论文标题
有效计算动态系统的极端偏移概率
Efficient computation of extreme excursion probabilities for dynamical systems
论文作者
论文摘要
我们开发了一种新的计算方法，用于评估非线性动力学系统随机初始化产生的极端偏移概率。该方法使用马尔可夫链蒙特卡洛或拉普拉斯近似方法来构建一个偏见分布，而偏置分布又将其用于重要性采样程序，以估计极端的偏移概率。通过使用RICE的公式从偏移概率理论中获得偏见分布的先验和可能性。我们使用高斯混合物偏置分布，并通过矩的方法近似非高斯初始激发，以规避偏移概率理论所需的线性和高斯假设。我们证明了该计算框架对多达100个维度的非线性动力学系统的有效性。
We develop a novel computational method for evaluating the extreme excursion probabilities arising for random initialization of nonlinear dynamical systems. The method uses a Markov chain Monte Carlo or a Laplace approximation approach to construct a biasing distribution that in turn is used in an importance sampling procedure to estimate the extreme excursion probabilities. The prior and likelihood of the biasing distribution are obtained by using Rice's formula from excursion probability theory. We use Gaussian mixture biasing distributions and approximate the non-Gaussian initial excitation by the method of moments to circumvent the linearity and Gaussianity assumptions needed by excursion probability theory. We demonstrate the effectiveness of this computational framework for nonlinear dynamical systems of up to 100 dimensions.
