13 papers
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…
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…
Fredholm Neural Networks for inverse problems in elliptic PDEs
Kyriakos C. Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos
Building on our previous work on Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to inverse problems for linear and nonlinear…
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…
Learning Contractive Integral Operators with Fredholm Integral Neural Operators
Kyriakos C. Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos
We generalize the framework of Fredholm Neural Networks, to learn non-expansive integral operators arising in Fredholm Integral Equations (FIEs) of the second kind in arbitrary dim…
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 address a numerical framework for the stability and bifurcation analysis of nonlinear partial differential equations (PDEs) in which the solution is sought in the function space…