64 citations · 563 across the 39 of their papers we have counts for
39 papers
Optimizing bounds for energy-constrained optimal cooling problems in two dimensions
Pedro Blöss Braga, Giovanni Fantuzzi
We study optimal control problems for incompressible fluids in two-dimensional domains with a cold boundary and internal heat sources and sinks. Given a kinetic energy budget, meas…
Polyconvexity with Moments and Sums of Squares
Giovanni Fantuzzi, Didier Henrion, Martin Kru{ž}ík +2
A function of a matrix is polyconvex when it can be expressed as a convex function of the matrix minors. Polyconvexity is a regularity condition ensuring existence of minimizers in…
Internal heating profiles for which downward conduction is impossible
Ali Arslan, Giovanni Fantuzzi, John Craske +1
We consider an internally heated fluid between parallel plates with fixed thermal fluxes. For a large class of heat sources that vary in the direction of gravity, we prove that $\l…
Data-driven Discovery of Invariant Measures
Jason J. Bramburger, Giovanni Fantuzzi
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gat…
Finite element approximation of the Hardy constant
Francesco Della Pietra, Giovanni Fantuzzi, Liviu I. Ignat +3
We consider finite element approximations to the optimal constant for the Hardy inequality with exponent in bounded domains of dimension or . For finite eleme…
Global minimization of polynomial integral functionals
Giovanni Fantuzzi, Federico Fuentes
We describe a `discretize-then-relax' strategy to globally minimize integral functionals over functions in a Sobolev space subject to Dirichlet boundary conditions. The strateg…
Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization
Jason J. Bramburger, Giovanni Fantuzzi
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 appro…
Bounds on heat transfer by incompressible flows between balanced sources and sinks
Binglin Song, Giovanni Fantuzzi, Ian Tobasco
Internally heated convection involves the transfer of heat by fluid motion between a distribution of sources and sinks. Focusing on the balanced case where the total heat added by…
Uncertainty propagation for nonlinear dynamics: A polynomial optimization approach
Francesca Covella, Giovanni Fantuzzi
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consid…
Sharpness and non-sharpness of occupation measure bounds for integral variational problems
Giovanni Fantuzzi, Ian Tobasco
We analyze two recently proposed methods to establish a priori lower bounds on the minimum of general integral variational problems. The methods, which involve either `occupation m…
Rigorous scaling laws for internally heated convection at infinite Prandtl number
Ali Arslan, Giovanni Fantuzzi, John Craske +1
New bounds are proven on the mean vertical convective heat transport, , for uniform internally heated (IH) convection in the limit of infinite Prandt…
Verification of some functional inequalities via polynomial optimization
Giovanni Fantuzzi
Motivated by the application of Lyapunov methods to partial differential equations (PDEs), we study functional inequalities of the form where is…
Analytical bounds on the heat transport in internally heated convection
Anuj Kumar, Ali Arslan, Giovanni Fantuzzi +2
We obtain an analytical bound on the mean vertical convective heat flux between two parallel boundaries driven by uniform internal heating. We consider two co…
Convex relaxations of integral variational problems: pointwise dual relaxation and sum-of-squares optimization
Alexander Chernyavsky, Jason J. Bramburger, Giovanni Fantuzzi +1
We present a method for finding lower bounds on the global infima of integral variational problems, wherein is minimized over functions $u\col…
Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization
Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou
Chordal and factor-width decomposition methods for semidefinite programming and polynomial optimization have recently enabled the analysis and control of large-scale linear systems…
The background method: Theory and computations
Giovanni Fantuzzi, Ali Arslan, Andrew Wynn
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 numeri…
Bounds for internally heated convection with fixed boundary heat flux
Ali Arslan, Giovanni Fantuzzi, John Craske +1
We prove a new rigorous bound for the mean convective heat transport , where and are the nondimensional vertical velocity and temperature, in internall…
Bounds on heat transport for convection driven by internal heating
Ali Arslan, Giovanni Fantuzzi, John Craske +1
The mean vertical heat transport in convection between isothermal plates driven by uniform internal heating is investigated by means of rigorous bounds. These…
Finding unstable periodic orbits: a hybrid approach with polynomial optimization
Mayur Lakshmi, Giovanni Fantuzzi, Sergei Chernyshenko +1
We present a novel method to compute unstable periodic orbits (UPOs) that optimize the infinite-time average of a given quantity for polynomial ODE systems. The UPO search procedur…
Sum-of-squares chordal decomposition of polynomial matrix inequalities
Yang Zheng, Giovanni Fantuzzi
We prove decomposition theorems for sparse positive (semi)definite polynomial matrices that can be viewed as sparsity-exploiting versions of the Hilbert--Artin, Reznick, Putinar, a…
Rigorous bounds on the heat transport of rotating convection with Ekman pumping
B. Pachev, J. P. Whitehead, G. Fantuzzi +1
We establish rigorous upper bounds on the time-averaged heat transport for a model of rotating Rayleigh-Benard convection between no-slip boundaries at infinite Prandtl number and…
New bounds on the vertical heat transport for Bénard-Marangoni convection at infinite Prandtl number
Giovanni Fantuzzi, Camilla Nobili, Andrew Wynn
We prove a new rigorous upper bound on the vertical heat transport for Bénard-Marangoni convection of a two- or three-dimensional fluid layer with infinite Prandtl number. Precisel…
Bounding extreme events in nonlinear dynamics using convex optimization
Giovanni Fantuzzi, David Goluskin
We study a convex optimization framework for bounding extreme events in nonlinear dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs). This fram…
Duality of convex relaxations for constrained variational problems
Giovanni Fantuzzi
We prove weak duality between two recent convex relaxation methods for bounding the optimal value of a constrained variational problem in which the objective is an integral functio…