Publications
Shafqat Ali, Francesco Ballarin, and Gianluigi Rozza. An online stabilization method for parametrized viscous flows. In Gianluigi Rozza, Giovanni Stabile, Max Gunzburger, and Marta D'Elia, editors, Reduction, Approximation, Machine Learning, Surrogates, Emulators and Simulators: RAMSES, pages 1–16. Springer Nature Switzerland, 2024. doi:10.1007/978-3-031-55060-7_1.
Francesco Ballarin, Giulia Bevilacqua, Luca Lussardi, and Alfredo Marzocchi. Elastic membranes spanning deformable curves. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 104(6):e202300890, 2024. arXiv:2207.13614, doi:10.1002/zamm.202300890.
Francesco Ballarin, Enrique Delgado Ávila, Andrea Mola, and Gianluigi Rozza. Mathematical modelling and computational reduction of molten glass fluid flow in a furnace melting basin. Computational and Applied Mathematics, 43(7):407, 2024. arXiv:2307.14700, doi:10.1007/s40314-024-02921-1.
Francesco Ballarin and Traian Iliescu. A priori error bounds for POD-ROMs for fluids: a brief survey. Submitted, 2024. arXiv:2409.00621.
Francesco Ballarin, Sanghyun Lee, and Son-Young Yi. Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity. Results in Applied Mathematics, 21:100430, 2024. arXiv:2309.01004, doi:10.1016/j.rinam.2023.100430.
Julien Genovese, Francesco Ballarin, Gianluigi Rozza, and Claudio Canuto. Weighted reduced order methods for uncertainty quantification in computational fluid dynamics. In Gianluigi Rozza, Giovanni Stabile, Max Gunzburger, and Marta D'Elia, editors, Reduction, Approximation, Machine Learning, Surrogates, Emulators and Simulators: RAMSES, pages 127–151. Springer Nature Switzerland, 2024. arXiv:2303.14432, doi:10.1007/978-3-031-55060-7_6.
Ian Moore, Anna Sanfilippo, Francesco Ballarin, and Traian Iliescu. A priori error bounds for the approximate deconvolution Leray reduced order model. Submitted, 2024. arXiv:2410.02673.
Gianluigi Rozza, Francesco Ballarin, Leonardo Scandurra, and Federico Pichi. Real Time Reduced Order Computational Mechanics. SISSA Springer Series. Springer Cham, 2024. ISBN 978-3-031-49891-6.
Imran Shah, Milad Samaee, Atefeh Razavi, Fateme Esmailie, Francesco Ballarin, Lakshmi P. Dasi, and Alessandro Veneziani. Reduced order modeling for real-time stent deformation simulations of transcatheter aortic valve prostheses. Annals of Biomedical Engineering, 52(2):208–225, 2024. doi:10.1007/s10439-023-03360-5.
Shafqat Ali, Francesco Ballarin, and Gianluigi Rozza. A reduced basis stabilization for the unsteady Stokes and Navier-Stokes equations. Advances in Computational Science and Engineering, 1(2):180–201, 2023. arXiv:2103.03553, doi:10.3934/acse.2023008.
Fabian Key, Max von Danwitz, Francesco Ballarin, and Gianluigi Rozza. Model order reduction for deforming domain problems in a time-continuous space-time setting. International Journal for Numerical Methods in Engineering, 124(23):5125–5150, 2023. arXiv:2303.16662, doi:10.1002/nme.7342.
Jaemin Kim, Ida Ang, Francesco Ballarin, Chung-Yuen Hui, and Nikolaos Bouklas. A finite element implementation of finite deformation surface and bulk poroelasticity. Computational Mechanics, 2023. arXiv:2305.08805, doi:10.1007/s00466-023-02398-5.
Monica Nonino, Francesco Ballarin, Gianluigi Rozza, and Yvon Maday. A reduced basis method by means of transport maps for a fluid-structure interaction problem with slowly decaying Kolmogorov n-width. Advances in Computational Science and Engineering, 1(1):36–58, 2023. arXiv:1911.06598, doi:10.3934/acse.2023002.
Monica Nonino, Francesco Ballarin, Gianluigi Rozza, and Yvon Maday. Projection based semi-implicit partitioned reduced basis method for fluid–structure interaction problems. Journal of Scientific Computing, 94(1):4, 2023. arXiv:2201.03236, doi:10.1007/s10915-022-02049-6.
