Analysis of the Identifying Regulation with Adversarial Surrogates Algorithm
This work offers theoretical guarantees for an existing algorithm in dynamical systems analysis, which is incremental as it builds on prior applications without introducing new methods.
The paper provides a rigorous analysis of the IRAS algorithm for identifying first integrals in noisy dynamical systems, showing that under linear first integrals and Gaussian noise, IRAS iterations relate to SCF iterations and deriving sufficient conditions for local convergence to the correct integral.
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.