Bayesian Tensor Autoencoder with Physics-informed Predictive Prior for Multi-dimensional Time Series Anomaly Detection

2026-09-25

AI Summary

This study addresses the degradation of tensor structures and the insufficient utilization of reconstruction and prediction information in multidimensional time series anomaly detection. To tackle these challenges, this work proposes the PPPTAE framework, which employs a tensor autoencoder as its backbone. The framework innovatively designs a physics-informed predictive prior and incorporates low-rank decomposition to mitigate over-generalization. Furthermore, it leverages Bayesian inference to integrate historical predictions with current reconstruction signals, thereby effectively preserving the intrinsic structure of the data. Experimental evaluations on real-world datasets demonstrate that the proposed method significantly enhances both the accuracy and robustness of anomaly detection.

Abstract

Multi-dimensional time series, inherently tensorial, are common in practice. Despite great progress in time series anomaly detection, most existing methods are confined to uni-/multi-variate time series. When handling multi-dimensional time series using these methods, reshaping operations are required, which inevitably break the intrinsic correlations and thus lead to performance degradation. In uni-/multi-variate time series anomaly detection, AutoEncoders (AEs) are widely adopted and generally categorized into reconstruction-based and prediction-based AEs. The reconstruction-based AE utilizes the current observation for reconstruction, while the prediction-based AE utilizes the historical information to predict the current observation. Thus, the two AEs utilize different information. To bridge the gap between reconstruction-based and prediction-based AEs, so as to fully leverage the available information and thus further enhance performance, we propose a predictive prior and incorporate it into the reconstruction-based AE. It may not be very difficult to conceive this idea, but designing the predictive prior so that it can work for tensor anomaly detection is non-trivial. Specifically, to avoid breaking the intrinsic correlations within the multi-dimensional time series, we use the tensor AE as the backbone. To incorporate the predictive prior into the reconstruction-based AE, we propose a Bayesian fusion approach and our analysis reveals that this approach can enhance the modeling capability of the model for normal data. To mitigate the over-generalization problem of AE, we incorporate physical laws, i.e. tensor low-rank decomposition rules, into the neural networks in the predictive prior, leading to the Physics-informed Predictive Prior Tensor AE (PPPTAE) framework. Experimental results on real-world datasets demonstrate the effectiveness of the proposed method.

Problem

• multi-dimensional time series
• anomaly detection
• tensor autoencoder
• over-generalization

Innovation

• Bayesian Tensor Autoencoder
• Physics-informed Predictive Prior
• Multi-dimensional Time Series
• Anomaly Detection
• Tensor Low-rank Decomposition