标题： 通过大偏差理论进行罕见事件的数值计算 显示英文标题

标题： Numerical computation of rare events via large deviation theory

摘要： 基于大偏差理论（LDT）的罕见事件算法综述。 它涵盖了在各种设置中计算大偏差最小值的数值方案，并讨论了最佳实践、常见陷阱和实现权衡。 提出了最小作用方法的推广、扩展和改进。 这些算法在示例问题上进行了测试，这些示例说明了可能出现的几种常见困难，例如。 当扰动是退化的或乘法的时候，或者系统是无限维的时候。 还讨论了到由非高斯噪声或随机初始数据和参数驱动的过程的推广，以及此处回顾的基于LDT的方法与其他方法（如随机场理论和最优控制）之间的联系。 最后，探索了将这种方法与重要性采样方法结合使用，例如。 系谱算法。 显示英文摘要

摘要： An overview of rare events algorithms based on large deviation theory (LDT) is presented. It covers a range of numerical schemes to compute the large deviation minimizer in various setups, and discusses best practices, common pitfalls, and implementation trade-offs. Generalizations, extensions, and improvements of the minimum action methods are proposed. These algorithms are tested on example problems which illustrate several common difficulties which arise e.g. when the forcing is degenerate or multiplicative, or the systems are infinite-dimensional. Generalizations to processes driven by non-Gaussian noises or random initial data and parameters are also discussed, along with the connection between the LDT-based approach reviewed here and other methods, such as stochastic field theory and optimal control. Finally, the integration of this approach in importance sampling methods using e.g. genealogical algorithms is explored.