52 citations · 70 across the 18 of their papers we have counts for
19 papers
Warm-starting PDE solvers with any-dimensional machine learning
Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith +1
Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and dimensions. Inspired by the G…
When Rates Are Geometric: Rate-Certificate Transfer for Contact Splittings in Optimization
George A Kevrekidis
Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algor…
Local Universal Splitting Integrators for Contact Hamiltonian Systems
George A Kevrekidis
Contact Hamiltonian systems extend symplectic Hamiltonian mechanics to dissipative settings while retaining geometric structure. We develop a structure-preserving splitting framewo…
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…
Neural Network Representations of Multiphase Equations of State
George A. Kevrekidis, Daniel A. Serino, Alexander Kaltenborn +3
Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Cli…
Practical identifiability and parameter estimation of compartmental epidemiological models
Q. Y. Chen, Z. Rapti, Y. Drossinos +3
Practical parameter identifiability in ODE-based epidemiological models is a known issue, yet one that merits further study. It is essentially ubiquitous due to noise and errors in…
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…
Towards fully covariant machine learning
Soledad Villar, David W. Hogg, Weichi Yao +2
Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corre…
MarkerMap: nonlinear marker selection for single-cell studies
Nabeel Sarwar, Wilson Gregory, George A Kevrekidis +2
Single-cell RNA-seq data allow the quantification of cell type differences across a growing set of biological contexts. However, pinpointing a small subset of genomic features expl…
The role of mobility in the dynamics of the COVID-19 epidemic in Andalusia
Z. Rapti, J. Cuevas-Maraver, E. Kontou +6
Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively us…
Backcasting COVID-19: A Physics-Informed Estimate for Early Case Incidence
G. A. Kevrekidis, Z. Rapti, Y. Drossinos +4
It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embed…
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…
Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning
Felix Dietrich, Alexei Makeev, George Kevrekidis +4
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surr…
Dynamics of two languages competing on a network: a case study
T. Kapitula, P. G. Kevrekidis
A language dynamics model on a square lattice, which is an extension of the one popularized by Abrams and Strogatz [1], is analyzed using ODE bifurcation theory. For this model we…
Estimation of the effective reproduction number for SARS-CoV-2 infection during the first epidemic wave in the metropolitan area of Athens, Greece
Konstantinos Kaloudis, George A. Kevrekidis, Helena C. Maltezou +3
Herein, we provide estimations for the effective reproduction number for the greater metropolitan area of Athens, Greece during the first wave of the pandemic (February 26-Ma…
Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples
P. G. Kevrekidis, J. Cuevas-Maraver, Y. Drossinos +2
We examine the spatial modeling of the outbreak of COVID-19 in two regions: the autonomous community of Andalusia in Spain and the mainland of Greece. We start with a 0D compartmen…