52 citations · 70 across the 18 of their papers we have counts for
5 papers · 1 filter
Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equations
Trung V. Phan, George A. Kevrekidis, Soledad Villar +2
The machine learning methods for data-driven identification of partial differential equations (PDEs) are typically defined for a given number of spatial dimensions and a choice of…
Data-Driven, ML-assisted Approaches to Problem Well-Posedness
Tom Bertalan, George A. Kevrekidis, Eleni D Koronaki +3
Classically, to solve differential equation problems, it is necessary to specify sufficient initial and/or boundary conditions so as to allow the existence of a unique solution. We…
Thinner Latent Spaces: Detecting Dimension and Imposing Invariance with Conformal Autoencoders
George A. Kevrekidis, Zan Ahmad, Mauro Maggioni +2
Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of d…
Conformal Disentanglement and Latent-Space Curation: A Neural Framework for Perspective Synthesis, Differentiation and Targeted Generation
George A. Kevrekidis, Eleni D. Koronaki, Dimitris G. Giovanis +1
Many scientific and engineering problems involve observing a common phenomenon through multiple heterogeneous sensors or measurement modalities. Such observations typically contain…
On the Parameter Combinations That Matter and on Those That do Not
Nikolaos Evangelou, Noah J. Wichrowski, George A. Kevrekidis +4
We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diff…