@misc{GonnellaDynamicalApproximationScheme2026,
author = {Gonnella, Isabella Carla and Mula, Olga and Pichi, Federico and Rozza, Gianluigi},
title = {A {{Dynamical Approximation Scheme}} on the {{Stiefel}} Manifold for {{Wasserstein Gradient Flows}}},
year = {2026},
number = {arXiv:2607.17235},
eprint = {2607.17235},
primaryclass = {math.NA},
publisher = {arXiv},
doi = {10.48550/arXiv.2607.17235},
urldate = {2026-07-21},
archiveprefix = {arXiv}
}

@misc{VenierStochasticBifurcationAnalysis2026,
author = {Venier, Giacomo and Gonnella, Isabella Carla and Pichi, Federico and Rozza, Gianluigi},
title = {{Stochastic Bifurcation Analysis via Polynomial Chaos: Consistency and Convergence of Branch-Approximating Solutions}},
year = {2026},
number = {arXiv:2605.31288},
eprint = {2605.31288},
primaryclass = {math.NA},
publisher = {arXiv},
doi = {10.48550/arXiv.2605.31288},
urldate = {2026-06-01},
archiveprefix = {arXiv}
}

@misc{ValentinoIntegratingArtificialIntelligence2026,
author = {Valentino, Carmine and Pichi, Federico and Colace, Francesco and Conte, Dajana and Rozza, Gianluigi},
title = {Integrating {{Artificial Intelligence}}, {{Physics}}, and {{Internet}} of {{Things}}: {{A Framework}} for {{Cultural Heritage Conservation}}},
shorttitle = {Integrating {{Artificial Intelligence}}, {{Physics}}, and {{Internet}} of {{Things}}},
year = {2026},
number = {arXiv:2604.03233},
eprint = {2604.03233},
primaryclass = {cs},
publisher = {arXiv},
doi = {10.48550/arXiv.2604.03233},
urldate = {2026-04-07},
archiveprefix = {arXiv}
}

@misc{KumarBifurcationCurveDetection2026,
author = {Kumar, Nitin and Pichi, Federico and Rozza, Gianluigi},
title = {Bifurcation Curve Detection with Deflation for Multiparametric {{PDEs}}},
year = {2026},
number = {arXiv:2602.12940},
eprint = {2602.12940},
primaryclass = {math},
publisher = {arXiv},
doi = {10.48550/arXiv.2602.12940},
urldate = {2026-02-16},
archiveprefix = {arXiv}
}

@misc{HirschConvergenceSketchingBasedEfficient2025a,
author = {Hirsch, Max and Pichi, Federico},
title = {Convergence and {{Sketching-Based Efficient Computation}} of {{Neural Tangent Kernel Weights}} in {{Physics-Based Loss}}},
year = {2025},
number = {arXiv:2511.15530},
eprint = {2511.15530},
primaryclass = {math},
publisher = {arXiv},
doi = {10.48550/arXiv.2511.15530},
urldate = {2025-11-20},
archiveprefix = {arXiv}
}

@misc{ChenTimeExtrapolationGraph2025,
author = {Chen, Yuanhong and Pichi, Federico and Gao, Zhen and Rozza, Gianluigi},
title = {Time {{Extrapolation}} with {{Graph Convolutional Autoencoder}} and {{Tensor Train Decomposition}}},
year = {2025},
number = {arXiv:2511.23037},
eprint = {2511.23037},
primaryclass = {math},
publisher = {arXiv},
doi = {10.48550/arXiv.2511.23037},
archiveprefix = {arXiv}
}

@misc{RomorROMViscousIncompressible2025,
author = {Romor, Francesco and Pichi, Federico and Stabile, Giovanni and Rozza, Gianluigi and Schwab, Christoph},
title = {{{ROM}} for {{Viscous}}, {{Incompressible Flow}} in {{Polygons}} – Exponential n-Width Bounds and Convergence Rate},
year = {2025},
number = {arXiv:2512.22567},
eprint = {2512.22567},
primaryclass = {math},
publisher = {arXiv},
doi = {10.48550/arXiv.2512.22567},
archiveprefix = {arXiv}
}

