题目：On the Applications of Optimization Methods in Geophysical Fluid Dynamics

报告人：史斌 教授（复旦大学）

地点：致远楼101室

时间：2025年6月23日 14:00–15:30

Abstract: In this talk, I will present recent progress in applying optimization techniques to geophysical fluid dynamics. In the first part, I introduce a linearized multi-block ADMM algorithm with regularization for solving the 4D variational data assimilation (4D-Var) problem. By formulating the Euler–Lagrange equations over the full model trajectory, the method reduces sensitivity to initial conditions and improves the use of observational data. Although it relies on adjoint models, the algorithm is robust to noise, parallelizable, and compatible with various numerical schemes—including finite difference, finite element, and spectral methods. We demonstrate its effectiveness on the 1D Burgers’ equation and in reconstructing vorticity in 2D turbulence. In the second part, I will introduce a (adjoint-free) sampling algorithm for computing conditional nonlinear optimal perturbations (CNOPs), which help analyze model sensitivity and error growth. These algorithms avoid gradient computation by using zeroth-order statistics, offering significant cost savings while preserving accuracy. Results on the Burgers and Lorenz-96 models show their reliability. When applied to the Zebiak–Cane model and more broadly to numerical models with dimensions on the order of 10^4 to 10^5, the sampling method exhibits high efficiency, particularly when implemented in a parallel computing framework.

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