Analysis of the Identifying Regulation with Adversarial Surrogates Algorithm

TL;DR

This paper rigorously analyzes the IRAS algorithm for identifying first integrals in noisy dynamical systems, establishing conditions for its convergence and relating it to SCF iterations in a Gaussian noise setting.

Contribution

It provides the first theoretical analysis of IRAS, linking it to SCF methods and deriving convergence conditions under Gaussian noise assumptions.

Findings

IRAS iterations relate to self-consistent-field methods.

Sufficient conditions for local convergence are established.

Analysis applies to systems with linear first integrals and Gaussian noise.

Abstract

Given a time-series of noisy measured outputs of a dynamical system z[k], k=1...N, the Identifying Regulation with Adversarial Surrogates (IRAS) algorithm aims to find a non-trivial first integral of the system, namely, a scalar function g() such that g(z[i]) = g(z[j]), for all i,j. IRAS has been suggested recently and was used successfully in several learning tasks in models from biology and physics. Here, we give the first rigorous analysis of this algorithm in a specific setting. We assume that the observations admit a linear first integral and that they are contaminated by Gaussian noise. We show that in this case the IRAS iterations are closely related to the self-consistent-field (SCF) iterations for solving a generalized Rayleigh quotient minimization problem. Using this approach, we derive several sufficient conditions guaranteeing local convergence of IRAS to the correct first integral.