Variational Data Assimilation with a Learned Inverse Observation Operator

This repository contains an implementation of the algorithm analyzed in our paper:

Variational Data Assimilation with a Learned Inverse Observation Operator

This is a research project, not an official Google product.

Repository Overview

The analysis notebooks reproducing our paper's results are:

Analysis_Lorenz96.ipynb Analysis_KolmogorovFlow.ipynb

The executables are:

run_data_assimilation.py: performs data assimilation

run_train_inverse_observations.py: trains an inverse observation operator

run_generate_training_data.py: generates trajectory data for dynamical systems for training an inverse observation operator

run_compute_correlation.py: computes spatial correlations for dynamical systems used for data assimilation

The code implements two dynamical systems, the Lorenz96 model and two-dimensional fluid with Kolmogorov forcing. These systems are defined at:

dynamical_system.py

Machine learning components to train their inverse operators and helper methods are defined at:

lorenz96_ml.py, lorenz96_methods.py

kolmogorov_ml.py, kolmogorov_methods.py

General machine learning and data assimilation helper methods are defined at:

ml_methods.py, da_methods.py

Installation requirements

Please install jaxlib==0.1.57 for your cuda version, e.g. for cuda 11.0,

pip install -U jaxlib==0.1.57+cuda110 -f https://storage.googleapis.com/jax-releases/jax_releases.html

The Navier-Stokes equations for the Kolmogorov flow dynamical system are solved using JAX-CFD. Please install jax_cfd==0.1.0,

pip install -U jax_cfd==0.1.0

All other dependencies are listed in requirements.txt.

Reproduce paper results

The quickest way

You may run the notebooks Analysis_Lorenz96.ipynb and Analysis_KolmogorovFlow.ipynb to reproduce our paper's plots based on the results we have uploaded to public cloud storage.

The quick way

Download data Create data base directory:

mkdir -p /data

Data assimilation requires spatial correlation data and inverse observation models for the respective dynamical system. Downloading these requires gsutil:

gsutil cp -r gs://gresearch/jax-cfd/projects/invobs-data-assimilation/invobs-da-data /data

This downloads into /data/invobs-da-data/ and all config files assume this path.

Run data assimilation

You may then perform data assimlation yourself by executing run_data_assimilation.py on the respective setting as defined via a config file at config_files/data_assimilation/, e.g.,

python run_data_assimilation.py --config config_files/data_assimilation/lorenz96_baselineinit_obsopt.config

Running this for the Lorenz96 model takes ~1.5h, for Kolmogorof flow ~10h on a single V100 GPU.

The manual way

You may run all components of the pipeline in the following order:

Create data directory

Create the data directory: mkdir -p /data/invobs-da-data/.

Generate training data

Generate training data with the config files specified at config_files/data_generation by running

python run_generate_training_data.py --config CONFIG

Train the approximate inverse observation model

Use the config files specified at config_files/invobs_training by running

python run_train_inverse_observations.py --config CONFIG

Compute spatial correlations

Use the config files specified at config_files/correlation by running

python run_compute_correlation.py --config CONFIG

Perform data assimilation

Follow instructions as described above for the quick way.

Paper Reference

@misc{invobs_da2021,
      title={Variational Data Assimilation with a Learned Inverse Observation Operator}, 
      author={
          Thomas Frerix 
          and Dmitrii Kochkov 
          and Jamie A. Smith 
          and Daniel Cremers 
          and Michael P. Brenner 
          and Stephan Hoyer
      },
      year={2021},
      eprint={2102.11192},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}