DLKoopman: A deep learning software package for Koopman theory

TL;DR

DLKoopman is a versatile deep learning software package that encodes nonlinear dynamical systems into linear space for prediction and analysis, supporting data-driven learning for any system.

Contribution

It introduces a generalized, user-friendly tool for Koopman theory that can learn encodings and linear dynamics from various data types, with new evaluation metrics and hyperparameter tuning.

Findings

Supports data from states or trajectories for flexible modeling

Includes a novel Average Normalized Absolute Error metric

Provides hyperparameter search for optimized performance

Abstract

We present DLKoopman -- a software package for Koopman theory that uses deep learning to learn an encoding of a nonlinear dynamical system into a linear space, while simultaneously learning the linear dynamics. While several previous efforts have either restricted the ability to learn encodings, or been bespoke efforts designed for specific systems, DLKoopman is a generalized tool that can be applied to data-driven learning and optimization of any dynamical system. It can either be trained on data from individual states (snapshots) of a system and used to predict its unknown states, or trained on data from trajectories of a system and used to predict unknown trajectories for new initial states. DLKoopman is available on the Python Package Index (PyPI) as 'dlkoopman', and includes extensive documentation and tutorials. Additional contributions of the package include a novel metric called Average Normalized Absolute Error for evaluating performance, and a ready-to-use hyperparameter search module for improving performance.