TIME: 3:30 PM

LOCATION: GMCS 314

SPEAKER: Jimmie Adriazola, Arizona State University

ABSTRACT: In the first part of this talk, we introduce an operator learning framework for computer-assisted discovery of integrability in Hamiltonian dynamical systems. Integrablity is a mathematically rich topic and often the starting point for analyzing more complex, nonintegrable equations. However, it is difficult to even recognize if a given system is integrable before investing effort into studying it. To overcome this, we formulate the computer-assisted discovery of integrability in dynamical systems as a symbolic regression task on an important and enabling class of operators called Lax pairs. Our approach is tested on a variety of systems ranging from nonlinear oscillators, to rigid bodies, to canonical Hamiltonian PDEs. We test robustness of the framework against nonintegrable perturbations, and, in all examples, reliably confirm or deny integrability. Moreover, using a thresholded regularization to promote sparsity, we recover expected and discover new Lax pairs despite wide hypotheses on the operators. Because of this sparse identification, we use these enabling Lax pairs in the context of the unified transform method to algorithmically discover integral transform pairs for PDEs. Time permitting, we will discuss future directions for adapting our framework toward further computer-assisted discoveries in mathematical physics and their potential to build reduced-order models and digital twins of complex physical scenarios. The second part of the talk will focus on data-driven discovery of Volterra integral equations that model non-Markovian dynamics typically present in open quantum systems, an important class of equations that can be used to model the dynamics of qubits interacting with environments while maintaining the memory of interaction. Although such inverse problems involving integral and integro-differential equations have a long history, our aim here is to uncover the quirks specific to non-Markovian qubit dynamics.

HOST: Ricardo Carretero