Publications

Simone Brivio, Stefania Fresca, Andrea Manzoni (2025). Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROMs. Computer Methods in Applied Mechanics and Engineering, 442, 117989.

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James Rowbottom, Stefania Fresca, Pietro Lio, Carola-Bibiane Schönlieb, Nicolas Boullé (2025). Multi-level Monte Carlo training of neural operators. arXiv:2505.12940.

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Nicola Farenga, Stefania Fresca, Simone Brivio, Andrea Manzoni (2025). On latent dynamics learning in nonlinear reduced order modeling. Neural Networks, 185, 107146.

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Niccolo Perrone, Fanny Lehmann, Hugo Gabrielidis, Stefania Fresca, Filippo Gatti (2025). Integrating Fourier neural operators with diffusion models to improve spectral representation of synthetic earthquake ground motion response. 28th International Conference on Structural Mechanics in Reactor Technology (SMIRT28).

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Niccolo Grillo, Andrea Toccaceli,, Benjamin Estermann, Joël Mathys, Stefania Fresca, Roger Wattenhofer (2025). Beyond Interpolation: Extrapolative reasoning with reinforcement learning and graph neural networks. 1st Workshop on Neural Reasoning and Mathematical Discovery – An Interdisciplinary Two-Way Street, NEURMAD@AAAI’25.

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Niccolo Botteghi, Stefania Fresca, Mengwu Guo, Andrea Manzoni (2025). HypeRL: Parameter-informed reinforcement learning for parametric PDEs. arXiv:2501.04538.

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Simone Brivio, Stefania Fresca, Andrea Manzoni (2024). PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs. Computer Methods in Applied Mechanics and Engineering, 432, 117404.

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Simone Brivio, Stefania Fresca, Nicola Rares Franco, Andrea Manzoni (2024). Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition. Advances in Computational Mathematics, 50, 33.

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Nicola Rares Franco, Stefania Fresca, Filippo Tombari, Andrea Manzoni (2023). Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(12):12312.

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Ludovica Cicci, Stefania Fresca, Andrea Manzoni, Alfio Quarteroni (2023). Efficient approximation of cardiac mechanics through reduced order modeling with deep learning-based operator approximation. International Journal for Numerical Methods in Biomedical Engineering, e3783.

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Ludovica Cicci, Stefania Fresca, Mengwu Guo, Andrea Manzoni, Paolo Zunino (2023). Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression. Computers and Mathematics with Applications, 149, 1-23.

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Stefania Fresca, Federico Fatone, Andrea Manzoni (2023). Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. Mathematics in Engineering, 5(6):1-36.

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Giorgio Gobat, Alessia Baronchelli, Stefania Fresca, Attilio Frangi (2023). Modeling the periodic response of Micro-Electromechanical Systems through deep learning-based approaches. Actuators, 12, 278.

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Nicola Rares Franco, Stefania Fresca, Andrea Manzoni, Paolo Zunino (2023). Approximation bounds for convolutional neural networks in operator learning. Neural Networks, 161, 129-141.

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Paolo Conti, Giorgio Gobat, Stefania Fresca, Andrea Manzoni, Attilio Frangi (2023). Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions. Computer Methods in Applied Mechanics and Engineering, 411, 116072.

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Giorgio Gobat, Stefania Fresca, Andrea Manzoni, Attilio Frangi (2023). Reduced order modelling of nonlinear vibrating multiphysics microstructures with deep learning-based approaches. Sensors, 23(6), 3001.

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Nicola Farenga, Stefania Fresca, Andrea Manzoni (2022). Neural latent dynamics models. 35th Conference on Neural Information Processing Systems (NeurIPS), The Symbiosis of Deep Learning and Differential Equations.

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Ludovica Cicci, Stefania Fresca, Andrea Manzoni (2022). Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs. Journal of Scientific Computing, 93:57.

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Stefania Fresca, Andrea Manzoni, Luca Dede', Alfio Quarteroni (2022). Deep learning-based reduced order models in cardiac electrophysiology. 7th International Conference on Computational and Mathematical Biomedical Engineering.

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Stefania Fresca, Giorgio Gobat, Patrick Fedeli, Attilio Frangi, Andrea Manzoni (2022). Deep learning-based reduced order models for the real-time simulation of the nonlinear dynamics of microstructures. International Journal for Numerical Methods in Engineering, 123(20):4749-4777.

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Giorgio Gobat, Andrea Opreni, Stefania Fresca, Andrea Manzoni, Attilio Frangi (2022). Reduced order modeling of nonlinear microstructures through Proper Orthogonal Decomposition. Mechanical Systems and Signal Processing, 171, 108864.

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Ludovica Cicci, Stefania Fresca, Stefano Pagani, Andrea Manzoni, Alfio Quarteroni (2022). Projection-based reduced order models for parameterized nonlinear time-dependent problems arising in cardiac mechanics. Mathematics in Engineering, 5(2):1-38.

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Stefania Fresca, Andrea Manzoni (2022). POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering, 388, 114181.

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Federico Fatone, Stefania Fresca, Andrea Manzoni (2021). Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based ROMs. 35th Conference on Neural Information Processing Systems (NeurIPS), The Symbiosis of Deep Learning and Differential Equations.

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Stefania Fresca, Andrea Manzoni, Luca Dede', Alfio Quarteroni (2021). POD-enhanced deep learning-based reduced order models for the real-time simulation of cardiac electrophysiology in the left atrium. Frontiers in Physiology, 12, 1431.

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Stefania Fresca, Andrea Manzoni (2021). Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models. Fluids, 6(7), 259.

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Stefania Fresca, Andrea Manzoni, Luca Dede' (2021). A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs. Journal of Scientific Computing, 87(2):1-36.

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Stefania Fresca, Andrea Manzoni, Luca Dede', Alfio Quarteroni (2020). Deep learning-based reduced order models in cardiac electrophysiology. PLOS ONE, 15(10):1-32.

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