Recipes for adjoint code construction Adjoint models are increasingly being developed for use in meteorology and oceanography. Typical applications are data assimilation, model tuning, sensitivity analysis, and determination of singular vectors. The adjoint model computes the gradient of a cost function with respect to control variables. Generation of adjoint code may be seen as the special case of differentiation of algorithms in reverse mode, where the dependent function is a scalar. The described method for adjoint code generation is based on a few basic principles, which permits the establishment of simple construction rules for adjoint statements and complete adjoint subprograms. These rules are presented and illustrated with some examples.par Conflicts that occur due to loops and redefinition of variables are also discussed. Direct coding of the adjoint of a more sophisticated model is extremely time consuming and subject to errors. Hence, automatic generation of adjoint code represents a distinct advantage. An implementation of the method, described in this article, is the tangent linear and adjoint model compiler.

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  1. Gratton, Serge; Gürol, Selime; Toint, Philippe L.: Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems (2013)
  2. Hascoet, Laurent; Pascual, Valérie: The Tapenade automatic differentiation tool, principles, model, and specification (2013)
  3. Cioaca, Alexandru; Alexe, Mihai; Sandu, Adrian: Second-order adjoints for solving PDE-constrained optimization problems (2012)
  4. Hossen, M.J.; Navon, I.M.; Daescu, D.N.: Effect of random perturbations on adaptive observation techniques (2012)
  5. Wunsch, Carl: Discrete inverse and state estimation problems. With geophysical fluid applications. (2012)
  6. Espath, L.F.R.; Linn, R.V.; Awruch, A.M.: Shape optimization of shell structures based on NURBS description using automatic differentiation (2011)
  7. Godinez, Humberto C.; Daescu, Dacian N.: Observation targeting with a second-order adjoint method for increased predictability (2011)
  8. Jones, Dominic; Müller, Jens-Dominik; Christakopoulos, Faidon: Preparation and assembly of discrete adjoint CFD codes (2011)
  9. Liao, Wenyuan: A computational method to estimate the unknown coefficient in a wave equation using boundary measurements (2011)
  10. Ulbrich, Michael: Semismooth Newton methods for variational inequalities and constrained optimization problems in function spaces (2011)
  11. Zamani, Ahmadreza; Azimian, Ahmadreza; Heemink, Arnold; Solomatine, Dimitri: Non-linear wave data assimilation with an ANN-type wind-wave model and ensemble Kalman filter (EnKF) (2010)
  12. Alexe, Mihai; Sandu, Adrian: On the discrete adjoints of adaptive time stepping algorithms (2009)
  13. Alexe, Mihai; Sandu, Adrian: Forward and adjoint sensitivity analysis with continuous explicit Runge-Kutta schemes (2009)
  14. Jiang, L.; Douglas, C.C.: An analysis of 4D variational data assimilation and its application (2009)
  15. Stemler, Thomas; Judd, Kevin: A guide to using shadowing filters for forecasting and state estimation (2009)
  16. Bischof, Christian H.; Hovland, Paul D.; Norris, Boyana: On the implementation of automatic differentiation tools (2008)
  17. Giles, M.B.: Monte Carlo evaluation of sensitivities in computational finance (2008)
  18. Papadakis, Nicolas; Mémin, Étienne: Variational assimilation of fluid motion from image sequence (2008)
  19. Papadimitriou, Dimitrios I.; Giannakoglou, Kyriakos C.: Aerodynamic shape optimization using first and second order adjoint and direct approaches (2008)
  20. Protas, Bartosz; Liao, Wenyuan: Adjoint-based optimization of PDEs in moving domains (2008)

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