8 citations · 16 across the 13 of their papers we have counts for
14 papers
On the dispersionless limit of the Manakov system, its Riemann invariants, and the modulational stability of its counterpropagating plane waves
Jimmie Adriazola, Gino Biondini
We study the dispersionless limit of the Manakov system, the integrable two-component generalization of the nonlinear Schrödinger equation. We derive the resulting four-component g…
Learning Lax Pairs: Revisiting the Classical Paradigm
Jimmie Adriazola, Gino Biondini, Wei Zhu +1
A Lax pair is sometimes thought of as a structural certificate, in that the spatial operator carries the spectral data of an integrable system, and its isospectral evol…
Structure-Preserving Optimal Control of Maxwell's Equations with Applications to Source Cloaking
Harbir Antil, Yaw Owusu-Agyemang, Rohit Khandelwal +2
We develop a structure-preserving solution framework for the optimal control of the time-dependent Maxwell's equations. Building on a well-posedness theory for a weak form of the f…
Learning Volterra Memory Kernels for Non-Markovian Qubit Dynamics
Jimmie Adriazola, Katarzyna Roszak
We develop a data-driven framework for identifying non-Markovian equations of motion for open quantum systems, demonstrated here for qubit-environment dynamics. Starting from the N…
Machine Learning of Nonlinear Waves: Data-Driven Methods for Computer-Assisted Discovery of Equations, Symmetries, Conservation Laws, and Integrability
Jimmie Adriazola, Panayotis G. Kevrekidis, Vassilis Koukouloyannis +1
The purpose of this article is to provide a perspective---admittedly, a rather subjective one---of recent developments at the interface of machine learning (ML)/data-driven methods…
Computer Assisted Discovery of Integrability via SILO: Sparse Identification of Lax Operators
Jimmie Adriazola, Wei Zhu, Panayotis Kevrekidis +1
We formulate the discovery of Lax integrability of Hamiltonian dynamical systems as a symbolic regression problem, which, loosely speaking, seeks to maximize the compatibility betw…
A Non-Convex Optimization Strategy for Computing Convex-Roof Entanglement
Jimmie Adriazola, Katarzyna Roszak
We develop a numerical methodology for the computation of entanglement measures for mixed quantum states. Using the well-known Schrödinger-HJW theorem, the computation of convex ro…
On the fractal dimension of non-Newtonian Hele-Shaw flow subject to Saffman-Taylor instability
J. Adriazola, B. Gu, L. Cummings +1
We introduce a discrete numerical method based on the diffusion-limited aggregation (DLA) approach to simulate two-fluid Hele-Shaw flow subject to the Saffman-Taylor interfacial in…
Experimentally Tractable Generation of High-Order Rogue Waves in Bose-Einstein Condensates
Jimmie Adriazola, Panayotis Kevrekidis
In this work, we study a prototypical, experimentally accessible scenario that enables the systematic generation of so-called high-order rogue waves in atomic Bose-Einstein condens…
On the Role of Tikhonov Regularizations in Standard Optimization Problems
J. Adriazola
Tikhonov regularization is a common technique used when solving poorly behaved optimization problems. Often, and with good reason, this technique is applied by practitioners in an…
Apodizer Design to Efficiently Couple Light into a Fiber Bragg Grating
J. Adriazola, R. H. Goodman
We provide an optimal control framework for efficiently coupling light in a bare fiber into Bragg gratings with a cubic nonlinearity. The light-grating interaction excites gap soli…
Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential
J. Adriazola, R. H. Goodman, P. G. Kevrekidis
We pose the problem of transferring a Bose-Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-de…
An Optimal Control Approach to Gradient-Index Design for Beam Reshaping
Jimmie Adriazola, Roy H. Goodman
We address the problem of reshaping light in the Schrödinger optics regime from the perspective of optimal control theory. In technological applications, Schrödinger optics is ofte…
A Reduction-Based Strategy for Optimal Control of Bose-Einstein Condensates
Jimmie Adriazola, Roy H. Goodman
Applications of Bose-Einstein Condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a…