“Exploring the Hidden Patterns of Complexity with intersection of AI/ML and Numerical Analysis”

Breaking News

• New Arxiv preprint:
  • 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.

• New SIAM Journal on Mathematics of Data Science paper published (my first single-author work)
  • Fabiani, G., Random projection neural networks of best approximation: Convergence theory and practical applications, SIAM Journal on Mathematics of Data Science 7 (2), 385-409, 2025
• New J Comp. Phys. paper published
  • Fabiani, G., Kevrekidis, I. G., Siettos, C., & Yannacopoulos, A. N., RandONets: Shallow-Networks with Random Projections for learning linear and nonlinear operators, Journal of Computational Physics, Volume 520, 113433, 2025
  • Code public in a GitHub repository

Recent publications in

• Nature Communications 15:
  • Fabiani, G., Evangelou, N., Cui, T. et al. Task-oriented machine learning surrogates for tipping points of agent-based models. Nat Commun 15, 4117 (2024).

• SIAM Journal on Scientific Computing 46 (4), C297-C322, Slow invariant manifolds of singularly perturbed systems via physics-informed machine learning, D Patsatzis, G Fabiani, L Russo, C Siettos

• Chaos, Solitons & Fractals 186, 115215, Nonlinear discrete-time observers with physics-informed neural networks HV Alvarez, G Fabiani, N Kazantzis, IG Kevrekidis, C Siettos

• Journal of Physical Oceanography 54 (7), 1389-1409, Tipping points in overturning circulation mediated by ocean mixing and the configuration and magnitude of the hydrological cycle: A simple model, A Gnanadesikan, G Fabiani, J Liu, R Gelderloos, GJ Brett, Y Kevrekidis, …
• Soft Computing, On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon, F Auricchio, MR Belardo, F Calabrò, G Fabiani, AF Pascaner

Research Group Photo

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From left to right: Dr. Dimitrios Patsatzis, Hector Vargas Alvarez, Me, Prof. Constantinos Siettos, Dr. Lucia Russo, Prof. Ioannis Kevrekidis, Prof. Felix Dietrich, Dr. Nikolaos Evangelou

Introduction

I am a Postdoctoral fellow at the Hopkins Extreme Materials Institute, Johns Hopkins University, JHU. Formerly, I was a PhD student in Modeling and Engineering Risk and Complexity (MERC) at Scuola Superiore Meridionale (SSM), Naples, Italy. I also got a Master’s Degree in Applied Mathematics at Federico II University. My research interests concern numerical analysis, machine learning, bifurcation analysis and mathematical modeling with particular emphasis on problems that arise in multiscale and multiphase complex systems.

Disciplines

Computing in Mathematics, Natural Science, Engineering and Applied Mathematics

Skills and expertise

Programming in MATLAB, C, Fortran, Python, TensorFlow

Research Topics

1. Random Projection Neural Networks
2. Machine Learning
3. Neural Networks and Artificial Intelligence
4. Numerical Analysis of Partial Differential Equations
5. Complex Systems
6. System Identification and Data-Driven Discovery of Governing Equations
7. Numerical Bifurcation Analysis
8. Complex Networks
9. Pattern Recognition
10. Operator Learning for PDEs
11. Surrogate Modeling for Multi-scale Systems
12. Physics-Informed Neural Networks (PINNs)
13. Equation-Free Multiscale Computation
14. High-Dimensional Approximation Techniques
15. Nonlinear Dynamical Systems
16. Koopman Operator Theory in Machine Learning
17. Spatiotemporal Chaos and Turbulence Modeling
18. Phase-Field Modeling and Free Energy Analysis
19. Rare Events and Tipping Points in Dynamical Systems
20. Model Reduction Techniques (e.g., POD, DMD, Autoencoders)
21. Graph Neural Networks for Dynamical Systems
22. Inverse Problems and Data Assimilation
23. Stochastic Processes and Stochastic PDEs
24. Uncertainty Quantification in Physical Models
25. Functional Analysis for Neural Networks and Neural Operators