Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients. - Francesco Calabrò; Gianluca Fabiani; Constantinos I. Siettos (CoRR, 2020)

Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines. - Gianluca Fabiani; Francesco Calabrò; Lucia Russo; Constantinos I. Siettos (J. Sci. Comput., 2021)

Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approach. - Evangelos Galaris; Gianluca Fabiani; Ioannis Gallos; Ioannis G. Kevrekidis; Constantinos I. Siettos (CoRR, 2022)

Parsimonious Physics-Informed Random Projection Neural Networks for Initial-Value Problems of ODEs and index-1 DAEs. - Gianluca Fabiani; Evangelos Galaris; Lucia Russo; Constantinos I. Siettos (CoRR, 2022)

Numerical Bifurcation Analysis of PDEs From Lattice Boltzmann Model Simulations: a Parsimonious Machine Learning Approach. - Evangelos Galaris; Gianluca Fabiani; Ioannis Gallos; Ioannis G. Kevrekidis; Constantinos I. Siettos (J. Sci. Comput., 2022)

Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points. - Gianluca Fabiani; Nikolaos Evangelou; Tianqi Cui; Juan M. Bello-Rivas; Cristina P. Martin-Linares; Constantinos I. Siettos; Ioannis G. Kevrekidis (CoRR, 2023)

Discrete-time nonlinear feedback linearization via physics-informed machine learning. - Hector Vargas Alvarez; Gianluca Fabiani; Nikolaos Kazantzis; Constantinos I. Siettos; Ioannis G. Kevrekidis (J. Comput. Phys., 2023)

Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks. - Hector Vargas Alvarez; Gianluca Fabiani; Ioannis G. Kevrekidis; Nikolaos Kazantzis; Constantinos I. Siettos (CoRR, 2024)

RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operators. - Gianluca Fabiani; Ioannis G. Kevrekidis; Constantinos I. Siettos; Athanasios N. Yannacopoulos (CoRR, 2024)

Stability Analysis of Physics-Informed Neural Networks for Stiff Linear Differential Equations. - Gianluca Fabiani; Erik Bollt; Constantinos I. Siettos; Athanasios N. Yannacopoulos (CoRR, 2024)

Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learning. - Dimitrios G. Patsatzis; Gianluca Fabiani; Lucia Russo; Constantinos I. Siettos (SIAM J. Sci. Comput., 2024)

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; Francesco Calabrò; Gianluca Fabiani; Ariel F. Pascaner (Soft Comput., 2024)

RandONets: Shallow networks with random projections for learning linear and nonlinear operators. - Gianluca Fabiani; Ioannis G. Kevrekidis; Constantinos I. Siettos; Athanasios N. Yannacopoulos (J. Comput. Phys., 2025)

Random Projection Neural Networks of Best Approximation: Convergence Theory and Practical Applications. - Gianluca Fabiani (SIAM J. Math. Data Sci., 2025)

Enabling Local Neural Operators to perform Equation-Free System-Level Analysis. - Gianluca Fabiani; Hannes Vandecasteele; Somdatta Goswami; Constantinos I. Siettos; Ioannis G. Kevrekidis (CoRR, 2025)