Small probability events for two-layer geophysical flows under uncertainty

逃逸概率、平均停留时间与地球物理流体粒子动力学

Escape Probability, Mean Residence Time and Geophysical Fluid Particle Dynamics

针对随机扰动下的准地转蜿蜒射流模型，利用逃逸概率和平均停留时间量化不同特征运动流态间的流体输运。

从统计物理与动力系统视角看地球物理极端事件

A statistical physics and dynamical systems perspective on geophysical extreme events

针对现有统计极值分析无法解释地球物理极端事件底层物理机制的问题，本文梳理了相关研究空白与挑战，提出新理论形式，并指出定制化随机方法可助力深化对这类事件的理解。

Probabilistic Dynamics of Two-Layer Geophysical Flows

The two-layer quasigeostrophic flow model is an intermidiate system between the single-layer 2D barotropic flow model and the continuously stratified, 3D baroclinic flow model. This model is widely used to investigate basic mechanisms in geophysical flows, such as baroclinic effects, the Gulf Stream and subtropical gyres. The wind forcing acts only on the top layer. We consider the two-layer quasigeostrophic model under stochastic wind forcing. We first transformed this system into a coupled system of random partial differential equations and then show that the asymptotic probabilistic dynamic…

Quantifying model uncertainty in non-Gaussian dynamical systems with observations on mean exit time or escape probability

Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape probability for the system evolution. It is based on solving an inverse problem for a deterministic, non-local partial differential equation via numerical optimization. The existing methods for estimating parameters require observations on system state sample paths for long time periods or probability densities at large spatial ranges. The method proposed here, instea…

Global Symplectic Uncertainty Propagation on SO(3)

This paper introduces a global uncertainty propagation scheme for rigid body dynamics, through a combination of numerical parametric uncertainty techniques, noncommutative harmonic analysis, and geometric numerical integration. This method is distinguished from prior approaches, as it allows one to consider probability densities that are global, and are not supported on only a single coordinate chart on the manifold. The use of Lie group variational integrators, that are symplectic and stay on the Lie group, as the underlying numerical propagator ensures that the advected probability densities…

Optimal Design of Networks of Positive Linear Systems under Stochastic Uncertainty

In this paper, we study networks of positive linear systems subject to time-invariant and random uncertainties. We present linear matrix inequalities for checking the stability of the whole network around the origin with prescribed probability and decay rate. Based on this condition, we then give an efficient method, based on geometric programming, to find the optimal parameters of the probability distribution describing the uncertainty. We illustrate our results by analyzing the stability of a viral spreading process in the presence of random uncertainties.