49 citations · 271 across the 22 of their papers we have counts for
9 papers · 1 filter
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…
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…
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)…
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…
On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon
Ferdinando Auricchio, Maria Roberta Belardo, Gianluca Fabiani +2
In the present paper, we consider one-hidden layer ANNs with a feedforward architecture, also referred to as shallow or two-layer networks, so that the structure is determined by t…
Parsimonious Physics-Informed Random Projection Neural Networks for Initial-Value Problems of ODEs and index-1 DAEs
Gianluca Fabiani, Evangelos Galaris, Lucia Russo +1
We address a physics-informed neural network based on the concept of random projections for the numerical solution of IVPs of nonlinear ODEs in linear-implicit form and index-1 DAE…
Numerical Solution of Stiff ODEs with Physics-Informed RPNNs
Evangelos Galaris, Gianluca Fabiani, Francesco Calabrò +2
We propose a numerical method based on physics-informed Random Projection Neural Networks for the solution of Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs…
Numerical Solution and Bifurcation Analysis of Nonlinear Partial Differential Equations with Extreme Learning Machines
Gianluca Fabiani, Francesco Calabrò, Lucia Russo +1
We address a new numerical scheme based on a class of machine learning methods, the so-called Extreme Learning Machines with both sigmoidal and radial-basis functions, for the comp…
Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients
Francesco Calabrò, Gianluca Fabiani, Constantinos Siettos
We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal funct…