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.

鉴于一系列嘈杂测量输出的动力系统z[k]，k=1...N，鉴管-反抗拟合(IRAS)算法旨在找到系统的非平凡第一积分，即一个标量函数g()，使得对于所有i、j，有g(z[i]) = g(z[j])。在本文中，我们首次对该算法在特定环境下进行了严格分析，假设观测结果具有线性第一积分并受到高斯噪声的污染。我们证明在这种情况下，IRAS迭代与求解广义瑞利商最小化问题的自洽场(SCF)迭代密切相关。利用这种方法，我们得出了几个充分条件，保证了IRAS收敛到正确的第一积分。

对具有对抗替代算法的标识规制的分析