- Updated: July 15, 2026
- 1 min read
Deep Learning Method for Stationary Distribution of Reflected Brownian Motion
Deep Learning Method for Stationary Distribution of Reflected Brownian Motion
Authors: Jim Dai, Zhanhao Zhang
Published: July 11, 2026
Reflected Brownian motion (RBM) is a cornerstone model for high‑dimensional stochastic systems, yet analytical solutions for its stationary distribution are scarce. In this groundbreaking study, the authors present a deep learning framework that accurately learns the Laplace transform of RBMs by leveraging the basic adjoint relationship (BAR). The method combines a custom loss function, strategic data sampling, and a tailored neural network architecture to deliver near‑perfect tail‑probability predictions, even in dimensions where traditional techniques fail.
The approach is validated on benchmark RBM instances with known ground‑truth tail probabilities. Results demonstrate exceptional accuracy and computational efficiency, positioning the model as a versatile tool for analyzing complex stochastic systems beyond analytically tractable regimes.
For a deeper dive into the methodology, implementation details, and code repository, visit the project page on ubos.tech. The open‑source code is available at GitHub, enabling researchers and engineers to reproduce and extend the results.
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Andrii Bidochko
CTO UBOS
Andrii Bidochko is an AI entrepreneur and researcher focused on AI agents, reinforcement learning, and autonomous systems. He writes about the technologies shaping the future of machine intelligence, from frontier models and agent architectures to real-world AI applications.