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

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