1.9k citations · 6.2k across the 179 of their papers we have counts for
12 papers · 1 filter
Learning emergent PDEs in a learned emergent space
Felix P. Kemeth, Tom Bertalan, Thomas Thiem +4
We extract data-driven, intrinsic spatial coordinates from observations of the dynamics of large systems of coupled heterogeneous agents. These coordinates then serve as an emergen…
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis +1
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux-Lie theorem, the phase flow of a Poiss…
Coarse-grained and emergent distributed parameter systems from data
Hassan Arbabi, Felix P. Kemeth, Tom Bertalan +1
We explore the derivation of distributed parameter system evolution laws (and in particular, partial differential operators and associated partial differential equations, PDEs) fro…
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
Hassan Arbabi, Judith E. Bunder, Giovanni Samaey +2
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural…
A Normal Form for the Onset of Collapse: the Prototypical Example of the Nonlinear Schrodinger Equation
S. J. Chapman, M. E. Kavousanakis, I. G. Kevrekidis +1
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the…
Exploring Critical Points of Energy Landscapes: From Low-Dimensional Examples to Phase Field Crystal PDEs
Priya Subramanian, Ioannis G. Kevrekidis, Panayotis G. Kevrekidis
In the present work we explore the application of a few root-finding methods to a series of prototypical examples. The methods we consider include: (a) the so-called continuous-tim…