Variational Data Assimilation with a Learned Inverse Observation Operator
Thomas Frerix, Dmitrii Kochkov, Jamie Smith, Daniel Cremers, Michael Brenner, Stephan Hoyer
Abstract
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a cornerstone of large scale forecasting applications such as numerical weather prediction. As such, it is implemented in current operational systems of weather forecasting agencies across the globe. However, finding a good initial state poses a difficult optimization problem in part due to the non-invertible relationship between physical states and their corresponding observations. We learn a mapping from observational data to physical states and show how it can be used to improve optimizability. We employ this mapping in two ways: to better initialize the non-convex optimization problem, and to reformulate the objective function in better behaved physics space instead of observation space. Our experimental results for the Lorenz96 model and a two-dimensional turbulent fluid flow demonstrate that this procedure significantly improves forecast quality for chaotic systems.
BibTeX
@InProceedings{pmlr-v139-frerix21a,
title = {Variational Data Assimilation with a Learned Inverse Observation Operator},
author = {Frerix, Thomas and Kochkov, Dmitrii and Smith, Jamie and Cremers, Daniel and Brenner, Michael and Hoyer, Stephan},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {3449--3458},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/frerix21a/frerix21a.pdf},
url = {https://proceedings.mlr.press/v139/frerix21a.html},
abstract = {Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a cornerstone of large scale forecasting applications such as numerical weather prediction. As such, it is implemented in current operational systems of weather forecasting agencies across the globe. However, finding a good initial state poses a difficult optimization problem in part due to the non-invertible relationship between physical states and their corresponding observations. We learn a mapping from observational data to physical states and show how it can be used to improve optimizability. We employ this mapping in two ways: to better initialize the non-convex optimization problem, and to reformulate the objective function in better behaved physics space instead of observation space. Our experimental results for the Lorenz96 model and a two-dimensional turbulent fluid flow demonstrate that this procedure significantly improves forecast quality for chaotic systems.}
}