Simulation of Rare Events in Lightwave Systems

本提案中概述的工作目标是开发基于蒙特卡罗的统计技术，以计算光通信系统中丢失比特等罕见事件的可能性。 这些技术将适用于非常复杂的问题（例如通过非线性和非自治项），以至于难以分析，用于计算非常罕见的事件的概率，以至于无法使用标准计算方法进行量化。 该技术将依赖于使用微扰方法和变分原理，结合优化方法，以减少基本的偏微分方程的维数，以确定适当的采样prostitics.The立即应用这项工作将是确定的影响时，暴露于随机损伤，如放大器噪声的光纤通信线路的鲁棒性的调制格式。 更广泛地说，光通信中的严格容差（每传输一个千兆比特或太比特就有一个丢失的比特）在工业中带来了大量的问题，这些技术将很好地适应这些问题。 最后，在工业和自然界中出现了许多情况，人们希望在随机非线性波背景下确定罕见事件的概率;这项工作将提供实现这一目标的技术。 该GOALI项目由数学科学部（DMS）和MPS多学科活动办公室（OMA）共同资助。

The goal of the work outlined in this proposal is to develop Monte Carlo-based statistical techniques to calculate the likelihood of rare events such as dropped bits in optical communications systems. These techniques will be applicable to problems that are so complex (through nonlinear and nonautonomous terms, for example) as to be analytically intractable, for calculating the probability of events that are so rare as to be impossible to quantify using standard computational methods. The techniques will rely on using perturbation methods and variational principles, in conjunction with optimization methods, to reduce the dimension of the underlying partial differential equations in order to determine appropriate sampling heuristics.The immediate application of this work will be to determine the impact of modulation formats on the robustness of a fiber-optic communications line when exposed to random impairments such as amplifier noise. More broadly, the strict tolerances in optical communications (a single dropped bit for each gigabit or terabit transmitted) provide for a large host of problems in the industry to which these techniques will be well suited. Finally, there are many situations that arise in industry and nature where one would liketo determine the probability of a rare event in the context of a stochastic nonlinear wave setting; this work will provide techniques to accomplish this. This GOALI project was jointly funded by the Division of Mathematical Sciences (DMS) and the MPS Office of Multidisciplinary Activities (OMA).