49 citations · 271 across the 22 of their papers we have counts for
23 papers
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…
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…
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)…
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…
Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications
Gianluca Fabiani
We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs…
Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points
Gianluca Fabiani, Nikolaos Evangelou, Tianqi Cui +4
We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipp…
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…
Tipping points in overturning circulation mediated by ocean mixing and the configuration and magnitude of the hydrological cycle: A simple model
Anand Gnanadesikan, Gianluca Fabiani, Jingwen Liu +7
The current configuration of the ocean overturning involves upwelling predominantly in the Southern Ocean and sinking predominantly in the Atlantic basin. The reasons for this rema…
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…
Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learning
Hector Vargas Alvarez, Gianluca Fabiani, Nikolaos Kazantzis +2
We present a physics-informed machine learning (PIML) scheme for the feedback linearization of nonlinear discrete-time dynamical systems. The PIML finds the nonlinear transformatio…
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…
Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approach
Evangelos Galaris, Gianluca Fabiani, Ioannis Gallos +2
We address a three-tier data-driven approach to solve the inverse problem in complex systems modelling from spatio-temporal data produced by microscopic simulators using machine le…
Parametrically driven THz magnon-pairs: predictions towards ultimately fast and minimally dissipative switching
G. Fabiani, J. H. Mentink
Findings ways to achieve switching between magnetic states at the fastest possible time scale that simultaneously dissipates the least amount of energy is one of the main challenge…
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…
Role of stochastic noise and generalization error in the time propagation of neural-network quantum states
Damian Hofmann, Giammarco Fabiani, Johan H. Mentink +2
Neural-network quantum states (NQS) have been shown to be a suitable variational ansatz to simulate out-of-equilibrium dynamics in two-dimensional systems using time-dependent vari…
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…
Supermagnonic propagation in two-dimensional antiferromagnets
G. Fabiani, M. D. Bouman, J. H. Mentink
We investigate the propagation of magnons after ultrashort perturbations of the exchange interaction in the prototype two-dimensional Heisenberg antiferromagnet. Using the recently…
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…
Ultrafast dynamics of entanglement in Heisenberg antiferromagnets
G. Fabiani, J. H. Mentink
We investigate entanglement dynamics in the antiferromagnetic Heisenberg model in two dimensions following a spatially anisotropic quench of the exchange interactions. Opposed to e…
Investigating ultrafast quantum magnetism with machine learning
G. Fabiani, J. H. Mentink
We investigate the efficiency of the recently proposed Restricted Boltzmann Machine (RBM) representation of quantum many-body states to study both the static properties and quantum…