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
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
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
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
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
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