Optimization and/or uncertainty analysis of a computer model requires information about result sensitivities to problem parameters. Automatic differentiation (AD) is applied to a two-dimensional Eulerian hydrocode and a casting model to provide these sensitivities (the Jacobian). AD is examined in both the forward and reverse mode using Automatic DIfferentiation of FORtran (ADIFOR). For comparison, the sensitivities are also determined by finite differences. The hydrocode problem set includes simulation of Taylor-Cylinder impact tests that have long been used to calibrate equation-of-state and material-strength models. Reverse-mode methods are found to provide the most efficient use of computational resources when there are 9 or more parameters. As a preliminary step towards a complete sensitivity analysis of a three-dimensional casting simulation, a one-dimensional version of a metal-alloy phase-change conductive-heat-transfer model is examined. The forward and reverse AD code run times were similar and were approximately 24% faster than those of the finite-difference sensitivities. Real problems in three dimensions will certainly have many more parameters. If, as is expected, the trend seen here holds true, reverse-mode AD is favored since the computational time increases only slightly for additional parameters.
To send e-mail to author: rjh@lanl.gov