no code implementations • 24 Oct 2023 • Eleni D. Koronaki, Nikolaos Evangelou, Cristina P. Martin-Linares, Edriss S. Titi, Ioannis G. Kevrekidis
Both Black-Box and (theoretically-informed and data-corrected) Gray-Box models are described; the necessity for the latter arises when truncated Galerkin projections are so inaccurate as to not be amenable to post-processing.
no code implementations • 25 Sep 2023 • Gianluca Fabiani, Nikolaos Evangelou, Tianqi Cui, Juan M. Bello-Rivas, Cristina P. Martin-Linares, Constantinos Siettos, Ioannis G. Kevrekidis
We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipping points in the emergent behavior of complex systems, and (b) characterizing probabilities of rare events (here, catastrophic shifts) near them.