3 papers
nlin.SI2026
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…
nlin.PS2026
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…
nlin.SI2025
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…