SHIFTING TIME: TIME-SERIES FORECASTING WITH KHATRI-RAO NEURAL OPERATORS
Keywords: time-series modeling, spatio-temporal modeling, time-shift operator, Khatri-Rao neural operator, neural operator, operator learning
TL;DR: We present a new operator-theoretic paradigm for temporal and spatio-temporal forecasting problems by learning a continuous time-shift operator.
Abstract: We present an operator-theoretic framework for time-series forecasting that involves learning a continuous time-shift operator associated with temporal and spatio-temporal problems. The time-shift operator learning paradigm offers a continuous relaxation of the discrete lag factor used in traditional autoregressive models enabling the history of a function up to a given time to be mapped to its future values. To parametrize the operator learning problem, we propose Khatri-Rao neural operators -- a new architecture for defining non-stationary integral transforms which achieves almost linear cost on spatial and spatio-temporal problems. From a practical perspective, the advancements made in this work allow us to handle irregularly sampled observations and forecast at super-resolution in both space and time. Detailed numerical studies across a wide range of temporal and spatio-temporal benchmark problems suggest that the proposed approach is highly scalable and provides results that compares favourably with the state-of-the-art methods.
Primary Area: learning on time series and dynamical systems
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Submission Number: 12103
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