Sonnet: Spectral Operator Neural Network for Multivariable Time Series Forecasting

TL;DR

Sonnet introduces a spectral operator neural network that leverages wavelet transformations and spectral coherence to improve multivariable time series forecasting, outperforming existing models in accuracy.

Contribution

The paper presents a novel architecture, Sonnet, combining spectral analysis with learnable wavelet transforms and a new attention mechanism, MVCA, to better model variable dependencies over time.

Findings

Sonnet outperforms baselines on 34 of 47 forecasting tasks.

MVCA reduces MAE by 10.7% on challenging tasks.

Sonnet achieves an average MAE reduction of 2.2% across benchmarks.

Abstract

Multivariable time series forecasting methods can integrate information from exogenous variables, leading to significant prediction accuracy gains. The transformer architecture has been widely applied in various time series forecasting models due to its ability to capture long-range sequential dependencies. However, a na\"ive application of transformers often struggles to effectively model complex relationships among variables over time. To mitigate against this, we propose a novel architecture, termed Spectral Operator Neural Network (Sonnet). Sonnet applies learnable wavelet transformations to the input and incorporates spectral analysis using the Koopman operator. Its predictive skill relies on the Multivariable Coherence Attention (MVCA), an operation that leverages spectral coherence to model variable dependencies. Our empirical analysis shows that Sonnet yields the best performance on $34$ out of $47$ forecasting tasks with an average mean absolute error (MAE) reduction of $2.2\%$ against the most competitive baseline. We further show that MVCA can remedy the deficiencies of na\"ive attention in various deep learning models, reducing MAE by $10.7\%$ on average in the most challenging forecasting tasks.