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Data assimilation is the process of fusing information from imperfectcomputer simulations with noisy, sparse measurements of reality to obtainimproved estimates of the state or parameters of a dynamical system ofinterest. The data assimilation procedures used in many geoscienceapplications, such as numerical weather forecasting, are variants of theour-dimensional variational (4D-Var) algorithm. The cost of solving theunderlying 4D-Var optimization problem is dominated by the cost of repeatedforward and adjoint model runs. This motivates substituting the evaluations ofthe physical model and its adjoint by fast, approximate surrogate models.Neural networks offer a promising approach for the data-driven creation ofsurrogate models. The accuracy of the surrogate 4D-Var solution depends on theaccuracy with each the surrogate captures both the forward and the adjointmodel dynamics. We formulate and analyze several approaches to incorporateadjoint information into the construction of neural network surrogates. Theresulting networks are tested on unseen data and in a sequential dataassimilation problem using the Lorenz-63 system. Surrogates constructed usingadjoint information demonstrate superior performance on the 4D-Var dataassimilation problem compared to a standard neural network surrogate that usesonly forward dynamics information.

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