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00925njm 22002777a 4500 dc Sibuet Ruiz, Nicolás author Ares de Parga Regalado, Sebastian author Bravo Martínez, José Raúl author Rossi, Riccardo author 2025-05-20 This paper presents a physics-informed training framework for projection-based Reduced-Order Models (ROMs). We extend the original PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual loss, bridging the gap between traditional projection-based ROMs and physics-informed neural networks (PINNs). Unlike conventional PINNs that rely on analytical PDEs, our approach leverages FEM residuals to guide the learning of the ROM approximation manifold. Our key contributions include the following: (1) a parameter-agnostic, discrete residual loss applicable to nonlinear problems, (2) an architectural modification to PROM-ANN improving accuracy for fast-decaying singular values, and (3) an empirical study on the proposed physics-informed training process for ROMs. The method is demonstrated on a nonlinear hyperelasticity problem, simulating a rubber cantilever under multi-axial loads. The main accomplishment in regards to the proposed residual-based loss is its applicability on nonlinear problems by interfacing with FEM software while maintaining reasonable training times. The modified PROM-ANN outperforms POD by orders of magnitude in snapshot reconstruction accuracy, while the original formulation is not able to learn a proper mapping for this use case. Finally, the application of physics-informed training in ANN-PROM modestly narrows the gap between data reconstruction and ROM accuracy; however, it highlights the untapped potential of the proposed residual-driven optimization for future ROM development. This work underscores the critical role of FEM residuals in ROM construction and calls for further exploration on architectures beyond PROM-ANN. N.S. acknowledges the Secretariat of Universities and Research of the Department of Research and Universities of the Generalitat of Catalonia, as well as the European Social Plus Fund for their financial support through the predoctoral scholarship AGAUR-FI (2024 FI-1 00089) Joan Oró. S.A.d.P. and J.R.B. acknowledge the Departament de Recerca i Universitats de la Generalitat de Catalunya for the financial support through the FI-SDUR 2020 and FI-SDUR 2021 scholarships. S.A.d.P. also acknowledges support from the Fulbright Commission Spain through the Fulbright Predoctoral Research Fellowship (2024–2025). Peer Reviewed 9.2 - Promoure una industrialització inclusiva i sostenible i, a tot tardar el 2030, augmentar de manera significativa la contribució de la indústria a l’ocupació i al producte interior brut, d’acord amb les circumstàncies nacionals, i duplicar aquesta contribució als països menys avançats 9.4 - Per a 2030, modernitzar les infraestructures i reconvertir les indústries perquè siguin sostenibles, usant els recursos amb més eficàcia i promovent l’adopció de tecnologies i processos industrials nets i racionals ambientalment, i aconseguint que tots els països adoptin mesures d’acord amb les capacitats respectives 9 - Indústria, Innovació i Infraestructura Postprint (published version) Àrees temàtiques de la UPC::Enginyeria civil::Materials i estructures::Càlcul d'estructures Reduced-order model (ROM) Physics-informed neural networks (PINNs) Artificial neural network Discrete physics-informed training for projection-based reduced-order models with neural networks