Prof. Dr. Giovanni Fantuzzi
Email • PhD in Aeronautics, Imperial College
Optimization, dynamical systems, fluid mechanics, and partial differential equations (PDEs)
W1 Professor | Senior Scientist
Room 03.318 | FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship
FAU MoD member, Research Center for Mathematics of Data
Friedrich-Alexander-Universität Erlangen-Nürnberg
Naturwissenschaftliche Fakultät. Department Mathematik
ORCID | Google Scholar | LinkedIn | X
I am a W1 Professor in the Department of Mathematics at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg.
Before joining FAU, I held an Imperial College Research Fellowship in the Department of Aeronautics, where I also received a PhD and a Master Eng. in Aeronautics degrees.
Alongside my PhD, I held a research position in Engineering Science at the University of Oxford.
I was awarded a Geophysical Fluid Dynamics Fellowship at WHOI (2015) and an EPSRC Doctoral Prize Fellowship (2018).
• PhD Thesis: Construction of optimal background fields using semidefinite programming (May 2018)
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Research interests
My work spans optimization, dynamical systems, fluid mechanics, and partial differential equations (PDEs).
In particular, I seek to study nonlinear differential equations using a mix of mathematical analysis and numerical tools for convex optimization.
I used this multidisciplinary approach to derive a priori scaling laws for heat transport problems and, more recently, to construct numerical schemes that provably approximate global optimizers of nonlinear PDE-constrained problems.
I am also interested in developing fast algorithms for large-scale optimization problems with structure, especially conic problems and polynomial optimization problems.
Projects
• DTN ModConFlex. Modelling and control of flexible structures interacting with fluids (2023 – 2027)
Awards
• Geophysical Fluid Dynamics Fellowship (2015) WHOI
• EPSRC Doctoral Prize Fellowship (2018) Imperial College London
Academy
• WS 24/25: Data-driven methods for dynamical systems (2024 – 2025)
• WS 24/25: Polynomial optimization and applications (2024 – 2025)
• WS 23/24: Data-driven methods for dynamical systems (2023 – 2024)
• WS 23/24: Polynomial optimization and applications (2023 – 2024)
• WS 22/23: Conic Optimization and Applications. Lectures and exercises (2022 – 2023)
• WS 22/23: Mathematik für Ingenieure B1. Exercise class in English (2022 – 2023)
Posts on Math & Research
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Sentiment Analysis with Transformers
Authors: Albert Alcalde, Giovanni Fantuzzi
Date: November 14, 2025
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News / Initiatives
Lyapunov meets Koopman: a new approach to data-driven analysis of nonlinear dynamics. FAU MoD Workshop, Erlangen – Bavaria (Germany)
Authors: Giovanni Fantuzzi
Date: December 10, 2025
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Sentimentanalyse mit Transformern in Aktion. #NdW25 Long Night Sciences
Authors: Giovanni Fantuzzi, Albert Alcalde
Date: October 25, 2025
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Poster: Clustering in Pure-attention Hardmax Transformers and Its Role in Sentiment Analysis
Authors: Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua
Date: October 01, 2024
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Exact sequence prediction with transformers. FAU MoD Lecture & Workshop: AI for maths and maths for AI
Authors: François Charton, Giovanni Fantuzzi
Date: June 24, 2025
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#MLPDES25. Data-driven system analysis: Polynomial optimization meets Koopman Machine Learning and PDEs Workshop (2025)
Authors: Giovanni Fantuzzi (speaker)
Date: April 28 – 30, 2025
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Data-driven system analysis: Polynomial optimization meets Koopman. IMC Seminar (UC Chile University)
Authors: Giovanni Fantuzzi
Date: October 30, 2024
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Clustering in Pure-attention Hardmax Transformers and Its Role in Sentiment Analysis. Conference on Control, Inversion and Numerics for PDEs. Fudan University (Shanghai)
Authors: Albert Alcalde, Giovanni Fantuzzi, Enrique Zuazua
Date: October 7 – 10, 2024
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Polynomial Optimization for Nonlinear Dynamics: Theory, Algorithms, and Applications. Oberwolfach Seminar (2431)
Authors: Giovanni Fantuzzi (FAU), David Goluskin (Victoria), Jean-Bernard Lasserre
Date: July 28 – August 02, 2024
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Moment-Sum-of-Squares relaxations for variational problems. Nečas Seminar on Continuum Mechanics
Authors: Giovanni Fantuzzi
Date: May 13, 2024
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Data-driven system analysis: Polynomial optimization meets Koopman. Aerodynamics & Control Seminars
Authors: Giovanni Fantuzzi
Date: October 19, 2023
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Discovering scaling laws for heat transport with convex optimization. FAU DCN-AvH Seminar
Authors: Giovanni Fantuzzi
Date: November 10, 2022
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Publications
2026
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Exact Sequence Classification with Transformers (Conference contribution, accepted)
URL: https://arxiv.org/abs/2502.02270
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Exact Sequence Interpolation with Transformers
(2026)
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2025
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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
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2024
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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
BibTeX: Download - , :
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
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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
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Finite Element Approximation of the Hardy Constant
In: Journal of Convex Analysis 31 (2024), p. 497-523
ISSN: 0944-6532
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Global minimization of polynomial integral functionals
In: SIAM Journal on Scientific Computing 46 (2024)
ISSN: 1064-8275
DOI: 10.1137/23M1592584
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2023
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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
BibTeX: Download - , :
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
BibTeX: Download - , , , :
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
BibTeX: Download - , , :
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
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2022
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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
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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
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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
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2021
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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
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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
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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
BibTeX: Download - , :
Sum-of-squares chordal decomposition of polynomial matrix inequalities
In: Mathematical Programming (2021)
ISSN: 0025-5610
DOI: 10.1007/s10107-021-01728-w
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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
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2020
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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
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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
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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
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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
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2019
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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
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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
BibTeX: Download - , , :
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
BibTeX: Download - 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
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2018
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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
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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
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Decomposition methods for large-scale semidefinite programs with chordal aggregate sparsity and partial orthogonality
DOI: 10.1007/978-3-319-97478-1_3
BibTeX: Download - , , :
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
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2017
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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
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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
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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
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Fast ADMM for homogeneous self-dual embedding of sparse SDPs
In: IFAC-PapersOnLine 2017
DOI: 10.1016/j.ifacol.2017.08.1569
BibTeX: Download - 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
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2016
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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
BibTeX: Download - , :
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
BibTeX: Download - , :
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
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2015
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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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