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Long-Term Time Series Forecasting is the process of predicting future values of a sequence over an extended time horizon, such as weeks, months, or years. It uses historical data patterns—like trends, seasonality, and cycles—to model and anticipate future behavior. Techniques include statistical methods (e.g., ARIMA), machine learning, and deep learning (e.g., LSTM, Transformer models). Long-term forecasting is crucial in sectors like energy, finance, and supply chain management, helping with strategic planning, resource allocation, and risk management.

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Multivariate Long-Term State Forecasting in Cyber-Physical Systems: A Sequence to Sequence Approach

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Cyber-physical systems (CPS) are ubiquitous in several critical infrastructure applications. Forecasting the state of CPS, is essential for better planning, resource allocation and minimizing operational costs. It is imperative to forecast the state of a CPS multiple steps into the future to afford enough time for planning of CPS operation to minimize costs and component wear. Forecasting system state also serves as a precursor to detecting process anomalies and faults. Concomitantly, sensors used for data collection are commodity hardware and experience frequent failures resulting in periods with sparse or no data. In such cases, re-construction through imputation of the missing data sequences is imperative to alleviate data sparsity and enable better performance of down-stream analytic models. In this paper, we tackle the problem of CPS state forecasting and data imputation and characterize the performance of a wide array of deep learning architectures – unidirectional gated and non-gated recurrent architectures, sequence to sequence (Seq2Seq) architectures as well as bidirectional architectures – with a specific focus towards applications in CPS. We also study the impact of procedures like scheduled sampling and attention, on model training. Our results indicate that Seq2Seq models are superior to traditional step ahead forecasting models and yield an improvement of at least 28.5% for gated recurrent architectures and about 87.6% for non-gated architectures in terms of forecasting performance. We also notice that bidirectional models learn good representations for forecasting as well as for data imputation. Bidirectional Seq2Seq models show an average improvement of 17.6% in forecasting performance over their unidirectional counterparts. We also demonstrate the effect of employing an attention mechanism in the context of Seq2Seq architectures and find that it provides an average improvement of 57.12% in the case of unidirectional Seq2Seq architectures while causing a performance decline in the case of bidirectional Seq2Seq architectures. Finally, we also find that scheduled sampling helps in training better models that yield significantly lower forecasting error.

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