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arXiv Statistics ML By Hang Ye, Yi Liu, Haipeng Xing

QD-PINN:A Physics-Informed Neural Network Approach to Bayesian Quickest Detection in High-Dimensional Diffusions

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The paper introduces QD-PINN, a physics-informed neural network framework for estimating optimal stopping boundaries in quickest detection problems involving high-dimensional diffusion processes. It establishes a theoretical equivalence between the free-boundary PDE and an infinite-dimensional stochastic optimization problem, justifying the use of finite-dimensional neural networks. The authors demonstrate the method’s robustness by quantifying uncertainty with deep ensembles and Monte Carlo dropout, showing low variability and close agreement with reference numerical solutions.

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