64 citations · 563 across the 39 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…
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…
Finding extremal periodic orbits with polynomial optimisation, with application to a nine-mode model of shear flow
Mayur Lakshmi, Giovanni Fantuzzi, Jesús Fernández-Caballero +2
Tobasco et al. [Physics Letters A, 382:382-386, 2018; see https://doi.org/10.1016/j.physleta.2017.12.023] recently suggested that trajectories of ODE systems that optimize the infi…
Bounds on mean energy in the Kuramoto-Sivashinsky equation computed using semidefinite programming
David Goluskin, Giovanni Fantuzzi
We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov fun…
Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization
Giovanni Fantuzzi, David Goluskin, Deqing Huang +1
We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynami…