20 citations · 42 across the 14 of their papers we have counts for
16 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…
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 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…
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…
HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEs
Kyriakos Georgiou, Gianluca Fabiani, Constantinos Siettos +1
We deal with the solution of the forward problem for high-dimensional parabolic PDEs with random feature (projection) neural networks (RFNNs). We first prove that there exists a si…
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…
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…
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…
Enabling Local Neural Operators to perform Equation-Free System-Level Analysis
Gianluca Fabiani, Hannes Vandecasteele, Somdatta Goswami +2
Neural Operators (NOs) provide a powerful framework for computations involving physical laws that can be modelled by (integro-) partial differential equations (PDEs), directly lear…
Linear Stability Analysis of Physics-Informed Random Projection Neural Networks for ODEs
Gianluca Fabiani, Erik Bollt, Constantinos Siettos +1
We present a linear stability analysis of physics-informed random projection neural networks (PI-RPNNs), for the numerical solution of {the initial value problem (IVP)} of (stiff)…
Fredholm Neural Networks
Kyriakos Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos
Within the family of explainable machine-learning, we present Fredholm neural networks (Fredholm NNs): deep neural networks (DNNs) architectures motivated by fixed-point iteration…
RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operators
Gianluca Fabiani, Ioannis G. Kevrekidis, Constantinos Siettos +1
Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their imple…
Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks
Hector Vargas Alvarez, Gianluca Fabiani, Ioannis G. Kevrekidis +2
We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization…