用深度学习精准计算高维反射布朗运动的稳态分布，突破解析解局限。
Deep Learning Method for Stationary Distribution of Reflected Brownian Motion
- 基于基本伴随关系设计神经网络损失函数与采样策略
- 在高维场景下对尾概率预测接近完美，误差极低
- 适合研究复杂随机系统性能分析的科研人员使用
反射布朗运动（RBM）的稳态分布对高维随机系统分析至关重要，但闭式解仅适用于少数特殊情况。计算关键性能指标如尾概率更为困难，尽管其具有实际意义。本文提出一种深度学习方法，基于基本伴随关系（BAR），高效准确地学习高维RBM的拉普拉斯变换。框架融合精心设计的损失函数、训练数据采样流程与神经网络结构。我们在已知真实尾概率的RBM实例上评估该方法，在高维设置中实现近乎完美的预测，凸显其作为超越解析可处理范围的一般性工具的巨大潜力。代码见 https://github.com/zhangz73/NN4MGF。
原文摘要 · Abstract (English)
The stationary distribution of reflected Brownian motion (RBM) plays an important role in the analysis of high-dimensional stochastic systems, yet closed-form solutions are known only for a few special cases. Computing important performance metrics, such as tail probabilities, is even more intractable, despite their practical relevance. In this paper, we develop a deep learning approach that accurately and efficiently learns the Laplace transform of high-dimensional RBMs based on the basic adjoint relationship (BAR). Our framework combines a careful design of the loss function, training data sampling procedure, and neural network architecture. We evaluate the proposed method on RBM instances with known ground-truth tail probabilities and demonstrate near-perfect prediction in high-dimensional settings, highlighting its potential as a general tool for analyzing stochastic systems beyond analytically tractable regimes. Our code can be found at https://github.com/zhangz73/NN4MGF.
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