Giovanni Fantuzzi

2025

• Alcalde Zafra A., Fantuzzi G., Zuazua Iriondo E.:
  Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis
  In: SIAM Journal on Mathematics of Data Science 7 (2025)
  ISSN: 2577-0187
  DOI: 10.1137/24M167086X
  URL: https://arxiv.org/abs/2407.01602
• Alcalde Zafra A., Fantuzzi G., Zuazua Iriondo E.:
  Exact Sequence Classification with Hardmax Transformers (Conference contribution, submitted)
  URL: https://arxiv.org/abs/2502.02270

2024

• Arslan A., Fantuzzi G., Craske J., Wynn A.:
  Internal heating profiles for which downward conduction is impossible
  In: Journal of Fluid Mechanics 993 (2024)
  ISSN: 0022-1120
  DOI: 10.1017/jfm.2024.590
• Bramburger JJ., Fantuzzi G.:
  Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization
  In: Journal of Nonlinear Science 34 (2024), Article No.: 8
  ISSN: 0938-8974
  DOI: 10.1007/s00332-023-09990-2
  URL: https://arxiv.org/abs/2303.01483
• Bramburger JJ., Fantuzzi G.:
  Data-driven discovery of invariant measures
  In: Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences 480 (2024), Article No.: 20230627
  ISSN: 1364-5021
  DOI: 10.1098/rspa.2023.0627
• Della Pietra F., Fantuzzi G., Ignat LI., Masiello AL., Paoli G., Zuazua Iriondo E.:
  Finite Element Approximation of the Hardy Constant
  In: Journal of Convex Analysis 31 (2024), p. 497-523
  ISSN: 0944-6532
• Fantuzzi G., Fuentes F.:
  Global minimization of polynomial integral functionals
  In: SIAM Journal on Scientific Computing 46 (2024)
  ISSN: 1064-8275
  DOI: 10.1137/23M1592584
• Fantuzzi G., Tobasco I.:
  Sharpness and non-sharpness of occupation measure bounds for integral variational problems
  (2024)
  Open Access: https://arxiv.org/abs/2207.13570
  URL: https://arxiv.org/abs/2207.13570

2023

• Arslan A., Fantuzzi G., John C., Wynn A.:
  Rigorous scaling laws for internally heated convection at infinite Prandtl number
  In: Journal of Mathematical Physics 64 (2023), Article No.: 023101
  ISSN: 0022-2488
  DOI: 10.1063/5.0098250
• Covella F., Fantuzzi G.:
  Uncertainty propagation for nonlinear dynamics: A polynomial optimization approach
  American Control Conference (ACC) (San Diego, CA, May 31, 2023 - June 2, 2023)
  In: IEEE (ed.): 2023 American Control Conference (ACC) 2023
  DOI: 10.23919/ACC55779.2023.10156169
  URL: https://arxiv.org/abs/2209.07432
• Fantuzzi G., Chernyavsky A., Goluskin D., Bramburger J.:
  Convex Relaxations of Integral Variational Problems: Pointwise Dual Relaxation and Sum-of-Squares Optimization
  In: SIAM Journal on Optimization (2023)
  ISSN: 1052-6234
  DOI: 10.1137/21m1455127
• Song B., Fantuzzi G., Tobasco I.:
  Bounds on heat transfer by incompressible flows between balanced sources and sinks
  In: Physica D-Nonlinear Phenomena 444 (2023), Article No.: 133591
  ISSN: 0167-2789
  DOI: 10.1016/j.physd.2022.133591

2022

• Fantuzzi G.:
  Verification of some functional inequalities via polynomial optimization
  18th IFAC Workshop on Control Applications of Optimization, CAO 2022 (Gif sur Yvette, July 18, 2022 - July 22, 2022)
  In: Filippova Tatiana (ed.): IFAC-PapersOnLine 2022
  DOI: 10.1016/j.ifacol.2022.09.018
• Fantuzzi G., Arslan A., Wynn A.:
  The background method: Theory and computations
  In: Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences 380 (2022), Article No.: 20210038
  ISSN: 1364-503X
  DOI: 10.1098/rsta.2021.0038
• Kumar A., Arslan A., Fantuzzi G., Craske J., Wynn A.:
  Analytical bounds on the heat transport in internally heated convection
  In: Journal of Fluid Mechanics 938 (2022), Article No.: A26
  ISSN: 0022-1120
  DOI: 10.1017/jfm.2022.170

