@unpublished{TomadaLatentDynamicsGraph2026,
title = {Latent {{Dynamics Graph Convolutional Networks}} for Model Order Reduction of Parameterized Time-Dependent {{PDEs}}},
author = {Tomada, Lorenzo and Pichi, Federico and Rozza, Gianluigi},
year = 2026,
number = {arXiv:2601.11259},
eprint = {2601.11259},
primaryclass = {cs},
publisher = {arXiv},
doi = {10.48550/arXiv.2601.11259},
archiveprefix = {arXiv} }

@unpublished{RomorROMViscousIncompressible2025,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

@unpublished{HirschConvergenceSketchingBasedEfficient2025a,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

@unpublished{ChenTimeExtrapolationGraph2025,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

@unpublished{GonnellaNonlinearReductionStrategies2025,
title = {Nonlinear Reduction Strategies for Data Compression: A Comprehensive Comparison from Diffusion to Advection Problems},
shorttitle = {Nonlinear Reduction Strategies for Data Compression},
author = {Gonnella, Isabella Carla and Pichi, Federico and Rozza, Gianluigi},
year = {2025},
note = {arXiv:2501.12816},
eprint = {2501.12816},
primaryclass = {math},
publisher = {arXiv},
doi = {10.48550/arXiv.2501.12816},
archiveprefix = {arXiv} }

@unpublished{GonnellaStochasticPerturbationApproach2024,
title = {A Stochastic Perturbation Approach to Nonlinear Bifurcating Problems},
author = {Gonnella, Isabella Carla and Khamlich, Moaad and Pichi, Federico and Rozza, Gianluigi},
year = {2024},
note = {arXiv:2402.16803},
eprint = {2402.16803},
publisher = {{arXiv}},
doi = {10.48550/arXiv.2402.16803},
archiveprefix = {arxiv} }

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

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

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

@article{KhamlichOptimalTransportbasedDisplacement2025,
title = {Optimal Transport-Based Displacement Interpolation with Data Augmentation for Reduced Order Modeling of Nonlinear Dynamical Systems},
author = {Khamlich, Moaad and Pichi, Federico and Girfoglio, Michele and Quaini, Annalisa and Rozza, Gianluigi},
year = {2025},
journal = {Journal of Computational Physics},
volume = {531},
pages = {113938},
doi = {10.1016/j.jcp.2025.113938},
urldate = {2025-03-20} }

@article{KhamlichOptimalTransportInspired2025,
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}}},
author = {Khamlich, Moaad and Pichi, Federico and Rozza, Gianluigi},
year = {2025},
journal = {SIAM Journal on Scientific Computing}, pages = {C235-C264},
publisher = {{Society for Industrial and Applied Mathematics}},
doi = {10.1137/23M1604680} }

@article{PichiDeflationbasedCertifiedGreedy2025a,\

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

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

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

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

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

@article{PichiDrivingBifurcatingParametrized2022,
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},
author = {Pichi, F. and Strazzullo, M. and Ballarin, F. and Rozza, G.},
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{Pichi2020,
author = {F. Pichi and A. Quaini and G. Rozza},
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{Pichi2019,
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{RozzaRealTimeReduced2024,
title = {Real {{Time Reduced Order Computational Mechanics}}: {{Parametric PDEs Worked Out Problems}}},
shorttitle = {Real {{Time Reduced Order Computational Mechanics}}},
author = {Rozza, Gianluigi and Ballarin, Francesco and Scandurra, Leonardo and Pichi, Federico},
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{PichiReducedOrderModels2024,
title = {Reduced {{Order Models}} for the {{Buckling}} of {{Hyperelastic Beams}}},
booktitle = {Reduction, {{Approximation}}, {{Machine Learning}}, {{Surrogates}}, {{Emulators}} and {{Simulators}}: {{RAMSES}}},
author = {Pichi, Federico and Rozza, Gianluigi}, editor = {Rozza, Gianluigi and Stabile, Giovanni and Gunzburger, Max and D’Elia, Marta},
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,
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}}},
author = {Khamlich, M. and Pichi, F. and Rozza, G.},
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,
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}}},
author = {Pichi, F. and Ballarin, F. and Rozza, G.},
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,
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}}},
author = {Pichi, F. and Strazzullo, M. and Ballarin, F. and Rozza, G.},
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” }