This repository contains a PyTorch implementation of the paper Learning to Assimilate in Chaotic Dynamical Systems (https://papers.nips.cc/paper/2021/hash/65cc2c8205a05d7379fa3a6386f710e1-Abstract.html).

Abstract: The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions by systematically combining noisy, incomplete observations and numerical models of system dynamics to produce effective estimation schemes. We introduce amortized assimilation, a framework for learning to assimilate in dynamical systems from sequences of noisy observations with no need for ground truth data. We motivate the framework by extending powerful results from self-supervised denoising to the dynamical systems setting through the use of differentiable simulation.

This code can be memory heavy as each experiment unrolls at least 40 assimilation steps (which from a memory perspective is equivalent to a 40x deeper network plus whatever is needed for the simulation). Current settings are optimized to max out memory usage on a GTX1070 GPU. The easiest ways to tune memory usage are network width and ensemble size. Checkpointing could significantly improve memory utilization but is not currently implemented.

To install the dependencies, use the provided requirements.txt file:

pip install -r requirements.txt 

There is also a dependency on torchdiffeq. Instructions for installing torchdiffeq can be found at https://github.com/rtqichen/torchdiffeq, but are also copied below:

pip install git+https://github.com/rtqichen/torchdiffeq

To run the DA comparison models, you will need to install DAPPER. Instructions can be found here: https://github.com/nansencenter/DAPPER.

A setup.py file has been included for installation. Navigate to the home folder and run:

pip install -e . 

All experiments can be run from experiments/run_*.py. Default settings are those used in the paper. First navigate to the experiments directory then execute:

L96 Full Observations

python run_L96Conv.py --obs_conf full_obs

L96 Partial Observations (every fourth).

python run_L96Conv.py --obs_conf every_4th_dim_partial_obs

VL20 Partial

python run_VLConv.py --obs_conf every_4th_dim_partial_obs

KS Full

python run_KS.py 

Other modifications of interest might be to adjust the step size for the integrator (--step_size, default .1), observation error(--noise, default 1.), ensemble size (--m, default 10), or network width (--hidden_size, default 64 for conv). The L96 code also includes options for self-supervised and supervised analysis losses (ss_analysis, clean_analysis) used for creating Figure 6 from the paper. Custom observation operators can be created in the same style as those found in obs_configs.py.

Parameters for traditional DA approaches were tuned via grid search over smaller sequences. Those hyperparameters were then used for longer assimilation sequences.

To test a new architecture, you'll want to ensure it's obeying the same API as the models in models.py, but otherwise it should slot in without major issues.

Code is included for generating the Lorenz 96, VL 20 and KS datasets. This can be found under amortized_assimilation/data_utils.py

DAPPER: Raanes, P. N., & others. (2018). nansencenter/DAPPER: Version 0.8. https://doi.org/10.5281/zenodo.2029296

This material is based upon work supported by the National Science Foundation under Grant No. 1835825. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

If you found the code or ideas in this repository useful, please consider citing:

@article{mccabe2021l2assim,
  title={Learning to Assimilate in Chaotic Dynamical Systems},
  author={McCabe, Michael and Brown, Jed},
  journal={Advances in Neural Information Processing Systems},
  year={2021}
}