10 papers
Geometry-Preserving Neural Architectures on Manifolds with Boundary
Karthik Elamvazhuthi, Shiba Biswal, Kian Rosenblum +4
A growing number of neural architectures have been proposed to enforce geometric constraints, including projection-based networks, exponential-map updates, constrained output layer…
From Schrodinger Bridge to Optimal Transport over Sub-Riemannian Manifolds
Daniel Owusu Adu, Karthik Elamvazhuthi, Bahman Gharesifard
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-R…
Flow Matching for Measure Transport and Feedback Stabilization of Control-Affine Systems
Karthik Elamvazhuthi
We develop a \emph{flow-matching framework} for transporting probability measures under control-affine dynamics and for steering systems to points or target sets. Starting from the…
Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems
Karthik Elamvazhuthi, Darshan Gadginmath, Fabio Pasqualetti
In this paper, we propose a deterministic diffusion-based framework for controlling the probability density of nonlinear control-affine systems, with theoretical guarantees for dri…
Discrete Diffusion with Sample-Efficient Estimators for Conditionals
Karthik Elamvazhuthi, Abhijith Jayakumar, Andrey Y. Lokhov
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for gener…
Uniform Sampling from the Reachable Set Using Optimal Transport
Karthik Elamvazhuthi, Sachin Shivakumar
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sample…