Simona Perotto, Gloria Bellini, Francesco Ballarin, Karol Calò, Valentina Mazzi, and Umberto Morbiducci. Isogeometric hierarchical model reduction for advection-diffusion process simulation in microchannels. In Francisco Chinesta, Elías Cueto, Yohan Payan, and Jacques Ohayon, editors, Reduced Order Models for the Biomechanics of Living Organs, Biomechanics of Living Organs, pages 197–211. Academic Press, 2023. arXiv:2205.08127, doi:10.1016/B978-0-32-389967-3.00014-7.
Federico Pichi, Francesco Ballarin, Gianluigi Rozza, and Jan S. Hesthaven. An artificial neural network approach to bifurcating phenomena in computational fluid dynamics. Computers & Fluids, 254:105813, 2023. arXiv:2109.10765, doi:10.1016/j.compfluid.2023.105813.
Ivan Prusak, Monica Nonino, Davide Torlo, Francesco Ballarin, and Gianluigi Rozza. An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations. Computers & Mathematics with Applications, 151:172–189, 2023. arXiv:2211.14528, doi:10.1016/j.camwa.2023.09.039.
Anna Sanfilippo, Ian Moore, Francesco Ballarin, and Traian Iliescu. Approximate deconvolution Leray reduced order model for convection-dominated flows. Finite Elements in Analysis and Design, 226:104021, 2023. arXiv:2307.10817, doi:10.1016/j.finel.2023.104021.
Pierfrancesco Siena, Michele Girfoglio, Francesco Ballarin, and Gianluigi Rozza. Data-driven reduced order modelling for patient-specific hemodynamics of coronary artery bypass grafts with physical and geometrical parameters. Journal of Scientific Computing, 94(2):38, 2023. arXiv:2203.13682, doi:10.1007/s10915-022-02082-5.
Maria Strazzullo, Francesco Ballarin, Traian Iliescu, and Claudio Canuto. New feedback control and adaptive evolve-filter-relax regularization for the Navier-Stokes equations in the convection-dominated regime. Submitted, 2023. arXiv:2307.00675.
Francesco Ballarin, Gianluigi Rozza, and Maria Strazzullo. Space-time POD-Galerkin approach for parametric flow control. In Emmanuel Trélat and Enrique Zuazua, editors, Numerical Control: Part A, volume 23 of Handbook of Numerical Analysis, pages 307–338. Elsevier, 2022. arXiv:2011.12101, doi:10.1016/bs.hna.2021.12.009.
Michele Girfoglio, Francesco Ballarin, Giuseppe Infantino, Francesca Nicolò, Andrea Montalto, Gianluigi Rozza, Roberto Scrofani, Marina Comisso, and Francesco Musumeci. Non-intrusive PODI-ROM for patient-specific aortic blood flow in presence of a LVAD device. Medical Engineering & Physics, 107:103849, 2022. arXiv:2007.03527, doi:10.1016/j.medengphy.2022.103849.
Teeratorn Kadeethum, Francesco Ballarin, Youngsoo Choi, Daniel O'Malley, Hongkyu Yoon, and Nikolaos Bouklas. Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques. Advances in Water Resources, 160:104098, 2022. arXiv:2107.11460, doi:10.1016/j.advwatres.2021.104098.
Teeratorn Kadeethum, Francesco Ballarin, Daniel O'Malley, Youngsoo Choi, Nikolaos Bouklas, and Hongkyu Yoon. Reduced order modeling for flow and transport problems with Barlow twins self-supervised learning. Scientific Reports, 12(1):20654, 2022. arXiv:2202.05460, doi:10.1038/s41598-022-24545-3.
Teeratorn Kadeethum, Daniel O'Malley, Francesco Ballarin, Ida Ang, Jan N. Fuhg, Nikolaos Bouklas, Vinicius L. Silva, Pablo Salinas, Claire E. Heaney, Christopher C. Pain, Sanghyun Lee, Hari S. Viswanathan, and Hongkyu Yoon. Enhancing high-fidelity nonlinear solver with reduced order model. Scientific Reports, 12(1):20229, 2022. doi:10.1038/s41598-022-22407-6.
Efthymios N. Karatzas, Monica Nonino, Francesco Ballarin, and Gianluigi Rozza. A reduced order cut finite element method for geometrically parametrized steady and unsteady Navier–Stokes problems. Computers & Mathematics with Applications, 116:140–160, 2022. arXiv:2010.04953, doi:10.1016/j.camwa.2021.07.016.
Federico Pichi, Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza. Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier-Stokes equations with model order reduction. ESAIM: Mathematical Modelling and Numerical Analysis, 56(4):1361–1400, 2022. arXiv:2010.13506, doi:10.1051/m2an/2022044.
