Zobrazeno 1 - 10
of 72
pro vyhledávání: '"Elamvazhuthi, Karthik"'
This paper investigates the use of transformer architectures to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and engine
Externí odkaz:
http://arxiv.org/abs/2410.16295
Autor:
Elamvazhuthi, Karthik
This is a note on the extension of the Benamou-Brenier formulation of optimal transport to nonlinear control affine systems on $\mathbb{R}^d$. They are the non-compact version of the author and collaborators' previous result on compact manifolds, sta
Externí odkaz:
http://arxiv.org/abs/2407.16088
Autor:
Elamvazhuthi, Karthik
It is known that if a nonlinear control affine system without drift is bracket generating, then its associated sub-Laplacian is invertible under some conditions on the domain. In this note, we investigate the converse. We show how invertibility of th
Externí odkaz:
http://arxiv.org/abs/2405.09108
In the present work, we develop a novel particle method for a general class of mean field control problems, with source and terminal constraints. Specific examples of the problems we consider include the dynamic formulation of the p-Wasserstein metri
Externí odkaz:
http://arxiv.org/abs/2402.10124
We propose a novel approach based on Denoising Diffusion Probabilistic Models (DDPMs) to control nonlinear dynamical systems. DDPMs are the state-of-art of generative models that have achieved success in a wide variety of sampling tasks. In our frame
Externí odkaz:
http://arxiv.org/abs/2402.02297
Autor:
Elamvazhuthi, Karthik, Jacobs, Matt
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI system. In thi
Externí odkaz:
http://arxiv.org/abs/2312.10197
In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterparts. This paper delves into the heart of this phenomenon, comparing neu
Externí odkaz:
http://arxiv.org/abs/2312.07851
Autor:
Elamvazhuthi, Karthik, Berman, Spring
In this article, we consider the problem of stabilizing stochastic processes, which are constrained to a bounded Euclidean domain or a compact smooth manifold, to a given target probability density. Most existing works on modeling and control of robo
Externí odkaz:
http://arxiv.org/abs/2308.15755
In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural ordinary diffe
Externí odkaz:
http://arxiv.org/abs/2305.08849
We consider the controllability problem for the continuity equation, corresponding to neural ordinary differential equations (ODEs), which describes how a probability measure is pushedforward by the flow. We show that the controlled continuity equati
Externí odkaz:
http://arxiv.org/abs/2205.09241