8 papers
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…
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/data-driven methods an…
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…
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…
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…