Gianluigi Rozza, Giovanni Stabile, and Francesco Ballarin. Advanced Reduced Order Methods and Applications in Computational Fluid Dynamics. Computational science and engineering. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2022. ISBN 978-1-611977-24-0. doi:10.1137/1.9781611977257.
Nirav V. Shah, Michele Girfoglio, Peregrina Quintela, Gianluigi Rozza, Alejandro Lengomin, Francesco Ballarin, and Patricia Barral. Finite element based model order reduction for parametrized one-way coupled steady state linear thermo-mechanical problems. Finite Elements in Analysis and Design, 212:103837, 2022. arXiv:2111.08534, doi:10.1016/j.finel.2022.103837.
Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza. POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations. Journal of Numerical Mathematics, 3(1):63–84, 2022. arXiv:2003.09695, doi:10.1515/jnma-2020-0098.
Maria Strazzullo, Michele Girfoglio, Francesco Ballarin, Traian Iliescu, and Gianluigi Rozza. Consistency of the full and reduced order models for evolve-filter-relax regularization of convection-dominated, marginally-resolved flows. International Journal for Numerical Methods in Engineering, 123(14):3148–3178, 2022. arXiv:2110.05093, doi:10.1002/nme.6942.
Giuseppe Carere, Maria Strazzullo, Francesco Ballarin, Gianluigi Rozza, and Rob Stevenson. A weighted POD-reduction approach for parametrized PDE-constrained optimal control problems with random inputs and applications to environmental sciences. Computers & Mathematics with Applications, 102:261–276, 2021. arXiv:2103.00632, doi:10.1016/j.camwa.2021.10.020.
Elisa Fevola, Francesco Ballarin, Laura Jiménez-Juan, Stephen Fremes, Stefano Grivet-Talocia, Gianluigi Rozza, and Piero Triverio. An optimal control approach to determine resistance-type boundary conditions from in-vivo data for cardiovascular simulations. International Journal for Numerical Methods in Biomedical Engineering, 37(10):e3516, 2021. arXiv:2104.13284, doi:10.1002/cnm.3516.
Michele Girfoglio, Leonardo Scandurra, Francesco Ballarin, Giuseppe Infantino, Francesca Nicolò, Andrea Montalto, Gianluigi Rozza, Roberto Scrofani, Marina Comisso, and Francesco Musumeci. Non-intrusive data-driven ROM framework for hemodynamics problems. Acta Mechanica Sinica, 37:1183–1191, 2021. arXiv:2010.08139, doi:10.1007/s10409-021-01090-2.
Teeratorn Kadeethum, Francesco Ballarin, and Nikolaos Bouklas. Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation. GEM - International Journal on Geomathematics, 12:12, 2021. arXiv:2101.11810, doi:10.1007/s13137-021-00180-4.
Teeratorn Kadeethum, Sanghyun Lee, Francesco Ballarin, Jinhyun Choo, and Hamid M. Nick. A locally conservative mixed finite element framework for coupled hydro-mechanical-chemical processes in heterogeneous porous media. Computers & Geosciences, 152:104774, 2021. arXiv:2010.04994, doi:10.1016/j.cageo.2021.104774.
Teeratorn Kadeethum, Hamid M. Nick, Sanghyun Lee, and Francesco Ballarin. Enriched Galerkin discretization for modeling poroelasticity and permeability alteration in heterogeneous porous media. Journal of Computational Physics, 427:110030, 2021. arXiv:2010.06653, doi:10.1016/j.jcp.2020.110030.
Monica Nonino, Francesco Ballarin, and Gianluigi Rozza. A monolithic and a partitioned, reduced basis method for fluid-structure interaction problems. Fluids, 6(6):229, 2021. arXiv:2104.09882, doi:10.3390/fluids6060229.
Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza. A certified reduced basis method for linear parametrized parabolic optimal control problems in space-time formulation. Submitted, 2021. arXiv:2103.00460.
Maria Strazzullo, Zakia Zainib, Francesco Ballarin, and Gianluigi Rozza. Reduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences. In Fred J. Vermolen and Cornelis Vuik, editors, Numerical Mathematics and Advanced Applications ENUMATH 2019, 841–850. Springer International Publishing, 2021. arXiv:1912.07886, doi:10.1007/978-3-030-55874-1_83.
Zakia Zainib, Francesco Ballarin, Stephen Fremes, Piero Triverio, Laura Jiménez-Juan, and Gianluigi Rozza. Reduced order methods for parametric optimal flow control in coronary bypass grafts, towards patient-specific data assimilation. International Journal for Numerical Methods in Biomedical Engineering, 37(12):e3367, 2021. arXiv:1911.01409, doi:10.1002/cnm.3367.
