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  1. Book ; Online: Auxiliary Functions as Koopman Observables

    Bramburger, Jason J. / Fantuzzi, Giovanni

    Data-Driven Analysis of Dynamical Systems via Polynomial Optimization

    2023  

    Abstract: We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented as a ... ...

    Abstract We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented as a semidefinite program that can be solved numerically. Furthermore, the method is agnostic of whether data is generated through a deterministic or stochastic process, so its implementation requires no prior adjustments by the user to accommodate these different scenarios. Rigorous convergence results justify the applicability of the method, while also extending and uniting similar results from across the literature. Examples on discovering Lyapunov functions, performing ergodic optimization, and bounding extrema over attractors for both deterministic and stochastic dynamics exemplify these convergence results and demonstrate the performance of the method.

    Comment: We have significantly expanded the presentation. This has improved the presentation and made the paper more readable. Comments welcome
    Keywords Mathematics - Dynamical Systems ; Computer Science - Machine Learning ; Mathematics - Optimization and Control
    Publishing date 2023-03-02
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Article ; Online: The background method: theory and computations.

    Fantuzzi, Giovanni / Arslan, Ali / Wynn, Andrew

    Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

    2022  Volume 380, Issue 2225, Page(s) 20210038

    Abstract: The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numerical implementation of the method. First, we describe how the background ... ...

    Abstract The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numerical implementation of the method. First, we describe how the background method can be formulated systematically within a broader 'auxiliary function' framework for bounding mean quantities, and explain how symmetries of the flow and constraints such as maximum principles can be exploited. All ideas are presented in a general setting and are illustrated on Rayleigh-Bénard convection between stress-free isothermal plates. Second, we review a semidefinite programming approach and a timestepping approach to optimizing bounds computationally, revealing that they are related to each other through convex duality and low-rank matrix factorization. Open questions and promising directions for further numerical analysis of the background method are also outlined. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.
    Language English
    Publishing date 2022-04-25
    Publishing country England
    Document type Journal Article ; Review
    ZDB-ID 208381-4
    ISSN 1471-2962 ; 0080-4614 ; 0264-3820 ; 0264-3952 ; 1364-503X
    ISSN (online) 1471-2962
    ISSN 0080-4614 ; 0264-3820 ; 0264-3952 ; 1364-503X
    DOI 10.1098/rsta.2021.0038
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Book ; Online: Bounds for internally heated convection with fixed boundary heat flux

    Arslan, Ali / Fantuzzi, Giovanni / Craske, John / Wynn, Andrew

    2021  

    Abstract: We prove a new rigorous bound for the mean convective heat transport $\langle w T \rangle$, where $w$ and $T$ are the nondimensional vertical velocity and temperature, in internally heated convection between an insulating lower boundary and an upper ... ...

    Abstract We prove a new rigorous bound for the mean convective heat transport $\langle w T \rangle$, where $w$ and $T$ are the nondimensional vertical velocity and temperature, in internally heated convection between an insulating lower boundary and an upper boundary with a fixed heat flux. The quantity $\langle wT \rangle$ is equal to half the ratio of convective to conductive vertical heat transport, and also to $\frac12$ plus the mean temperature difference between the top and bottom boundaries. An analytical application of the background method based on the construction of a quadratic auxiliary function yields $\langle w T \rangle \leq \tfrac{1}{2}\big(\tfrac{1}{2}+ \tfrac{1}{\sqrt{3}} \big) - 1.6552\, R^{-\frac13}$ uniformly in the Prandtl number, where $R$ is the nondimensional control parameter measuring the strength of the internal heating. Numerical optimisation of the auxiliary function suggests that the asymptotic value of this bound and the $-1/3$ exponent are optimal within our bounding framework. This new result halves the best existing (uniform in $R$) bound (Goluskin 2016, Springer, Table 1.2) and its dependence on $R$ is consistent with previous conjectures and heuristic scaling arguments. Contrary to physical intuition, however, it does not rule out a mean heat transport larger than $\frac12$ at high $R$, which corresponds to the top boundary being hotter than the bottom one on average.

