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In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the…
We investigate the well-posedness theory of the 2-D fractional nonlinear Schr\"odinger equation (NLSE) with a mixed degree of derivatives. Motivated by models in optics and photonics where the light propagation is governed by non-quadratic,…
We propose and experimentally demonstrate a nonlinear-optics approach to pattern recognition with single-pixel imaging and deep neural network. It employs mode selective image up-conversion to project a raw image onto a set of coherent…
Non linear fiber optics concerns with the non linear optical phenomena occurring inside optical fibers. The propagation of light in single-mode fibers is governed by the one-dimensional nonlinear Schr\"odinger equation (NLS) in the presence…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…
Non-Markovian stochastic Schr\"odinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only…
Using the path-integral technique we examine the mutual information for the communication channel modelled by the nonlinear Schr\"odinger equation with additive Gaussian noise. The nonlinear Schr\"odinger equation is one of the fundamental…
Starting from the 3D Gross-Pitaevskii equation we revisit the dimensional reduction to an effective one-dimensional wave-equation that describes the longitudinal dynamics of a Bose condensate in an axially-symmetric external potential.…
We study a stochastic version of the one-dimensional discrete nonlinear Schr{\"o}dinger equation (DNSE), which is derived from first principles, and thus possesses all the properties required by statistical mechanics, such as detailed…
We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs consisting of three bonds. It is shown that the…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the…
Single-shot imaging with femtosecond X-ray lasers is a powerful measurement technique that can achieve both high spatial and temporal resolution. However, its accuracy has been severely limited by the difficulty of applying conventional…
We consider vector Non-linear Schrodinger Equation(NLSE) with balanced loss-gain(BLG), linear coupling(LC) and a general form of cubic nonlinearity. We use a non-unitary transformation to show that the system can be exactly mapped to the…
In model-based reinforcement learning, most algorithms rely on simulating trajectories from one-step models of the dynamics learned on data. A critical challenge of this approach is the compounding of one-step prediction errors as the…
We implement the Numerical Unified Transform Method to solve the Nonlinear Schr\"odinger equation on the half-line. For so-called linearizable boundary conditions, the method solves the half-line problems with comparable complexity as the…
We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…
Supervised convolutional neural networks (CNNs) are widely used to solve imaging inverse problems, achieving state-of-the-art performance in numerous applications. However, despite their empirical success, these methods are poorly…
Line spectral estimation (LSE) from multi snapshot samples is studied utilizing the variational Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) method for a single snapshot, we develop the…
Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE). More precisely, we give nonasymptotic expected $l^2$-distance bounds between the LSE and the true regression…