SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting (paper link)

This paper has been accepted at ICML 2025.

In this work, we consider the task of time-series forecasting and establish both an explicit connection and a direct architectural match between Koopman operator approximation and linear RNNs. Building on this connection, we introduce Structured Koopman Operator Linear RNN (SKOLR). SKOLR implements a structured Koopman operator through a highly parallel linear RNN stack. Through a learnable spectral decomposition of the input signal, the RNN chains jointly attend to different dynamical patterns from different representation subspaces, creating a theoretically-grounded yet computationally efficient design that naturally aligns with Koopman principles.

Getting Started

1. Install requirements. pip install -r requirements.txt

2. Download data. You can download all the datasets from Autoformer. Create a seperate folder ./dataset and put all the csv files in the directory.

Training

All the scripts are in the directory ./scripts. For example,

sh ./scripts/etth2.sh