27 citations · 66 across the 12 of their papers we have counts for
13 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…
RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservation
Dimitrios G. Patsatzis, Alessandro Della Pia, Lucia Russo +1
We introduce RANDSMAPs (Random-feature/multi-scale neural decoders with Mass Preservation), numerical analysis-informed, explainable neural decoders designed to explicitly respect…
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…
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…
Surrogate normal-forms for the numerical bifurcation and stability analysis of navier-stokes flows via machine learning
Alessandro Della Pia, Dimitrios G. Patsatzis, Gianluigi Rozza +2
Inspired by the Equation-Free paradigm, we propose an ``embed-learn-lift'' framework for constructing minimal-dimensional surrogate ROMs for the numerical analysis of high-fidelity…
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…
GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws
Dimitrios G. Patsatzis, Mario di Bernardo, Lucia Russo +1
We present GoRINNs: numerical analysis-informed (shallow) neural networks for the solution of inverse problems of non-linear systems of conservation laws. GoRINNs is a hybrid/blend…
Learning the Latent dynamics of Fluid flows from High-Fidelity Numerical Simulations using Parsimonious Diffusion Maps
Alessandro Della Pia, Dimitris Patsatzis, Lucia Russo +1
We use parsimonious diffusion maps (PDMs) to discover the latent dynamics of high-fidelity Navier-Stokes simulations with a focus on the 2D fluidic pinball problem. By varying the…
A physics-informed neural network method for the approximation of slow invariant manifolds for the general class of stiff systems of ODEs
Dimitrios G. Patsatzis, Lucia Russo, Constantinos Siettos
We present a physics-informed neural network (PINN) approach for the discovery of slow invariant manifolds (SIMs), for the most general class of fast/slow dynamical systems of ODEs…
Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learning
Dimitrios G. Patsatzis, Gianluca Fabiani, Lucia Russo +1
We present a physics-informed machine-learning (PIML) approach for the approximation of slow invariant manifolds (SIMs) of singularly perturbed systems, providing functionals in an…
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…
A Numerical Method for the Parametrization of Stable and Unstable Manifolds of Microscopic Simulators
Constantinos Siettos, Lucia Russo
We address a numerical methodology for the computation of coarse-grained stable and unstable manifolds of saddle equilibria/stationary states of multiscale/stochastic systems for w…
A timestepper approach for the systematic bifurcation and stability analysis of polymer extrusion dynamics
M. E. Kavousanakis, L. Russo, C. I. Siettos +2
We discuss how matrix-free/timestepper algorithms can efficiently be used with dynamic non-Newtonian fluid mechanics simulators in performing systematic stability/bifurcation analy…