5 papers
On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers
Sixu Li, Thomas Jacob Maranzatto, Jan Peszek +5
We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems. In this perspective, tokens are modeled as particles…
Hybrid operator learning of wave scattering maps in high-contrast media
Advait Balaji, Trevor Teolis, S. David Mis +3
Surrogate modeling of wave propagation and scattering (i.e. the wave speed and source to wave field map) in heterogeneous media has significant potential in applications such as se…
Unconditional alignment of solutions to the Fokker-Planck-Navier-Stokes system with locally averaged Brinkman force
Roman Shvydkoy, Trevor Teolis
We study a coupled Fokker-Planck--Navier-Stokes (FPNS) system modeling the dynamics of interacting particles suspended in a viscous incompressible fluid, where the coupling occurs…
Modulation of the Monokinetic Limit for Models of Collective Dynamics
Alina Chertock, Roman Shvydkoy, Trevor Teolis
In this work, we perform modulation analysis of monokinetic limits from the kinetic Cucker- Smale model to the pressureless Euler alignment system. Two regimes are considered -- a…
Microscopic, mesoscopic, and macroscopic descriptions of the Euler alignment system with adaptive communication strength
Roman Shvydkoy, Trevor Teolis
This is a continuation of our previous joint work on the $\st$-model in[\textit{Well-posedness and long time behavior of the Euler Alignment System with adaptive communication stre…