Gianluca Fabiani

Gianluca Fabiani

Postdoctoral Fellow at the Hopkins Extreme Materials Institute (HEMI)

Preprints

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

HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEs

Online in Arxiv, 2025

HEATNET, a random feature neural network built from heat-kernel Green’s functions, provides an unbiased and scalable universal approximator for high-dimensional parabolic PDEs, achieving high accuracy up to 2,000 dimensions with relatively few features.

Recommended citation: Georgiou K., Fabiani G., Siettos C., Yannacopoulos A.N. (2025). HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEs. arXiv preprint arXiv:2511.00886. https://arxiv.org/abs/2511.00886

Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators

Online in Arxiv, 2025

We propose a framework, using data-driven local neural operators within Krylov subspace methods, to enable efficient model reduction and feedback control of high-dimensional systems without explicit coarse equations.

Recommended citation: Fabiani, G., Siettos, C., & Kevrekidis, I. G. (2025). Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators. arXiv preprint arXiv:2509.23975. https://www.arxiv.org/abs/2509.23975

Going with the Flow: Solving for Symmetry-Driven PDE dynamics with Physics-informed Neural Networks

Online in Arxiv, 2025

We developed a PINN-based framework that factors out continuous symmetries in nonlinear PDEs, transforming them into high-index DAE systems to simultaneously compute invariant solutions and symmetry parameters like wave speeds or scaling rates.

Recommended citation: Kavousanakis, M., Fabiani, G., Georgiou, A., Siettos, C., Kevrekidis, P., & Kevrekidis, I. (2025). Going with the Flow: Solving for Symmetry-Driven PDE dynamics with Physics-informed Neural Networks. arXiv preprint arXiv:2509.15963. https://arxiv.org/abs/2509.15963

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