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This repo implements the EDMD algorithm, EDMDDL algorithm [1] and the learning of parametric Koopman decomposition [2].

Getting Started¶

To set up the environment, please refer to Set up the environment. This repository is designed to be user-friendly. You only need a few lines of code to run a simple example. For a quick start, please check out the Quick Start. A few examples are provided in the example folder of this repository.

User Guide¶

• Customizing Input Parameters and Solver: Input Guide.
• Customizing Observable Functions: Custom Observable Guide.
• Customizing ODE: Custom ODE Guide.
• Customizing ODE Solver: Custom ODE Solver Guide.
• Enhancing Performance with GPU and Multithreading: Parallel Computing Guide.

Class References¶

Most of the symbols in this documentation can be found at [2].

• Dictionary: ObservableFunction, Dictionary, TrainableDictionary, RBFDictionary.
• Koopman Operator: Koopman, ParamKoopman, KoopmanDynamics.
• Solver: EDMDSolver, EDMDDLSolver, ParamKoopmanDLSolver, KoopmanDynamics.
• SolverWrapper: SolverWrapper, EDMDRBFSolverWrapper, EDMDDLSolverWrapper, ParamKoopmanDLSolverWrapper.
• ODEs: AbstractODE, DiscreteDynamics.
• ODE Solver: ODESolver.
• Data Management: KoopmanDataSet, ParamKoopmanDataSet.
• Neural Network: FullConnBaseNet, FullConnNet, FullConnResNet.
• Control Solver: KoopmanMPCSolver.

References¶

[1]: Li, Q., Dietrich, F., Bollt, E. M., & Kevrekidis, I. G. (2017). Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(10), 103111.

[2]: Guo, Yue, Milan Korda, Ioannis G. Kevrekidis, and Qianxiao Li. "Learning Parametric Koopman Decompositions for Prediction and Control." arXiv preprint arXiv:2310.01124 (2023).