10 citations · 33 across the 24 of their papers we have counts for
26 papers
Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learning
Mohammad Shah Alam, William Ott, Ilya Timofeyev
In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto-Sivashinsky (gKS) equation, an archetypal nonlinear PDE that exhibi…
Using Echo-State Networks to Reproduce Rare Events in Chaotic Systems
Anton Erofeev, Balasubramanya T. Nadiga, Ilya Timofeyev
Echo-State Networks (ESNs) are known to reproduce trajectories and main properties of chaotic attractors. Here, we investigate the question of whether ESNs can reproduce rare event…
Parametric Reduced Order Models for the Generalized Kuramoto--Sivashinsky Equations
Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev
The paper studies parametric Reduced Order Models (ROMs) for the Kuramoto--Sivashinsky (KS) and generalized Kuramoto--Sivashinsky (gKS) equations. We consider several POD and POD-D…
Role of Non-Exponential Reversal times in Aggregation Models of Bacterial Populations
Michael Batista, Patrick Murphy, Oleg A. Igoshin +2
In this paper, we consider 1D agent-based and kinetic models of aggregation with reversals. In particular, we fit a Gamma distribution to represent the run times in myxobacteria an…
Application of Machine Learning and Convex Limiting to Subgrid Flux Modeling in the Shallow-Water Equations
Ilya Timofeyev, Alexey Schwarzmann, Dmitri Kuzmin
We propose a combination of machine learning and flux limiting for property-preserving subgrid scale modeling in the context of flux-limited finite volume methods for the one-dimen…
Existence of weak solutions for the kinetic models of motion of myxobacteria with alignment and reversals
Patrick Murphy, Oleg Igoshin, Misha Perepelitsa +1
In this paper, we consider three non-linear kinetic partial differential equations that emerge in the modeling of motion of rod-shaped cells such as myxobacteria. This motion is ch…