@article{KhamlichMultifidelityParametricReducedorder2027,
author = {Khamlich, Moaad and Tonicello, Niccol{'o} and Pichi, Federico and Rozza, Gianluigi},
title = {A Multi-Fidelity and Parametric Reduced-Order Modeling Framework with Optimal Transport-Based Interpolation: {{Applications}} to Diffused-Interface Two-Phase Flows},
shorttitle = {A Multi-Fidelity and Parametric Reduced-Order Modeling Framework with Optimal Transport-Based Interpolation},
year = {2027},
journal = {Journal of Computational Physics},
volume = {569},
pages = {115481},
doi = {10.1016/j.jcp.2026.115481},
urldate = {2026-10-12}
}

@article{TomadaLatentDynamicsGraph2026a,
author = {Tomada, Lorenzo and Pichi, Federico and Rozza, Gianluigi},
title = {Latent Dynamics Graph Convolutional Networks for Model Order Reduction of Parameterized Time-Dependent {{PDEs}}},
year = {2026},
journal = {Journal of Computational Physics},
volume = {564},
pages = {115150},
doi = {10.1016/j.jcp.2026.115150},
urldate = {2026-06-25}
}

@article{GonnellaStochasticPerturbationApproach2026,
author = {Gonnella, Isabella Carla and Khamlich, Moaad and Pichi, Federico and Rozza, Gianluigi},
title = {A {{Stochastic Perturbation Approach}} to {{Nonlinear Bifurcating Problems}}},
year = {2026},
journal = {Journal of Scientific Computing},
volume = {108},
number = {1},
pages = {20},
doi = {10.1007/s10915-026-03338-0},
urldate = {2026-06-01}
}

@article{HirschNeuralEmpiricalInterpolation2025,
author = {Hirsch, Max and Pichi, Federico and Hesthaven, Jan S.},
title = {Neural {{Empirical Interpolation Method}} for {{Nonlinear Model Reduction}}},
year = {2025},
journal = {SIAM Journal on Scientific Computing},
pages = {C1264-C1293},
publisher = {{Society for Industrial and Applied Mathematics}},
doi = {10.1137/24M1681434}
}

@article{TomadaSparseIdentificationBifurcating2025a,
author = {Tomada, Lorenzo and Khamlich, Moaad and Pichi, Federico and Rozza, Gianluigi},
title = {Sparse {{Identification}} for Bifurcating Phenomena in {{Computational Fluid Dynamics}}},
year = {2025},
journal = {Computers \& Fluids},
volume = {302},
pages = {106841},
doi = {10.1016/j.compfluid.2025.106841}
}

@article{PichiDeflationbasedCertifiedGreedy2025a,
author = {Pichi, Federico and Strazzullo, Maria},
title = {Deflation-Based Certified Greedy Algorithm and Adaptivity for Bifurcating Nonlinear {{PDEs}}},
year = {2025},
journal = {Communications in Nonlinear Science and Numerical Simulation},
volume = {149},
pages = {108941},
doi = {10.1016/j.cnsns.2025.108941}
}

@article{RathoreProjectionbasedReducedOrder2025a,
author = {Rathore, Surabhi and Africa, Pasquale C. and Ballarin, Francesco and Pichi, Federico and Girfoglio, Michele and Rozza, Gianluigi},
title = {Projection-Based Reduced Order Modelling for Unsteady Parametrized Optimal Control Problems in {{3D}} Cardiovascular Flows},
year = {2025},
journal = {Computer Methods and Programs in Biomedicine},
volume = {269},
pages = {108813},
doi = {10.1016/j.cmpb.2025.108813}
}

@article{KhamlichOptimalTransportbasedDisplacement2025,
author = {Khamlich, Moaad and Pichi, Federico and Girfoglio, Michele and Quaini, Annalisa and Rozza, Gianluigi},
title = {Optimal Transport-Based Displacement Interpolation with Data Augmentation for Reduced Order Modeling of Nonlinear Dynamical Systems},
year = {2025},
journal = {Journal of Computational Physics},
volume = {531},
pages = {113938},
doi = {10.1016/j.jcp.2025.113938}
}

@article{MorrisonGFNGraphFeedforward2024a,
author = {Morrison, Ois{'i}n M. and Pichi, Federico and Hesthaven, Jan S.},
title = {{{GFN}}: {{A}} Graph Feedforward Network for Resolution-Invariant Reduced Operator Learning in Multifidelity Applications},
shorttitle = {{{GFN}}},
year = {2024},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {432},
pages = {117458},
doi = {10.1016/j.cma.2024.117458}
}

