Shifting Time: Time-series Forecasting with Khatri-Rao Neural Operators

We present an operator-theoretic framework for temporal and spatio-temporal forecasting based on learning a continuous time-shift operator. Our operator learning paradigm offers a continuous relaxation of the discrete lag factor used in traditional autoregressive models, enabling the history of a system up to a given time to be mapped to its future values. We parametrize the time-shift operator using Khatri-Rao neural operators (KRNOs), a novel architecture based on non-stationary integral transforms with nearly linear computational scaling. Our framework naturally handles irregularly sampled observations and enables forecasting at super-resolution in both space and time. Extensive numerical studies across diverse temporal and spatio-temporal benchmarks demonstrate that our approach achieves state-of-the-art or competitive performance with leading methods.

Predicting the future, from weather patterns to financial markets, is a difficult task. It's even harder when the information we have is incomplete or collected at irregular intervals. Instead of just looking at isolated moments, our approach learns from the entire history of events to understand the continuous evolution of a system over time.To accomplish this, we built a new, highly efficient machine learning (ML) model, specifically designed to learn from complex spatio-temporal data, even if that data is irregularly sampled. This special ML model can create very detailed predictions that fill in the gaps, offering a much clearer picture of the future. When tested on different challenges in areas like physics, climate, and finance, our model achieved highly competitive results, providing a more powerful and flexible prediction tool for scientists and engineers.