Neural Bilinear Models Enhance Time Series Forecasting.

Many real-world time series data are generated by complex nonlinear systems, posing a significant challenge for accurate forecasting. Existing dynamic modeling approaches often simplify these systems by assuming linear dynamics or using Koopman-based linearizations, which can lead to inaccuracies and error accumulation, particularly in long-term predictions. To overcome these limitations, researchers propose the Neural Bilinear Dynamical Model (NBDM). NBDM models nonlinear system dynamics by lifting them into a higher-dimensional latent space using Koopman theory, where a bilinear dynamical model is then constructed to describe state evolution. An important addition is a parameterized error compensation term, designed to mitigate approximation errors inherent in bilinear representations. NBDM also explicitly integrates control inputs into its dynamics, using auxiliary variables when available or learning feedback signals otherwise. For scenarios where control inputs are missing, a memory-enhanced controller infers latent controls through multiplicative interactions between historical states and control signals. Extensive experiments on five real-world datasets demonstrate NBDM's consistent superiority over competitive baselines, especially for multi-step and long-horizon forecasting, in both scenarios with and without given control inputs.