EMForecaster: A Deep Learning Framework for Time Series Forecasting in Wireless Networks With Distribution-Free Uncertainty Quantification

With the recent advancements in wireless technologies, forecasting electromagnetic field (EMF) exposure has become increasingly critical to enable proactive network spectrum and power allocation, as well as network deployment planning. In this paper, we develop a deep learning (DL)-empowered time series forecasting framework referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EMForecaster</i>. The proposed DL architecture employs patching to process temporal patterns at multiple scales, complemented by reversible instance normalization and mixing operations along both temporal and patch dimensions for efficient feature extraction. We then augment EMForecaster with a conformal prediction mechanism, which is independent of the data distribution, to enhance the trustworthiness of model predictions through uncertainty quantification of forecasts. In particular, the conformal prediction mechanism ensures that the ground truth lies within a prediction interval with target error rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1-\alpha$</tex-math></inline-formula> is referred to as coverage. However, a trade-off exists, as increasing coverage often results in wider prediction intervals. To address this challenge, we propose a new metric referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Trade-off Score</i>, that balances the trustworthiness of the forecast (i.e., coverage) and the width of prediction interval. Our empirical evaluation demonstrates that EMForecaster achieves superior performance across diverse EMF datasets, spanning both short-term and long-term prediction horizons. In point forecasting tasks, EMForecaster substantially outperforms current state-of-the-art DL approaches, showing improvements of 53.97% over the Transformer architecture and 38.44% over the average of all baseline models. In terms of conformal prediction performance, EMForecaster exhibits excellent balance between prediction interval width and coverage, as measured by the coverage-width tradeoff score. This balance is comparable to DLinear's performance while showing marked improvements of 24.73% over the average baseline and 49.17% over the Transformer architecture. We have included all code used to produce the experiments at github.com/xmootoo/emforecaster.

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