12 citations · 48 across the 21 of their papers we have counts for
22 papers
Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events
Isabella S. Thiel, Juan Bello-Rivas, Yannis G. Kevrekidis +1
Extreme events in chaotic systems are difficult to learn from short trajectories because they are controlled by transient finite-time instability rather than by frequently observed…
The Right Space for Dynamics: Numerics with Diffeomorphism Equivariance
Wolf-Juergen Beyn, Michail E. Kavousanakis, Yannis G. Kevrekidis
Among many (equivalent, via invertible transformations) representations of the evolution of a dynamical system, which one is to be preferred? Here we show how the use of infinite-d…
A simulation that recapitulates the dynamics of PER-directed colloidal assembly
Cheng-Hung Chou, Pepijn G. Moerman, Sikao Guo +4
The self-assembly of DNA-coated colloids controlled by enzymatic reactions has the potential to enable the formation of materials with hierarchical organization and switchable conf…
The Future of Artificial Intelligence and the Mathematical and Physical Sciences (AI+MPS)
Andrew Ferguson, Marisa LaFleur, Lars Ruthotto +97
This community paper developed out of the NSF Workshop on the Future of Artificial Intelligence (AI) and the Mathematical and Physics Sciences (MPS), which was held in March 2025 w…
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…
Gaussian Processes simplify differential equations
Jonghyeon Lee, Boumediene Hamzi, Yannis Kevrekidis +1
In this paper we use Gaussian processes (kernel methods) to learn mappings between trajectories of distinct differential equations. Our goal is to simplify both the representation…
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…
Data-driven cold starting of good reservoirs
Lyudmila Grigoryeva, Boumediene Hamzi, Felix P. Kemeth +4
Using short histories of observations from a dynamical system, a workflow for the post-training initialization of reservoir computing systems is described. This strategy is called…
Social Physics of Bacteria: Avoidance of an Information Black Hole
Trung V. Phan, Shengkai Li, Domenic Ferreris +7
Social physics explores responses to information exchange in a social network, and can be mapped down to bacterial collective signaling. Here, we explore how social inter-bacterial…
Tipping points in overturning circulation mediated by ocean mixing and the configuration and magnitude of the hydrological cycle: A simple model
Anand Gnanadesikan, Gianluca Fabiani, Jingwen Liu +7
The current configuration of the ocean overturning involves upwelling predominantly in the Southern Ocean and sinking predominantly in the Atlantic basin. The reasons for this rema…
A Generative Adversarial Network for Climate Tipping Point Discovery (TIP-GAN)
Jennifer Sleeman, David Chung, Anand Gnanadesikan +10
We propose a new Tipping Point Generative Adversarial Network (TIP-GAN) for better characterizing potential climate tipping points in Earth system models. We describe an adversaria…
Using Artificial Intelligence to aid Scientific Discovery of Climate Tipping Points
Jennifer Sleeman, David Chung, Chace Ashcraft +10
We propose a hybrid Artificial Intelligence (AI) climate modeling approach that enables climate modelers in scientific discovery using a climate-targeted simulation methodology bas…
Identifying Equivalent Training Dynamics
William T. Redman, Juan M. Bello-Rivas, Maria Fonoberova +3
Study of the nonlinear evolution deep neural network (DNN) parameters undergo during training has uncovered regimes of distinct dynamical behavior. While a detailed understanding o…
Accurate and efficient multiscale simulation of a heterogeneous elastic beam via computation on small sparse patches
A. J. Roberts, Thien Tran-Duc, J. E. Bunder +1
Modern `smart' materials have complex microscale structure, often with unknown macroscale closure. The Equation-Free Patch Scheme empowers us to non-intrusively, efficiently, and a…
Benchmarking optimality of time series classification methods in distinguishing diffusions
Zehong Zhang, Fei Lu, Esther Xu Fei +3
Statistical optimality benchmarking is crucial for analyzing and designing time series classification (TSC) algorithms. This study proposes to benchmark the optimality of TSC algor…
Unsupervised learning of observation functions in state-space models by nonparametric moment methods
Qingci An, Yannis Kevrekidis, Fei Lu +1
We investigate the unsupervised learning of non-invertible observation functions in nonlinear state-space models. Assuming abundant data of the observation process along with the d…
An Operator Theoretic View on Pruning Deep Neural Networks
William T. Redman, Maria Fonoberova, Ryan Mohr +2
The discovery of sparse subnetworks that are able to perform as well as full models has found broad applied and theoretical interest. While many pruning methods have been developed…
Applications of Koopman Mode Analysis to Neural Networks
Iva Manojlović, Maria Fonoberova, Ryan Mohr +4
We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optim…
To Infinity and Beyond: Some ODE and PDE Case Studies
P. G. Kevrekidis, C. I. Siettos, I. G. Kevrekidis
When mathematical/computational problems reach infinity, extending analysis and/or numerical computation beyond it becomes a notorious challenge. We suggest that, upon suitable sin…
The Autohumidification Polymer Electrolyte Membrane Fuel Cell
J. B. Benziger, J. Moxley, S. Tulyani +3
A PEM fuel cell was specially constructed to determine kinetics under conditions of well-defined gas phase composition and cell temperature. Steady state multiplicity was discovere…