Physics informed AI predicts early change detection in complex data
QD-PINN:A Physics-Informed Neural Network Approach to Bayesian Quickest Detection in High-Dimensional Diffusions
Machine Learning
Summary
Detecting sudden changes quickly in complex, high-dimensional data is very challenging for traditional methods. The authors use a special type of AI called physics-informed neural networks (PINNs) to find the best time to detect these changes. They show that their method works well even with complicated data dependencies and is stable across many test runs. Their results match well with known numerical methods, proving the approach’s accuracy.
What this means in practice
- •For financial analysts: Identify the earliest time to detect critical changes in complex market data using a neural network approach that handles many variables efficiently.
- •For industrial process control teams: Use AI-driven detection boundaries to quickly signal operational changes in high-dimensional sensor data for improved monitoring.
Authors
Hang Ye, Yi Liu, Haipeng Xing
Abstract
Quickest detection problems (QDPs) arise in a wide range of applications. However, the complementarity structure of the associated variational inequalities poses substantial challenges for traditional numerical methods, particularly in high-dimensional settings. We propose a PINN-based framework for estimating the optimal stopping boundary in QDPs with high-dimensional diffusion processes and spatial dependence, while overcoming the curse of dimensionality. Theoretically, we establish a novel equivalence between the free-boundary PDE and an infinite-dimensional stochastic optimization problem, rigorously justifying the use of finite-dimensional neural networks to approximate the true solution. Furthermore, we assess the robustness of the proposed framework by quantifying uncertainty in the learned stopping boundaries using deep ensembles and Monte Carlo dropout. The results show low variability across independent training runs and stochastic forward passes, indicating stable and consistent boundary estimates. We also compare our PINN results with reference numerical solutions where available and find close agreement.