2021

• Arslan A., Fantuzzi G., Craske J., Wynn A.:
  Bounds for internally heated convection with fixed boundary heat flux
  In: Journal of Fluid Mechanics 922 (2021), Article No.: R1
  ISSN: 0022-1120
  DOI: 10.1017/jfm.2021.527
• Arslan A., Fantuzzi G., Craske J., Wynn A.:
  Bounds on heat transport for convection driven by internal heating
  In: Journal of Fluid Mechanics 919 (2021), Article No.: A15
  ISSN: 0022-1120
  DOI: 10.1017/jfm.2021.360
• Lakshmi MV., Fantuzzi G., Chernyshenko SI., Lasagna D.:
  Finding unstable periodic orbits: A hybrid approach with polynomial optimization
  In: Physica D-Nonlinear Phenomena 427 (2021), Article No.: 133009
  ISSN: 0167-2789
  DOI: 10.1016/j.physd.2021.133009
• Zheng Y., Fantuzzi G.:
  Sum-of-squares chordal decomposition of polynomial matrix inequalities
  In: Mathematical Programming (2021)
  ISSN: 0025-5610
  DOI: 10.1007/s10107-021-01728-w
• Zheng Y., Fantuzzi G., Papachristodoulou A.:
  Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization
  In: Annual Reviews in Control 52 (2021), p. 243-279
  ISSN: 1367-5788
  DOI: 10.1016/j.arcontrol.2021.09.001

2020

• Fantuzzi G., Goluskin D.:
  Bounding extreme events in nonlinear dynamics using convex optimization
  In: SIAM Journal on Applied Dynamical Systems 19 (2020), p. 1823-1864
  ISSN: 1536-0040
  DOI: 10.1137/19M1277953
• Lakshmi M., Fantuzzi G., Fernandez-Caballero JD., Hwang Y., Chernyshenko S.:
  Finding extremal periodic orbits with polynomial optimization, with application to a nine-mode model of shear flow
  In: SIAM Journal on Applied Dynamical Systems 19 (2020), p. 763-787
  ISSN: 1536-0040
  DOI: 10.1137/19M1267647
• Pachev B., Whitehead JP., Fantuzzi G., Grooms I.:
  Rigorous bounds on the heat transport of rotating convection with Ekman pumping
  In: Journal of Mathematical Physics 61 (2020), Article No.: 023101
  ISSN: 0022-2488
  DOI: 10.1063/1.5134054
• Zheng Y., Fantuzzi G., Papachristodoulou A., Goulart P., Wynn A.:
  Chordal decomposition in operator-splitting methods for sparse semidefinite programs
  In: Mathematical Programming 180 (2020), p. 489-532
  ISSN: 0025-5610
  DOI: 10.1007/s10107-019-01366-3

2019

• Fantuzzi G., Nobili C., Wynn A.:
  New bounds on the vertical heat transport for Bénard-Marangoni convection at infinite Prandtl number
  In: Journal of Fluid Mechanics 885 (2019), Article No.: R4
  ISSN: 0022-1120
  DOI: 10.1017/jfm.2019.1029
• Goluskin D., Fantuzzi G.:
  Bounds on mean energy in the Kuramoto-Sivashinsky equation computed using semidefinite programming
  In: Nonlinearity 32 (2019), p. 1705-1730
  ISSN: 0951-7715
  DOI: 10.1088/1361-6544/ab018b
• Zheng Y., Fantuzzi G., Papachristodoulou A.:
  Fast ADMM for sum-of-squares programs using partial orthogonality
  In: IEEETransactions on Automatic Control 64 (2019), p. 3869-3876
  ISSN: 0018-9286
  DOI: 10.1109/TAC.2018.2886170
• Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou:
  Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials
  2019 American Control Conference, ACC 2019 (Philadelphia, PA, July 10, 2019 - July 12, 2019)
  In: Proceedings of the American Control Conference 2019
  DOI: 10.23919/acc.2019.8814998

