32 citations · 75 across the 4 of their papers we have counts for
5 papers
A Geometric Theory for Nonequilibrium Transformer Dynamics
Aythami Bethencourt de León, Darryl D. Holm
We develop a variational and geometric theory based on statistical physics for the joint evolution of Transformer attention and token representations at fixed model parameters. To…
Modelling the climate and weather of a 2D Lagrangian-averaged Euler-Boussinesq equation with transport noise
Diego Alonso-Oran, Aythami Bethencourt de Leon, Darryl Holm +1
The prediction of climate change and its impact on extreme weather events is one of the great societal and intellectual challenges of our time. The first part of the problem is to…
Well-posedness by noise for linear advection of -forms
Aythami Bethencourt de Leon, So Takao
In this work, we extend existing well-posedness by noise results for the stochastic transport and continuity equations by treating them as special cases of the linear advection equ…
Implications of Kunita-Itô-Wentzell formula for -forms in stochastic fluid dynamics
Aythami Bethencourt de Léon, Darryl Holm, Erwin Luesink +1
We extend the Itô-Wentzell formula for the evolution of a time-dependent stochastic field along a semimartingale to -form-valued stochastic processes. The result is the Kunita-I…
On the well-posedness of stochastic Boussinesq equations with cylindrical multiplicative noise
Diego Alonso-Orán, Aythami Bethencourt de León
The Boussinesq equations are fundamental in meteorology. Among other aspects, they aim to model the process of front formation. We use the approach presented in [Hol15] to introduc…