提出新方法，高效生成满足复杂条件的随机路径。
Sampling conditioned diffusions via Pathspace Projected Monte Carlo
- 基于路径空间的马尔可夫链蒙特卡洛，约束采样路径
- 成功模拟相变、随机游走面积约束等复杂场景
- 适合研究随机动力系统与极端事件建模的学者
我们提出一种算法，用于对具有广泛约束条件的随机微分方程进行采样，包括积分约束、端点约束和随机积分约束。该算法是一种路径空间修正的流形蒙特卡洛方法，可在满足条件的实现路径子流形上进行采样。通过多个实例验证了其有效性：模拟动力学凝聚相变过程，对随机游走施加固定莱维随机面积约束，对非线性波动方程施加高振幅波约束，以及对湍流管道流动的随机偏微分方程模型施加层流化事件的条件采样。
原文摘要 · Abstract (English)
We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace Metropolis-adjusted manifold sampling scheme, which samples stochastic paths on the submanifold of realizations that adhere to the conditioning constraint. We demonstrate the effectiveness of the algorithm by sampling a dynamical condensation phase transition, conditioning a random walk on a fixed Levy stochastic area, conditioning a stochastic nonlinear wave equation on high amplitude waves, and sampling a stochastic partial differential equation model of turbulent pipe flow conditioned on relaminarization events.
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