@article{KhamlichOptimalTransportInspired2025,
author = {Khamlich, Moaad and Pichi, Federico and Rozza, Gianluigi},
title = {Optimal {{Transport}}–{{Inspired Deep Learning Framework}} for {{Slow-Decaying Kolmogorov}} n-{{Width Problems}}: {{Exploiting Sinkhorn Loss}} and {{Wasserstein Kernel}}},
shorttitle = {Optimal {{Transport}}–{{Inspired Deep Learning Framework}} for {{Slow-Decaying Kolmogorov}} n-{{Width Problems}}},
year = {2025},
journal = {SIAM Journal on Scientific Computing},
pages = {C235-C264},
publisher = {{Society for Industrial and Applied Mathematics}},
doi = {10.1137/23M1604680}
}

@article{PichiGraphConvolutionalAutoencoder2024,
author = {Pichi, Federico and Moya, Beatriz and Hesthaven, Jan S.},
title = {A Graph Convolutional Autoencoder Approach to Model Order Reduction for Parametrized {{PDEs}}},
year = {2024},
journal = {Journal of Computational Physics},
volume = {501},
pages = {112762},
doi = {10.1016/j.jcp.2024.112762}
}

@article{PichiArtificialNeuralNetwork2023,
author = {Pichi, Federico and Ballarin, Francesco and Rozza, Gianluigi and Hesthaven, Jan S.},
title = {An Artificial Neural Network Approach to Bifurcating Phenomena in Computational Fluid Dynamics},
year = {2023},
journal = {Computers \& Fluids},
volume = {254},
pages = {105813},
doi = {10.1016/j.compfluid.2023.105813}
}

@article{KhamlichModelOrderReduction2022,
author = {Khamlich, M. and Pichi, F. and Rozza, G.},
title = {Model Order Reduction for Bifurcating Phenomena in {{Fluid-Structure Interaction}} Problems},
year = {2022},
journal = {International Journal for Numerical Methods in Fluids},
doi = {10.1002/fld.5118}
}

@article{PichiDrivingBifurcatingParametrized2022,
author = {Pichi, F. and Strazzullo, M. and Ballarin, F. and Rozza, G.},
title = {Driving Bifurcating Parametrized Nonlinear {{PDEs}} by Optimal Control Strategies: Application to {{Navier-Stokes}} Equations with Model Order Reduction},
shorttitle = {Driving Bifurcating Parametrized Nonlinear {{PDEs}} by Optimal Control Strategies},
year = {2022},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
publisher = {{EDP Sciences}},
doi = {10.1051/m2an/2022044}
}

@article{pintore2019efficient,
author = {Pintore, M. and Pichi, F. and Hess, M. and Rozza, G. and Canuto, C.},
title = {Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method},
journal = {Advances in Computational Mathematics},
volume = {47},
number = {1},
year = {2020},
doi = {10.1007/s10444-020-09827-6}
}

@article{pichiquaini,
author = {Pichi, F. and Quaini, A. and Rozza, G.},
title = {A Reduced Order Modeling Technique to Study Bifurcating Phenomena: Application to the {G}ross-{P}itaevskii Equation},
journal = {SIAM Journal on Scientific Computing},
volume = {42},
number = {5},
pages = {B1115-B1135},
year = {2020},
doi = {10.1137/20M1313106}
}

@article{pichirozza,
AUTHOR = {Pichi, F. and Rozza, G.},
TITLE = {Reduced basis approaches for parametrized bifurcation problems held by non-linear {V}on {Karman} equations},
JOURNAL = {Journal of Scientific Computing},
YEAR = {2019},
DOI = {10.1007/s10915-019-01003-3},
VOLUME = {81},
NUMBER = {1},
PAGES = {112–135}
}

@book{PichiScientificMachineLearning2026,
author = {Pichi, Federico and Rozza, Gianluigi and Strazzullo, Maria and Torlo, Davide},
title = {Scientific {{Machine Learning}}: {{Emerging Topics}}},
shorttitle = {Scientific {{Machine Learning}}},
year = {2026},
series = {{{SEMA SIMAI Springer Series}}},
volume = {42},
publisher = {Springer Nature Switzerland},
address = {Cham},
doi = {10.1007/978-3-032-11527-0},
urldate = {2026-03-01},
isbn = {978-3-032-11526-3 978-3-032-11527-0}
}