Matteo Zancanaro, Francesco Ballarin, Simona Perotto, and Gianluigi Rozza. Hierarchical model reduction techniques for flow modeling in a parametrized setting. Multiscale Modeling & Simulation, 19(1):267–293, 2021. arXiv:1909.01668, doi:10.1137/19M1285330.
Shafqat Ali, Francesco Ballarin, and Gianluigi Rozza. Stabilized reduced basis methods for parametrized steady Stokes and Navier-Stokes equations. Computers & Mathematics with Applications, 80(11):2399–2416, 2020. arXiv:2001.00820, doi:10.1016/j.camwa.2020.03.019.
Francesco Ballarin, Tomás Chacón Rebollo, Enrique Delgado Ávila, Macarena Gómez Mármol, and Gianluigi Rozza. Certified reduced basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height. Computers & Mathematics with Applications, 80(5):973–989, 2020. arXiv:1902.05729, doi:10.1016/j.camwa.2020.05.013.
Saddam Hijazi, Shafqat Ali, Giovanni Stabile, Francesco Ballarin, and Gianluigi Rozza. The effort of increasing Reynolds number in projection-based reduced order methods: from laminar to turbulent flows. In Harald van Brummelen, Alessandro Corsini, Simona Perotto, and Gianluigi Rozza, editors, Numerical Methods for Flows: FEF 2017 Selected Contributions, 245–264. Springer International Publishing, 2020. arXiv:1807.11370, doi:10.1007/978-3-030-30705-9_22.
Teeratorn Kadeethum, Hamid M. Nick, Sanghyun Lee, and Francesco Ballarin. Flow in porous media with low dimensional fractures by employing enriched Galerkin method. Advances in Water Resources, 142:103620, 2020. doi:10.1016/j.advwatres.2020.103620.
Efthymios N. Karatzas, Francesco Ballarin, and Gianluigi Rozza. Projection-based reduced order models for a cut finite element method in parametrized domains. Computers & Mathematics with Applications, 79(3):833–851, 2020. arXiv:1901.03846, doi:10.1016/j.camwa.2019.08.003.
Simona Perotto, Michele Giuliano Carlino, and Francesco Ballarin. Model reduction by separation of variables: a comparison between hierarchical model reduction and proper generalized decomposition. In Spencer J. Sherwin, David Moxey, Joaquim Peiró, Peter E. Vincent, and Christoph Schwab, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, 61–77. Springer International Publishing, 2020. arXiv:1811.11486, doi:10.1007/978-3-030-39647-3_4.
Gianluigi Rozza, Martin Hess, Giovanni Stabile, Marco Tezzele, and Francesco Ballarin. Basic ideas and tools for projection-based model reduction of parametric partial differential equations. In Peter Benner, Stefano Grivet-Talocia, Alfio Quarteroni, Gianluigi Rozza, Wil H.A. Schilders, and Luís M. Silveira, editors, Model Order Reduction, Volume 2: Snapshot-Based Methods and Algorithms. De Gruyter, 2020. arXiv:1911.08954, doi:10.1515/9783110671490-001.
Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza. POD–Galerkin model order reduction for parametrized time dependent linear quadratic optimal control problems in saddle point formulation. Journal of Scientific Computing, 83(3):55, 2020. arXiv:1909.09631, doi:10.1007/s10915-020-01232-x.
Francesco Ballarin, Alessandro D'Amario, Simona Perotto, and Gianluigi Rozza. A POD-selective inverse distance weighting method for fast parametrized shape morphing. International Journal for Numerical Methods in Engineering, 117(8):860–884, 2019. arXiv:1710.09243, doi:10.1002/nme.5982.
Giovanni Stabile, Francesco Ballarin, Giacomo Zuccarino, and Gianluigi Rozza. A reduced order variational multiscale approach for turbulent flows. Advances in Computational Mathematics, 45(5):2349–2368, 2019. arXiv:1809.11101, doi:10.1007/s10444-019-09712-x.
Luca Venturi, Francesco Ballarin, and Gianluigi Rozza. A weighted POD method for elliptic PDEs with random inputs. Journal of Scientific Computing, 81(1):136–153, 2019. arXiv:1802.08724, doi:10.1007/s10915-018-0830-7.
Luca Venturi, Davide Torlo, Francesco Ballarin, and Gianluigi Rozza. Weighted reduced order methods for parametrized partial differential equations with random inputs. In Flavio Canavero, editor, Uncertainty Modeling for Engineering Applications, 27–40. Springer International Publishing, 2019. arXiv:1805.00828, doi:10.1007/978-3-030-04870-9_2.
