An observation sensitivity method to identify targeted observations is implemented in the context of four dimensional variational (4D-Var) data assimilation. This methodology is compared with the well-established adjoint sensitivity method using a nonlinear Burgers equation as a test model. Automatic differentiation software is used to implement the first order adjoint model to calculate the gr...

We present a new local-in-time discrete adjoint-based methodology for solving design optimization problems arising in unsteady aerodynamic applications. The new methodology circumvents storage requirements associated with the straightforward implementation of a global adjoint-based optimization method that stores the entire flow solution history for all time levels. This storage cost may quickl...

The adjoint method was first developed for aerodynamic shape optimization applications through the use of control theory by Jameson (1998) in the late 1980s and early 1990s, using ideas adapted from more general work by Lions (1971) on optimal control of systems governed by partial differential equations (PDEs). Over the past two decades, adjoint methods have been used in a variety of applicati...

An adjoint model for a 2D finite element Galerkin shallow water model is developed using the Independent Set Perturbation (ISP, [46]) sensitivity analysis. Its performance in a full 4-D Var setup with a limited area is assessed by comparing with the adjoint model derived by the automatic differentiation approach, where it is used for optimising the initial conditions. It is shown that the ISP s...

This paper presents a continuous adjoint-based optimization theory for a general closed-loop transport hyperbolic model controlled via a periodic boundary control to minimize a multi-objective cost functional. The periodic boundary control is subject to a nonlinear differential equation constraint, thus resulting in a coupling between the hyperbolic equation and the ordinary differential equati...

Single cells learn by tuning their synaptic conductances and redistributing their excitable machinery. To reveal its learning rules, one must therefore know how the cell remaps its ion channels in response to physiological stimuli. We here develop an adjoint approach for discerning the non-uniform distribution of a given channel type from knowledge of the time course of membrane potential at tw...

These Lecture Notes review the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solu...

Adjoint-based shape optimization methods have proven to be computationally efficient for aerodynamic problems. Themajority of the studies on adjoint methods have used structured grids to discretize the computational domain. Because of the potential advantages of unstructured grids for complex configurations, in this study we have developed and validated a continuous adjoint formulation for unst...

In order to decrease the fluid drag on an underwater robot manipulator, an optimal trajectory method based on the variational method is presented. By introducing the adjoint variables, which are Lagrange multipliers, we formulate a Lagrange function under certain constraints related to the target angle, target angular velocity, and dynamic equation of the robot manipulator. The state equation (...

The current work concerns the study and the implementation of a modern algorithm for error estimation in CFD computations. This estimate involves the dealing of the adjoint argument. By solving the adjoint problem, it is possible to obtain important information about the transport of the error towards the quantity of interest. The aim is to apply for the first time this procedure into Petrov-Ga...