Physics-Informed Diffusion Models for Unsupervised Anomaly Detection in Multivariate Time Series

TL;DR

This paper introduces a physics-informed diffusion model for unsupervised anomaly detection in multivariate time series, improving detection accuracy and data diversity by incorporating physics-based constraints during training.

Contribution

It presents a novel physics-informed loss function for diffusion models, enhancing their ability to learn the underlying data distribution for anomaly detection.

Findings

Improved F1 score in anomaly detection tasks.

Better data diversity and log-likelihood.

Outperforms baseline and prior physics-informed models.

Abstract

We propose an unsupervised anomaly detection approach based on a physics-informed diffusion model for multivariate time series data. Over the past years, diffusion model has demonstrated its effectiveness in forecasting, imputation, generation, and anomaly detection in the time series domain. In this paper, we present a new approach for learning the physics-dependent temporal distribution of multivariate time series data using a weighted physics-informed loss during diffusion model training. A weighted physics-informed loss is constructed using a static weight schedule. This approach enables a diffusion model to accurately approximate underlying data distribution, which can influence the unsupervised anomaly detection performance. Our experiments on synthetic and real-world datasets show that physics-informed training improves the F1 score in anomaly detection; it generates better data diversity and log-likelihood. Our model outperforms baseline approaches, additionally, it surpasses prior physics-informed work and purely data-driven diffusion models on a synthetic dataset and one real-world dataset while remaining competitive on others.