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

Srinath Dama, Kevin Course, Prasanth B. Nair
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:12402-12435, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-dama25a, title = {Shifting Time: Time-series Forecasting with Khatri-Rao Neural Operators}, author = {Dama, Srinath and Course, Kevin and Nair, Prasanth B.}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {12402--12435}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/dama25a/dama25a.pdf}, url = {https://proceedings.mlr.press/v267/dama25a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Shifting Time: Time-series Forecasting with Khatri-Rao Neural Operators %A Srinath Dama %A Kevin Course %A Prasanth B. Nair %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-dama25a %I PMLR %P 12402--12435 %U https://proceedings.mlr.press/v267/dama25a.html %V 267 %X 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.
APA
Dama, S., Course, K. & Nair, P.B.. (2025). Shifting Time: Time-series Forecasting with Khatri-Rao Neural Operators. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:12402-12435 Available from https://proceedings.mlr.press/v267/dama25a.html.

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