Maria Strazzullo, Francesco Ballarin, Renzo Mosetti, and Gianluigi Rozza. Model reduction for parametrized optimal control problems in environmental marine sciences and engineering. SIAM Journal on Scientific Computing, 40(4):B1055–B1079, 2018. arXiv:1710.01640, doi:10.1137/17M1150591.
Marco Tezzele, Francesco Ballarin, and Gianluigi Rozza. Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods. In Daniele Boffi, Luca F. Pavarino, Gianluigi Rozza, Simone Scacchi, and Christian Vergara, editors, Mathematical and Numerical Modeling of the Cardiovascular System and Applications, pages 185–207. Springer International Publishing, Cham, 2018. arXiv:1711.10884, doi:10.1007/978-3-319-96649-6_8.
Davide Torlo, Francesco Ballarin, and Gianluigi Rozza. Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs. SIAM/ASA Journal on Uncertainty Quantification, 6(4):1475–1502, 2018. arXiv:1711.11275, doi:10.1137/17M1163517.
Francesco Ballarin, Elena Faggiano, Andrea Manzoni, Alfio Quarteroni, Gianluigi Rozza, Sonia Ippolito, Carlo Antona, and Roberto Scrofani. Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts. Biomechanics and Modeling in Mechanobiology, 16(4):1373–1399, 2017. doi:10.1007/s10237-017-0893-7.
Francesco Ballarin, Gianluigi Rozza, and Yvon Maday. Reduced-order semi-implicit schemes for fluid-structure interaction problems. In Peter Benner, Mario Ohlberger, Anthony Patera, Gianluigi Rozza, and Karsten Urban, editors, Model Reduction of Parametrized Systems, volume 17, pages 149–167. Springer International Publishing, 2017. arXiv:1711.10829, doi:10.1007/978-3-319-58786-8_10.
Tomás Chacón Rebollo, Enrique Delgado Ávila, Macarena Gómez Mármol, Francesco Ballarin, and Gianluigi Rozza. On a certified Smagorinsky reduced basis turbulence model. SIAM Journal on Numerical Analysis, 55(6):3047–3067, 2017. arXiv:1709.00243, doi:10.1137/17M1118233.
Francesco Ballarin, Elena Faggiano, Sonia Ippolito, Andrea Manzoni, Alfio Quarteroni, Gianluigi Rozza, and Roberto Scrofani. Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization. Journal of Computational Physics, 315:609–628, 2016. doi:10.1016/j.jcp.2016.03.065.
Francesco Ballarin and Gianluigi Rozza. POD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems. International Journal for Numerical Methods in Fluids, 82(12):1010–1034, 2016. doi:10.1002/fld.4252.
Filippo Salmoiraghi, Francesco Ballarin, Giovanni Corsi, Andrea Mola, Marco Tezzele, and Gianluigi Rozza. Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives. In Manolis Papadrakakis, Vissarion Papadopoulos, George Stefanou, and Vagelis Plevris, editors, Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering. 2016. doi:10.7712/100016.1867.8680.
Filippo Salmoiraghi, Francesco Ballarin, Luca Heltai, and Gianluigi Rozza. Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes. Advanced Modeling and Simulation in Engineering Sciences, 3(1):21, 2016. doi:10.1186/s40323-016-0076-6.
Francesco Ballarin. Reduced order models for patient-specific haemodynamics of coronary artery bypass grafts. PhD thesis, Politecnico di Milano, 2015. URL: https://www.politesi.polimi.it/handle/10589/102804.
Francesco Ballarin, Andrea Manzoni, Alfio Quarteroni, and Gianluigi Rozza. Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations. International Journal for Numerical Methods in Engineering, 102(5):1136–1161, 2015. doi:10.1002/nme.4772.
Francesco Ballarin, Andrea Manzoni, Gianluigi Rozza, and Sandro Salsa. Shape optimization by free-form deformation: existence results and numerical solution for Stokes flows. Journal of Scientific Computing, 60(3):537–563, 2014. doi:10.1007/s10915-013-9807-8.
Francesco Ballarin. Shape optimization for tridimensional viscous flows in cardiovascular geometries. Master's thesis, Politecnico di Milano, 2011. URL: https://www.politesi.polimi.it/handle/10589/30601.
Francesco Ballarin and Simone Palamara. Macroscopic models and numerical simulations for traffic flow on networks. Bachelor's thesis, Politecnico di Milano, 2009. URL: https://www.mate.polimi.it/biblioteca/?pp=view&id=277&collezione=tesi&L=i.