Prof. Dr. Giovanni Fantuzzi
Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship
Friedrich-Alexander-Universität Erlangen-Nürnberg
giovanni.fantuzzi@fau.de
See my profile at FAU
optimization, dynamical systems, fluid mechanics, partial differential equations (PDEs), nonlinear differential equations, mathematical analysis, convex optimization
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IMC Seminar: Data-driven system analysis: Polynomial optimization meets Koopman, October 30, 2024
Poster: Clustering in Pure-attention Hardmax Transformers and Its Role in Sentiment Analysis (Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua) | see poster. Conference on Control, Inversion and Numerics for PDEs, October 7-10, 2024. Fudan University, Shanghai
Publications
2024
Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis
(2024)
DOI: 10.48550/arXiv.2407.01602
URL: https://arxiv.org/abs/2407.01602 , , :
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 , :
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 , :
Finite Element Approximation of the Hardy Constant
In: Journal of Convex Analysis 31 (2024), p. 497-523
ISSN: 0944-6532 , , , , , :
Finite element approximation of the Hardy constant
(2024)
DOI: 10.48550/arXiv.2308.01580 , , , , , :
Global minimization of polynomial integral functionals
In: SIAM Journal on Scientific Computing 46 (2024)
ISSN: 1064-8275
DOI: 10.1137/23M1592584 , :
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
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 , , , :
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 , :
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 , , , :
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
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 :
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 , , :
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
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 , , , :
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 , , , :
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 , , , :
Sum-of-squares chordal decomposition of polynomial matrix inequalities
In: Mathematical Programming (2021)
ISSN: 0025-5610
DOI: 10.1007/s10107-021-01728-w , :
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
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 , :
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 , , , , :
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 , , , :
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
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 , , :
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 , :
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
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 :
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 , , :
Decomposition methods for large-scale semidefinite programs with chordal aggregate sparsity and partial orthogonality
DOI: 10.1007/978-3-319-97478-1_3 , , :
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
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 , :
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 , , , :
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 , , :
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
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 , , , :
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 , :
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
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 , :
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