KALMAN-INVERSION-LIB PACKAGE

Intro

Welcome to the page of the kalman-inversion-lib package! This package contains Python implementations of Kalman Inversion algorithms.

The package is currently under development. The project structure undergoes changes.

Currently, the following algorithms are available:

• Ensemble Kalman Inversion, EKI
• Unscented Kalman Inversion, UKI
• Ensemble Kalman Sampler, EKS
• Gradient-Free ALDI, ALDI

The documentation is available for each class and its methods via help(), e.g. python help(EnsembleKalmanInversion). Later Wiki pages with a more thorough description for each algorithm are going to be published

Installation

$ python -m pip install kalman-inversion-lib

How to use

The directory examples contains Jupyter notebooks, which demonstrate the workflow for each available algorithm. For some notebooks one might need to install extra packages, e.g. ipympl for interactive plots.

NEW We enabled parallel computation of the forward-model evaluations using the joblib package. Just specify the 'n_jobs', 'prefer' or 'backend' arguments, as it is recommended for the Parallel class on https://joblib.readthedocs.io . You can also pass arguments as a dictionary '**backend_kwargs' to the constructor method of a Kalman algorithm.

List of the core packages

• NumPy https://numpy.org/
• SciPy https://scipy.org/
• tqdm https://tqdm.github.io/
• joblib https://joblib.readthedocs.io/

References

The list below contains references to the articles and insightful resources about Kalman Inversion methods.

• Daniel Zhengyu Huang, Tapio Schneider, and Andrew M. Stuart. "Iterated Kalman Methodology For Inverse Problems / Unscented Kalman Inversion."
• Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich, and Andrew M. Stuart. "Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems."
• Alfredo Garbuno-Inigo, Nikolas Nüsken and Sebastian Reich. "Affine Invariant Interacting Langevin Dynamics for Bayesian Inference."
• Alfredo Garbuno-Inigo, Franca Hoffmann, Wuchen Li, and Andrew M. Stuart. "Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler."
• Marco Iglesias and Yuchen Yang 2021 Inverse Problems 37. "Adaptive regularisation for ensemble Kalman inversion."
• https://github.com/PKU-CMEGroup/InverseProblems.jl/tree/master
• https://github.com/PKU-CMEGroup/InverseProblems.jl/blob/master/Lectures/KalmanInversionPartII.ipynb

Acknowledgements

This package is developed as a part of the research project "Intelligent Geosystems" (100693905) supported by ESF funding