ICML 2025

Shifting Time: Time-series Forecasting with Khatri-Rao Neural Operators
Srinath Dama 1 Kevin Course 1 Prasanth B. Nair 1
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 tradi-
tional 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 oper-
ator using Khatri-Rao neural operators (KRNOs),
a novel architecture based on non-stationary inte-
gral transforms with nearly linear computational
scaling. Our framework naturally handles irregu-
larly sampled observations and enables forecast-
ing at super-resolution in both space and time.
Extensive numerical studies across diverse tempo-
ral and spatio-temporal benchmarks demonstrate
that our approach achieves state-of-the-art or com-
petitive performance with leading methods.
1. Introduction
Time series forecasting is a fundamental problem in ma-
chine learning and statistics with applications to a broad
spectrum of problems encountered in all branches of sci-
ence, engineering, and finance (Roberts et al., 2013; Milani
et al., 2017; Siami-Namini & Namin, 2018). At a high-level,
time-series problems are concerned with forecasting the fu-
ture values of quantities of interest given past observations
of the same or correlated quantities.
The majority of methods for time-series forecasting largely
fall into the categories of autoregressive moving average
models and their variants (Box & Jenkins, 1976; Girard,
2004), and deep autoregressive models with memory (El-
man, 1990; Hochreiter & Schmidhuber, 1997; Salinas et al.,
2020). With the tremendous success of transformer-based
1Institute
for
Aerospace
Studies,
University
of
Toronto,
ON,
Canada.
Correspondence
to:
Srinath
Dama
<srinath.dama@mail.utoronto.ca>,
Kevin
Course
<kevin.course@mail.utoronto...