Monday, October 05, 11:30am - 12:30pm (HH410)
Variational data assimilation combines model predictions with observational and background information to estimate the state of dynamical systems. However, the high computational cost of four-dimensional variational data assimilation (4D-Var) can limit its application to large-scale problems. This work develops computationally efficient approaches to 4D-Var using adaptive wavelet methods and Fourier neural operators (FNOs).
First, an adaptive wavelet multigrid method is developed to accelerate the solution of the 4D-Var Hessian system by exploiting its multiscale structure. An adaptive wavelet approach is then introduced for incremental 4D-Var, reducing the computational cost of tangent linear model integrations while maintaining accurate reconstructions. Finally, an FNO-based approach is developed to learn mappings associated with the 4D-Var optimality conditions and provide efficient initializations for conventional solvers. The methods are evaluated using linear advection and viscous Burgers equations, with substantial reductions in computational cost and solver iterations. The applicability of incremental 4D-Var to the chaotic Kuramoto–Sivashinsky equation is also investigated. Overall, the results demonstrate how adaptive numerical methods and neural operators can improve the computational efficiency of variational data assimilation while preserving the robustness of standard 4D-Var frameworks.