@book{RozzaRealTimeReduced2024,
author = {Rozza, Gianluigi and Ballarin, Francesco and Scandurra, Leonardo and Pichi, Federico},
title = {Real {{Time Reduced Order Computational Mechanics}}: {{Parametric PDEs Worked Out Problems}}},
shorttitle = {Real {{Time Reduced Order Computational Mechanics}}},
year = {2024},
series = {{{SISSA Springer Series}}},
volume = {5},
publisher = {Springer Nature Switzerland},
address = {Cham},
doi = {10.1007/978-3-031-49892-3},
isbn = {978-3-031-49891-6 978-3-031-49892-3}
}

@incollection{GonnellaNonlinearReductionStrategies2026,
author = {Gonnella, Isabella Carla and Pichi, Federico and Rozza, Gianluigi},
editor = {Pichi, Federico and Rozza, Gianluigi and Strazzullo, Maria and Torlo, Davide},
title = {Nonlinear {{Reduction Strategies}} for~{{Data Compression}}: {{A~Comprehensive Comparison}} from~{{Diffusion}} to~{{Advection Problems}}},
shorttitle = {Nonlinear {{Reduction Strategies}} for~{{Data Compression}}},
booktitle = {Scientific {{Machine Learning}}},
year = {2026},
pages = {177–198},
publisher = {Springer Nature Switzerland},
address = {Cham},
doi = {10.1007/978-3-032-11527-0_9},
isbn = {978-3-032-11527-0}
}

@incollection{PichiReducedOrderModels2024,
author = {Pichi, Federico and Rozza, Gianluigi},
editor = {Rozza, Gianluigi and Stabile, Giovanni and Gunzburger, Max and D’Elia, Marta},
title = {Reduced {{Order Models}} for~the~{{Buckling}} of~{{Hyperelastic Beams}}},
booktitle = {Reduction, {{Approximation}}, {{Machine Learning}}, {{Surrogates}}, {{Emulators}} and {{Simulators}}: {{RAMSES}}},
year = {2024},
pages = {199–240},
publisher = {Springer Nature Switzerland},
address = {Cham},
doi = {10.1007/978-3-031-55060-7_9},
isbn = {978-3-031-55060-7}
}

@incollection{KhamlichChapter15Reduced2022,
author = {Khamlich, M. and Pichi, F. and Rozza, G.},
title = {Chapter 15: {{Reduced Order Models}} for {{Bifurcating Phenomena}} in {{Fluid-Structure Interaction Problems}}},
shorttitle = {Chapter 15},
booktitle = {Advanced {{Reduced Order Methods}} and {{Applications}} in {{Computational Fluid Dynamics}}},
year = {2022},
series = {Computational {{Science}} \& {{Engineering}}},
pages = {311–324},
publisher = {{Society for Industrial and Applied Mathematics}},
doi = {10.1137/1.9781611977257.ch15},
isbn = {978-1-61197-724-0}
}

@incollection{PichiChapterReducedBasis2022,
author = {Pichi, F. and Ballarin, F. and Rozza, G.},
title = {Chapter 5: {{Reduced Basis Approaches}} to {{Bifurcating Nonlinear Parametrized Partial Differential Equations}}},
shorttitle = {Chapter 5},
booktitle = {Advanced {{Reduced Order Methods}} and {{Applications}} in {{Computational Fluid Dynamics}}},
year = {2022},
series = {Computational {{Science}} \& {{Engineering}}},
pages = {97–123},
publisher = {{Society for Industrial and Applied Mathematics}},
doi = {10.1137/1.9781611977257.ch5},
isbn = {978-1-61197-724-0}
}

@incollection{PichiChapterFiniteElementBased2022,
author = {Pichi, F. and Strazzullo, M. and Ballarin, F. and Rozza, G.},
title = {Chapter 2: {{Finite Element-Based Reduced Basis Method}} in {{Computational Fluid Dynamics}}},
shorttitle = {Chapter 2},
booktitle = {Advanced {{Reduced Order Methods}} and {{Applications}} in {{Computational Fluid Dynamics}}},
year = {2022},
series = {Computational {{Science}} \& {{Engineering}}},
pages = {13–58},
publisher = {{Society for Industrial and Applied Mathematics}},
doi = {10.1137/1.9781611977257.ch2},
isbn = {978-1-61197-724-0}
}

@proceedings{Huynh2018,
author = {Huynh, D. B. P. and Pichi, F. and Rozza, G.},
title = {Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings},
bookTitle = {Numerical Methods for PDEs: State of the Art Techniques},
year = {2018},
publisher = {Springer International Publishing},
address = {Cham},
pages = {203–247},
isbn = {978-3-319-94676-4},
doi = {10.1007/978-3-319-94676-4_8}
}