Unsupervised Anomaly Prediction with N-BEATS and Graph Neural Network in Multi-variate Semiconductor Process Time Series

TL;DR

This work tackles unsupervised anomaly prediction in high-dimensional semiconductor multi-variate time series by proposing two forecast-based approaches: a univariate N-BEATS model applied per sensor and a Graph Neural Network that learns inter-sensor relations through a graph attention mechanism. Trained on anomaly-free data, both models forecast ahead by $H$ time steps and flag anomalies when the test forecast diverges from the training forecast beyond threshold $th$, with the GNN achieving higher accuracy and substantially fewer parameters. Results show strong forecasting up to $H=20$ and reliable anomaly detection up to $H=50$, with the GNN outperforming N-BEATS across datasets and offering favorable scalability for real-time manufacturing deployment. The study highlights a lightweight, deployable approach for real-time process monitoring in semiconductor fabrication and points to future work on adaptability across tools, causal interpretation, and linking process anomalies to device-level outcomes.

Abstract

Semiconductor manufacturing is an extremely complex and precision-driven process, characterized by thousands of interdependent parameters collected across diverse tools and process steps. Multi-variate time-series analysis has emerged as a critical field for real-time monitoring and fault detection in such environments. However, anomaly prediction in semiconductor fabrication presents several critical challenges, including high dimensionality of sensor data and severe class imbalance due to the rarity of true faults. Furthermore, the complex interdependencies between variables complicate both anomaly prediction and root-cause-analysis. This paper proposes two novel approaches to advance the field from anomaly detection to anomaly prediction, an essential step toward enabling real-time process correction and proactive fault prevention. The proposed anomaly prediction framework contains two main stages: (a) training a forecasting model on a dataset assumed to contain no anomalies, and (b) performing forecast on unseen time series data. The forecast is compared with the forecast of the trained signal. Deviations beyond a predefined threshold are flagged as anomalies. The two approaches differ in the forecasting model employed. The first assumes independence between variables by utilizing the N-BEATS model for univariate time series forecasting. The second lifts this assumption by utilizing a Graph Neural Network (GNN) to capture inter-variable relationships. Both models demonstrate strong forecasting performance up to a horizon of 20 time points and maintain stable anomaly prediction up to 50 time points. The GNN consistently outperforms the N-BEATS model while requiring significantly fewer trainable parameters and lower computational cost. These results position the GNN as promising solution for online anomaly forecasting to be deployed in manufacturing environments.

Figures (10)

• Figure 1: Example of a time series from a process in one chamber.
• Figure 2: Train-test dataset split visualized on one time series. The training data (blue) consists of the first two thirds of the data and the test data (orange) of the last third.
• Figure 3: Various examples of induced anomalies. In each example the non-anomalous signal (blue) and the corresponding induced anomaly (orange) are plotted. Figures a), c) and f) display amplitude shift anomalies, Figure b) displays a time shift anomaly and Figures d) and e) display step shift anomalies.
• Figure 4: N-BEATS model architecture. Image taken from original article, Oreshkin2019
• Figure 5: Forecast structure for a horizon $H$=4 of a single variable. The colour-coded diagonals highlight the forecasts of the same time point. At time step $t$, the first forecasted point is forecasted for the $H^{th}$ time. The various forecasts must be aggregated to compute an anomaly score.