Adjoint-Matching Neural Network Surrogates for Fast 4D-Var Data Assimilation

TL;DR

This paper develops neural network surrogate models that incorporate adjoint information to accelerate 4D-Var data assimilation, demonstrating improved accuracy and efficiency in a Lorenz-63 system application.

Contribution

It introduces methods to embed adjoint information into neural network surrogates for 4D-Var, enhancing their performance over standard models.

Findings

Adjoint-informed surrogates outperform standard neural networks in data assimilation tasks.

Surrogates effectively capture both forward and adjoint dynamics.

Improved surrogate models reduce computational costs in 4D-Var applications.

Abstract

Data assimilation is the process of fusing information from imperfect computer simulations with noisy, sparse measurements of reality to obtain improved estimates of the state or parameters of a dynamical system of interest. The data assimilation procedures used in many geoscience applications, such as numerical weather forecasting, are variants of the our-dimensional variational (4D-Var) algorithm. The cost of solving the underlying 4D-Var optimization problem is dominated by the cost of repeated forward and adjoint model runs. This motivates substituting the evaluations of the physical model and its adjoint by fast, approximate surrogate models. Neural networks offer a promising approach for the data-driven creation of surrogate models. The accuracy of the surrogate 4D-Var solution depends on the accuracy with each the surrogate captures both the forward and the adjoint model dynamics. We formulate and analyze several approaches to incorporate adjoint information into the construction of neural network surrogates. The resulting networks are tested on unseen data and in a sequential data assimilation problem using the Lorenz-63 system. Surrogates constructed using adjoint information demonstrate superior performance on the 4D-Var data assimilation problem compared to a standard neural network surrogate that uses only forward dynamics information.