2018

• Fantuzzi G.:
  Bounds for Rayleigh–Bénard convection between free-slip boundaries with an imposed heat flux
  In: Journal of Fluid Mechanics 837 (2018), Article No.: 837
  ISSN: 0022-1120
  DOI: 10.1017/jfm.2017.907
• Fantuzzi G., Pershin A., Wynn A.:
  Bounds on heat transfer for Bénard-Marangoni convection at infinite Prandtl number
  In: Journal of Fluid Mechanics 837 (2018), p. 562-596
  ISSN: 0022-1120
  DOI: 10.1017/jfm.2017.858
• Zheng Y., Fantuzzi G., Papachristodoulou A.:
  Decomposition methods for large-scale semidefinite programs with chordal aggregate sparsity and partial orthogonality
  DOI: 10.1007/978-3-319-97478-1_3
• Zheng Y., Papachristodoulou A., Fantuzzi G.:
  Decomposition and Completion of Sum-of-Squares Matrices
  57th IEEE Conference on Decision and Control, CDC 2018 (Miami, FL, USA, December 17, 2018 - December 19, 2018)
  In: Proceedings of the IEEE Conference on Decision and Control 2018
  DOI: 10.1109/CDC.2018.8619144

2017

• Fantuzzi G., Wynn A.:
  Exact energy stability of Bénard-Marangoni convection at infinite Prandtl number
  In: Journal of Fluid Mechanics 822 (2017), p. R1-
  ISSN: 0022-1120
  DOI: 10.1017/jfm.2017.323
• Fantuzzi G., Wynn A., Goulart PJ., Papachristodoulou A.:
  Optimization with affine homogeneous quadratic integral inequality constraints
  In: IEEETransactions on Automatic Control 62 (2017), p. 6221-6236
  ISSN: 0018-9286
  DOI: 10.1109/TAC.2017.2703927
• Zheng Y., Fantuzzi G., Papachristodoulou A.:
  Exploiting sparsity in the coefficient matching conditions in sum-of-squares programming using ADMM
  In: IEEE Control Systems Letters 1 (2017), p. 80-85
  ISSN: 2475-1456
  DOI: 10.1109/LCSYS.2017.2706941
• Zheng Y., Fantuzzi G., Papachristodoulou A., Goulart P., Wynn A.:
  Fast ADMM for homogeneous self-dual embedding of sparse SDPs
  In: IFAC-PapersOnLine 2017
  DOI: 10.1016/j.ifacol.2017.08.1569
• Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou, Paul Goulart, Andrew Wynn:
  Fast ADMM for semidefinite programs with chordal sparsity
  2017 American Control Conference, ACC 2017 (Seattle, WA, May 24, 2017 - May 26, 2017)
  In: Proceedings of the American Control Conference 2017
  DOI: 10.23919/ACC.2017.7963462

2016

• Fantuzzi G., Goluskin D., Huang D., Chernyshenko SI.:
  Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization
  In: SIAM Journal on Applied Dynamical Systems 15 (2016), p. 1962-1988
  ISSN: 1536-0040
  DOI: 10.1137/15M1053347
• Fantuzzi G., Wynn A.:
  Semidefinite relaxation of a class of quadratic integral inequalities
  55th IEEE Conference on Decision and Control, CDC 2016 (Las Vegas, NV, December 12, 2016 - December 14, 2016)
  In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016 2016
  DOI: 10.1109/CDC.2016.7799221
• Wynn A., Fantuzzi G.:
  Optimal bounds with semidefinite programming: An application to stress-driven shear flows
  In: Physical Review E 93 (2016), Article No.: 043308
  ISSN: 2470-0045
  DOI: 10.1103/PhysRevE.93.043308

2015

• Wynn A., Fantuzzi G.:
  Construction of an optimal background profile for the Kuramoto-Sivashinsky equation using semidefinite programming
  In: Physics Letters A 379 (2015), p. 23-32
  ISSN: 0375-9601
  DOI: 10.1016/j.physleta.2014.10.039