    Comment: 11 pages, 3 figures
    Keywords Physics - Fluid Dynamics
    Subject code 532 ; 551
    Publishing date 2021-03-30
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Book ; Online: Decomposition and Completion of Sum-of-Squares Matrices

    Zheng, Yang / Fantuzzi, Giovanni / Papachristodoulou, Antonis

    2018  

    Abstract: This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices that are ... ...

    Abstract This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices that are nonzero only on a principal submatrix. Also, the completion of an SOS matrix is equivalent to a set of SOS conditions on its principal submatrices and a consistency condition on the Gram representation of the principal submatrices. These results are partial extensions of chordal decomposition and completion of scalar matrices to matrices with polynomial entries. We apply the SOS decomposition result to exploit sparsity in matrix-valued SOS programs. Numerical results demonstrate the high potential of this approach for solving large-scale sparse matrix-valued SOS programs.

    Comment: 6 pages
    Keywords Mathematics - Optimization and Control ; Electrical Engineering and Systems Science - Systems and Control
    Subject code 519
    Publishing date 2018-04-08
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Book ; Online: Sparse sum-of-squares (SOS) optimization

    Zheng, Yang / Fantuzzi, Giovanni / Papachristodoulou, Antonis

    A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials

    2018  

    Abstract: Optimization over non-negative polynomials is fundamental for nonlinear systems analysis and control. We investigate the relation between three tractable relaxations for optimizing over sparse non-negative polynomials: sparse sum-of-squares (SSOS) ... ...

    Abstract Optimization over non-negative polynomials is fundamental for nonlinear systems analysis and control. We investigate the relation between three tractable relaxations for optimizing over sparse non-negative polynomials: sparse sum-of-squares (SSOS) optimization, diagonally dominant sum-of-squares (DSOS) optimization, and scaled diagonally dominant sum-of-squares (SDSOS) optimization. We prove that the set of SSOS polynomials, an inner approximation of the cone of SOS polynomials, strictly contains the spaces of sparse DSOS/SDSOS polynomials. When applicable, therefore, SSOS optimization is less conservative than its DSOS/SDSOS counterparts. Numerical results for large-scale sparse polynomial optimization problems demonstrate this fact, and also that SSOS optimization can be faster than DSOS/SDSOS methods despite requiring the solution of semidefinite programs instead of less expensive linear/second-order cone programs.

    Comment: 9 pages, 3 figures
    Keywords Mathematics - Optimization and Control ; Electrical Engineering and Systems Science - Systems and Control
    Subject code 511 ; 510
    Publishing date 2018-07-14
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Book: Notizie degli scrittori bolognesi,

    Fantuzzi, Giovanni

    1781  

    Author's details raccolte da Giovanni Fantuzzi
    Keywords Bologna / biobibliography ; Italian literature / Bologna - bibliography
    Language Italian
    Dates of publication 1781-1794
    Size 9 v.
    Publisher Stamperia di S. Tommaso d'Aquino
    Publishing place Bologna
    Document type Book
    Database Catalogue of the US National Library of Medicine (NLM)

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  7. Book: Memorie della vita di Ulisse Aldrovandi medico e filosofo Bolognese

    Fantuzzi, Giovanni

    con alcune lettere scelte d'uomini eruditi a lui scritte, e coll'indice delle sue opere mss., che si conservano nella Biblioteca dell'Istituto

    1774  

    MeSH term(s) Physicians
    Keywords Italy
    Language Italian
    Size vi, [2], 263, [1] p., [1] leaf of plate :, ill., port. ;, 20 cm. (8vo)
    Publisher Per le stampe di Lelio dalla Volpe
    Publishing place In Bologna
    Document type Book
    Note Author from dedication, p. iii. ; Signatures: a⁴ A-Q⁸ R⁴. ; Engraved frontispiece portrait. ; Engraved printer's device on t.p. ; Engraved medallion, p. [viii].
    Database Catalogue of the US National Library of Medicine (NLM)

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