Mth 664 Advanced Optimization and Data Assimilation I

Model-constrained optimization for analysis and prediction of complex dynamical systems. Differentiability in Hilbert spaces, adjoint models. Euler-Lagrange equations for linear and nonlinear dynamics, derivation and solution in continuous and discrete formulations. Four-dimensional variational and hybrid data assimilation. Applications to differential and partial differential equations systems, and neural networks. This is the first course in a sequence of two: Mth 664 and Mth 665. Expected preparation: Mth 464/Mth 564 and Mth 465/Mth 565, knowledge of a programming language.