Second order adjoints for solving PDE-constrained optimization problems

Inverse problems are of utmost importance in many fields of science and engineering. In the variational approach inverse problems are formulated as PDE-constrained optimization problems, where the optimal estimate of the uncertain parameters is the minimizer of a certain cost functional subject to the constraints posed by the model equations. The numerical solution of such optimization problems requires the computation of derivatives of the model output with respect to model parameters. The first order derivatives of a cost functional (defined on the model output) with respect to a large number of model parameters can be calculated efficiently through first order adjoint sensitivity analysis. Second order adjoint models give second derivative information in the form of matrix-vector products between the Hessian of the cost functional and user defined vectors. Traditionally, the construction of second order derivatives for large scale models has been considered too costly. Consequently, data assimilation applications employ optimization algorithms that use only first order derivative information, like nonlinear conjugate gradients and quasi-Newton methods. In this paper we discuss the mathematical foundations of second order adjoint sensitivity analysis and show that it provides an efficient approach to obtain Hessian-vector products. We study the benefits of using of second order information in the numerical optimization process for data assimilation applications. The numerical studies are performed in a twin experiment setting with a two-dimensional shallow water model. Different scenarios are considered with different discretization approaches, observation sets, and noise levels. Optimization algorithms that employ second order derivatives are tested against widely used methods that require only first order derivatives. Conclusions are drawn regarding the potential benefits and the limitations of using high-order information in large scale data assimilation problems

Testing campaign for ECRIDA: the UV resin 3D printer flying on REXUS

ECRIDA is a student project participating in the REXUS/BEXUS campaign that develops a UV resin 3D printer device capable of working in the low-gravity environment offered by the REXUS rocket flight. Our main objective is to describe the impact of low gravity on the UV resin 3D printing process by comparing samples printed on Earth with samples printed in space. Due to the requirements of the host vehicle and driven by the novel design of our device, a thorough testing campaign must be planned and completed to qualify the device for flight and maximise the success of the scientific objectives. This paper describes the requirements that the device must fulfil and goes into the design of our test plan describing the procedures and the results. Vacuum, vibration, pressure, and functional tests were performed and described together with our learned lessons and conclusions in our will to help student teams with their testing activitie

Efficient Computation of Observation Impact in 4D-Var Data Assimilation

Part 4: UQ PracticeInternational audienceData assimilation combines information from an imperfect model, sparse and noisy observations, and error statistics, to produce a best estimate of the state of a physical system. Different observational data points have different contributions to reducing the uncertainty with which the state is estimated. Quantifying the observation impact is important for analyzing the effectiveness of the assimilation system, for data pruning, and for designing future sensor networks. This paper is concerned with quantifying observation impact in the context of four dimensional variational data assimilation. The main computational challenge is posed by the solution of linear systems, where the system matrix is the Hessian of the variational cost function. This work discusses iterative strategies to efficiently solve this system and compute observation impacts