27 citations · 27 across the 9 of their papers we have counts for
9 papers
Autoencoders vs. Numerical Analysis--Informed Manifold Learning for Navier--Stokes Flows
Alessandro Della Pia, Lucia Russo, Ioannis Kevrekidis +1
Autoencoders (AEs) have become a dominant approach to nonlinear latent-space construction in data-driven reduced-order modelling (ROM), with their decoders lifting latent represent…
Dictionary learning for Kernel EDMD
Erik Lien Bolager, Boumediene Hamzi, Houman Owhadi +2
Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. T…
On the algebra of Koopman eigenfunctions and on some of their infinities
Zahra Monfared, Saksham Malhotra, Sekiya Hajime +2
For continuous-time dynamical systems with reversible trajectories, the nowhere-vanishing eigenfunctions of the Koopman operator of the system form a multiplicative group. Here, we…
Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach
Gianluca Fabiani, Michail E. Kavousanakis, Constantinos Siettos +1
We present a numerical framework for the stability and bifurcation analysis of nonlinear partial differential equations (PDEs) in which the solutions are sought in the function spa…
PDE-Free Mass-Constrained Learning of Complex Systems with Hidden States
Gianmaria Viola, Alessandro Della Pia, Lucia Russo +2
We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex system…
Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators
Gianluca Fabiani, Constantinos Siettos, Ioannis G. Kevrekidis
The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approac…
Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learning
Hector Vargas Alvarez, Dimitrios G. Patsatzis, Lucia Russo +2
Bridging the microscopic and macroscopic modelling scales in crowd dynamics constitutes an open challenge for systematic numerical analysis, optimization, and control. Here, we pro…
Invariant Manifolds of Discrete-time Dynamical Systems with Nonlinear Exosystems via Hybrid Physics-Informed Neural Networks
Dimitrios G. Patsatzis, Nikolaos Kazantzis, Ioannis G. Kevrekidis +2
We propose a hybrid physics-informed machine learning framework to approximate invariant manifolds (IMs) of discrete-time dynamical systems driven by exogenous autonomous dynamics…
Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach
Dimitrios G. Patsatzis, Lucia Russo, Ioannis G. Kevrekidis +1
We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems modelled via microscopic/agent-base…