Preprints

You can also find my preprints on my Google Scholar profile.

Enabling Local Neural Operators to perform Equation-Free System-Level Analysis

Online in Arxiv, 2025

We propose a framework that integrates Neural Operators (NOs) with Krylov subspace iterative methods for efficient stability and bifurcation analysis of large-scale dynamical systems, extending NO applications beyond temporal predictions to system-level numerical tasks

Recommended citation: Fabiani, G., Vandecasteele, H., Goswami, S., Siettos, C., & Kevrekidis, I. G. (2025). Enabling Local Neural Operators to perform Equation-Free System-Level Analysis. arXiv preprint arXiv:2505.02308. https://arxiv.org/abs/2505.02308

Stability Analysis of Physics-Informed Neural Networks for Stiff Linear Differential Equations

Online in Arxiv, 2024

This preprint is about the linear stability analysis and consistency of Phyisics-informed neural networks based on random projections (PIRPNNs)

Recommended citation: Fabiani, G., Bollt, E., Siettos, C., & Yannacopoulos, A. N. (2024). Stability Analysis of Physics-Informed Neural Networks for Stiff Linear Differential Equations. arXiv preprint arXiv:2408.15393. https://doi.org/10.48550/arXiv.2408.15393

Numerical Solution of Stiff ODEs with Physics-Informed RPNNs

Online in Arxiv, 2021

This preprint contains preliminary results about the solution of stiff ODEs with Random Projection Neural Networks

Recommended citation: Galaris, E., Fabiani, G., Calabrò, F., di Serafino, D., & Siettos, C. (2021). Numerical Solution of Stiff ODEs with Physics-Informed RPNNs. arXiv preprint arXiv:2108.01584. http://arxiv.org/pdf/2108.01584.pdf

Gianluca Fabiani

Preprints

Enabling Local Neural Operators to perform Equation-Free System-Level Analysis

Stability Analysis of Physics-Informed Neural Networks for Stiff Linear Differential Equations

Numerical Solution of Stiff ODEs with Physics-Informed RPNNs