need for fast surrogate models capable of handling physically and geometrically parametrized electromagnetic problems. Traditional ROM techniques like Proper Orthogonal Decomposition (POD) and Greedy algorithm have already been investigated in the literature, along with their inherent limitations in effectively capturing nonlinear phenomena. Here, we exploit a deep learning-based ROM strategy showing promising potential, the Graph Convolutional Autoencoder (GCA) method [1], serving as a nonlinear extension of POD compression, harnessing the power of Graph Neural Networks to induce a geometric bias in the learning process when dealing with complex and unstructured meshes. We propose a fully data-driven nonlinear ROM extending the GCA method [1] tailored for time-domain electromagnetics, fully exploiting the training dataset of high-order (in space and time) DGTD snapshots. Our approach relies on a two-stage training strategy that decouples spatial compression from temporal dynamics [2], enabling a more targeted learning. We further explore the use of advanced latent-space propagators to better capture the high-frequency behaviour of electromagnetic problems. This direction aims to unlock faster and more accurate surrogate models for time-domain electromagnetics, especially for applications requiring complex geometries [3]-[4].

## REFERENCES

[1] F. Pichi, B. Moya, and J. Hesthaven. (2024). A graph convolutional autencoder approach to model order reduction for parametrized PDEs. *Journal of Computational Physics*.

[2] Z. Li, S. Patil, F. Ogoke, D. Shu, W. Zhen, M. Schenier, J. R. Buchanan JR., A. B. Farimani. (2024). Latent Neural PDE solver: A reduced-order modeling framework for partial differential equations. *Journal of Computational Physics*.

[3] O.M. Morrison, F. Pichi and J.S. Hesthaven. (2024). GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications. *Computer Methods in Applied Mechanics and Engineering*.

[4] N. Rares Franco, S. Fresca, F. Tombari, A. Manzoni. (2024). Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks. *Chaos*.

<footnote n="1">¹Université Côte d'Azur, Inria, CNRS, LJAD.</footnote>

<footnote n="2004">2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France.</footnote>

<footnote n="2">²mathLab, Mathematics Area, SISSA,
Via Bonomea, 265, 34136 Trieste TS, Italia.</footnote>

<footnote n="3">³Politecnico di Torino, Department of Mathematical Sciences “Giuseppe Luigi Lagrange”,
Corso Duca degli Abruzzi 24, 10129, Turin, Italy.</footnote>

<footnote>e-mail: carlotta.filippin@inria.fr</footnote>