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Posts
Machine Learns the Secrets of Tipping Points
Published:
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
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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
Tipping points in overturning circulation mediated by ocean mixing and the configuration and magnitude of the hydrological cycle: A simple model
Online in Arxiv, 2023
This preprint 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. arXiv preprint arXiv:2308.03951. https://arxiv.org/abs/2308.03951
Slow invariant manifolds of singularly perturbed systems via physics-informed machine learning
Online in Arxiv, 2023
This preprint is about the solution of invariance equation associated with SIM via PINNs
Recommended citation: Patsatzis, D. G., Fabiani, G., Russo, L., & Siettos, C. (2023). Slow invariant manifolds of singularly perturbed systems via physics-informed machine learning. arXiv preprint arXiv:2309.07946. https://arxiv.org/abs/2309.07946
Tasks makyth models: Machine learning assisted surrogates for tipping points
Online in Arxiv, 2023
This preprint is about the multiscale inverse problem of High-dimensionale 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., Bello-Rivas, J. M., Martin-Linares, C. P., Siettos, C., & Kevrekidis, I. G. (2023). Tasks makyth models: Machine learning assisted surrogates for tipping points. arXiv preprint arXiv:2309.14334. https://arxiv.org/abs/2309.14334
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
Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks
Online in Arxiv, 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. arXiv preprint arXiv:2402.12360. https://arxiv.org/abs/2402.12360
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
Task-oriented machine learning surrogates for tipping points of agent-based models
Published in Nature Communications, 2024
This paper is about the multiscale inverse problem of High-dimensionale 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., Bello-Rivas, J. M., Martin-Linares, C. P., Siettos, C., & Kevrekidis, I. G. (2023). Task-oriented Machine learning assisted surrogates for tipping points of agent-based models, Nature Communications, 2024 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, 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, 2024 https://arxiv.org/abs/2309.07946
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
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 of functions on 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://arxiv.org/pdf/2308.10720
talks
Tipping Points via Machine Learning: Comparing Data-driven Global PDE and Local SDE surrogates
Published:
teaching
Mathematics for Data Modelling
Supplementary undergraduate course in Physics, Mathematics and Engineering. , University Scuola Superiore Meridionale, Modelling Engineering Risk and Complexity, 2023