1.9k citations · 6.2k across the 179 of their papers we have counts for
187 papers
A Theoretical Analysis of Generalization Dynamics in Neural Networks under Gradient Descent with Weight Decay
Yuqing Wang, Ioannis G. Kevrekidis, Mikhail Belkin
Understanding generalization remains a central challenge in machine learning because it requires jointly considering data, architecture, and training dynamics. In this paper, we de…
Blow-up Parameter Landscapes for Polynomial Dynamical Systems
Emil Graf, Ioannis G. Kevrekidis, Alex Townsend
Finite-time blow-up is one of the ways in which a dynamical model can become singular, often signaling the breakdown of either the modeled physical system or the model itself. Dete…
Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks
Hector Vargas Alvarez, Gianluca Fabiani, Ioannis G. Kevrekidis +2
We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization…
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…