1 citations · 1 across the 3 of their papers we have counts for
7 papers
Additive Noise, Shift Recovery, and Signed Signals in the Cumulative Distribution Transform
Harbir Antil, Ratna Khatri, Aryan Saxena
The cumulative distribution transform (CDT) is a quantile-based transport representation that exactly linearizes one-dimensional translations of positive densities. We study how th…
OCTANE -- Optimal Control for Tensor-based Autoencoder Network Emergence: Explicit Case
Ratna Khatri, Anthony Kolshorn, Colin Olson +1
This paper presents a novel, mathematically rigorous framework for autoencoder-type deep neural networks that combines optimal control theory and low-rank tensor methods to yield m…
Optimal Control, Numerics, and Applications of Fractional PDEs
Harbir Antil, Thomas S. Brown, Ratna Khatri +3
This article provides a brief review of recent developments on two nonlocal operators: fractional Laplacian and fractional time derivative. We start by accounting for several appli…
Fractional Deep Neural Network via Constrained Optimization
Harbir Antil, Ratna Khatri, Rainald Löhner +1
This paper introduces a novel algorithmic framework for a deep neural network (DNN), which in a mathematically rigorous manner, allows us to incorporate history (or memory) into th…
Bilevel Optimization, Deep Learning and Fractional Laplacian Regularization with Applications in Tomography
Harbir Antil, Zichao Di, Ratna Khatri
In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction…
External optimal control of nonlocal PDEs
Harbir Antil, Ratna Khatri, Mahamadi Warma
Very recently M. Warma has shown that for nonlocal PDEs associated with the fractional Laplacian, the classical notion of controllability from the boundary does not make sense and…