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Posts

Tipping Points in Ocean Currents Signal Climate Risks

less than 1 minute read

Published: September 25, 2024

Researchers use advanced models to uncover critical thresholds in global ocean circulation, highlighting potential climate impacts. Read the paper: Journal of Physical Oceanography 54(7).

Machine Learns the Secrets of Tipping Points

1 minute read

Published: May 18, 2024

Ever wondered what triggers sudden, dramatic shifts in complex systems? Our research takes a thrilling Machine Learning adventure to unravel the mysteries of “tipping points” - those critical junctures where small changes lead to big, often irreversible consequences. Read the paper: Nature Communications 15, 4117. Full blog post at Springer Nature Research Communities

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preprints

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

Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications

Online in Arxiv, 2024

This preprint is about the existence, uniqueness and exponential convergence of RPNN of best approximation.

Recommended citation: Fabiani, G. (2024). Random Projection Neural Networks of Best Approximation: Convergence theory and practical applications. arXiv preprint arXiv:2402.11397. http://arxiv.org/abs/2402.11397

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

publications

Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients

Published in Computer Methods in Applied Mechanics and Engineering 387, 114188, 2021

This paper is about the solution of linear stationary PDEs with Random Projection Neural Networks

Recommended citation: Calabrò, F., Fabiani, G., & Siettos, C. (2021). Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients. Computer Methods in Applied Mechanics and Engineering, 387, 114188. https://doi.org/10.1016/j.cma.2021.114188

Numerical Solution and Bifurcation Analysis of nonlinear partial differential equations with extreme learning machines

Published in Journal of Scientific Computing - Springer, 2021

This paper is about the efficient solution of steady state PDE problem via Machine Learning

Recommended citation: Fabiani, G., Calabrò, F., Russo, L., & Siettos, C. (2021). Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines. Journal of Scientific Computing, 89, 1-35. https://link.springer.com/article/10.1007/s10915-021-01650-5

Numerical bifurcation analysis of pdes from lattice Boltzmann model simulations: a parsimonious machine learning approach

Published in Journal of Scientific Computing, 92(2), 34, 2022

This paper is about the solution of the inverse problem for parametric PDEs ( system identification) and data-driven construction of bifurcation diagram

Recommended citation: Galaris, E., Fabiani, G., Gallos, I., Kevrekidis, I., & Siettos, C. (2022). Numerical bifurcation analysis of pdes from lattice Boltzmann model simulations: a parsimonious machine learning approach. Journal of Scientific Computing, 92(2), 34. https://link.springer.com/article/10.1007/s10915-021-01650-5

Parsimonious physics-informed random projection neural networks for initial value problems of ODEs and index-1 DAEs

Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(4), 2023

This paper was awarded with an Editor’s Pick badge. It is about the solution of stiff system of ODEs and DAEs (including PDEs) via time-adaptive Random Projection Neural Networks.

Recommended citation: Fabiani, G., Galaris, E., Russo, L., & Siettos, C. (2023). Parsimonious physics-informed random projection neural networks for initial value problems of ODEs and index-1 DAEs. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(4). https://pubs.aip.org/aip/cha/article-abstract/33/4/043128/2878586/Parsimonious-physics-informed-random-projection?redirectedFrom=fulltext

Discrete-time nonlinear feedback linearization via physics-informed machine learning

Published in Journal of Computational Physics Volume 492, 112408, 2023

This paper is about the one-step feedback linearization and control via PINNs

Recommended citation: Hector Vargas Alvarez, Gianluca Fabiani, Nikolaos Kazantzis, Constantinos Siettos, Ioannis G. Kevrekidis, Discrete-time nonlinear feedback linearization via physics-informed machine learning, Journal of Computational Physics, Volume 492, 2023, 112408, ISSN 0021-9991, https://doi.org/10.1016/j.jcp.2023.112408. https://www.sciencedirect.com/science/article/pii/S002199912300503X

Tipping points in overturning circulation mediated by ocean mixing and the configuration and magnitude of the hydrological cycle: A simple model

Published in Journal of Physical Oceanography, 2024

This paper is about the description and bifurcation analysis of a simple 6-box model for the AMOC

Recommended citation: Gnanadesikan, A., Fabiani, G., Liu, J., Gelderloos, R., Brett, G. J., Kevrekidis, Y., ... & Sleeman, J. (2023). Tipping points in overturning circulation mediated by ocean mixing and the configuration and magnitude of the hydrological cycle: A simple model. Journal of Physical Oceanography. https://doi.org/10.1175/JPO-D-23-0161.1

Task-oriented machine learning surrogates for tipping points of agent-based models

Published in Nature Communications 15, 2024

This paper is about the multiscale inverse problem of High-dimensional Agent based models via FNNs and RPNNs. For the data-driven reconstruction of bifurcation diagrams and rare event analysis. We learn both Integro-PDEs and low-dimensional SDEs (ML surrogates.)

Recommended citation: 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). https://doi.org/10.1038/s41467-024-48024-7 https://doi.org/10.1038/s41467-024-48024-7

Slow invariant manifolds of singularly perturbed systems via physics-informed machine learning

Published in SIAM Journal on Scientific Computing 46(4), 2024

This paper is about the solution of invariance equation associated with SIM via PINNs

Recommended citation: Patsatzis, D. G., Fabiani, G., Russo, L., & Siettos, C. (2024). Slow invariant manifolds of singularly perturbed systems via physics-informed machine learning. SIAM Journal on Scientific Computing 46(4) https://doi.org/10.1137/23M1602991

Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks

Published in Chaos Solitons & Fractals 186, 2024

This preprint is about the solution of nonlinear functional equations associated with the observer state estimation via PINNs

Recommended citation: Alvarez, H. V., Fabiani, G., Kevrekidis, I. G., Kazantzis, N., & Siettos, C. (2024). Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks. Chaos Solitons & Fractals 186. https://doi.org/10.1016/j.chaos.2024.115215

On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon

Published in Soft Computing, 2024

This paper is about the interpolation accuracy of Random featured Neural Networks, with particular focus on the possibility to use random grids, even for functions presenting the Runge-Phenomenon.

Recommended citation: Auricchio, F., Belardo, M. R., Calabrò, F., Fabiani, G. & Pascaner, A. F. (2024). On the accuracy of interpolation based on single-layer artificial neural networks. Soft Computing https://doi.org/10.1007/s00500-024-09918-2

RandONets: Shallow-Networks with Random Projections for learning linear and nonlinear operators

Published in Journal of Computational Physics, 2024

This paper propose a novel architecture, RandONets, for learning generic Operators. It leverages Random Projections and Nonlinear Random Features, as well as tailor-made numerical analysis method for improving significantly efficiency and accuracy. We demonstrate that RandONets outperforms DeepONets by 10 order of magnitudes. Also, we theoretically prove and extend the theorem of Chen and Chen (1995) to such randomized architectures.

Recommended citation: Fabiani, G., Kevrekidis, I. G., Siettos, C., & Yannacopoulos, A. N. RandONets: Shallow-Networks with Random Projections for learning linear and nonlinear operators. J Comp Phys (2024) https://doi.org/10.1016/j.jcp.2024.113433