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AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression
Mario De Florio, Ioannis G. Kevrekidis, George Em Karniadakis
Discovering mathematical models that characterize the observed behavior of dynamical systems remains a major challenge, especially for systems in a chaotic regime. The challenge is…
Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling
Nikolaos Evangelou, Tianqi Cui, Juan M. Bello-Rivas +2
We study the tipping point collective dynamics of an adaptive susceptible-infected-susceptible (SIS) epidemiological network in a data-driven, machine learning-assisted manner. We…
Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML era
Eleni D. Koronaki, Nikolaos Evangelou, Cristina P. Martin-Linares +2
This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assi…
Machine Learning for the identification of phase-transitions in interacting agent-based systems: a Desai-Zwanzig example
Nikolaos Evangelou, Dimitrios G. Giovanis, George A. Kevrekidis +2
Deriving closed-form, analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phas…
Learning Parametric Koopman Decompositions for Prediction and Control
Yue Guo, Milan Korda, Ioannis G. Kevrekidis +1
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously construc…
Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points
Gianluca Fabiani, Nikolaos Evangelou, Tianqi Cui +4
We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipp…