Low rank approach to computing first and higher order derivatives using automatic differentiation

Conference · Sun Jul 01 04:00:00 EDT 2012

OSTI ID:22105784

Reed, J. A.; Abdel-Khalik, H. S. ^[1]; Utke, J. ^[2]

---

1. North Carolina State Univ., Dept. of Nuclear Engineering, Raleigh, NC 27695-7909 (United States)
2. Mathematics and Computer Science Div., Argonne National Laboratory, Argonne, IL 60439 (United States)

This manuscript outlines a new approach for increasing the efficiency of applying automatic differentiation (AD) to large scale computational models. By using the principles of the Efficient Subspace Method (ESM), low rank approximations of the derivatives for first and higher orders can be calculated using minimized computational resources. The output obtained from nuclear reactor calculations typically has a much smaller numerical rank compared to the number of inputs and outputs. This rank deficiency can be exploited to reduce the number of derivatives that need to be calculated using AD. The effective rank can be determined according to ESM by computing derivatives with AD at random inputs. Reduced or pseudo variables are then defined and new derivatives are calculated with respect to the pseudo variables. Two different AD packages are used: OpenAD and Rapsodia. OpenAD is used to determine the effective rank and the subspace that contains the derivatives. Rapsodia is then used to calculate derivatives with respect to the pseudo variables for the desired order. The overall approach is applied to two simple problems and to MATWS, a safety code for sodium cooled reactors. (authors)

• Research Organization: American Nuclear Society, Inc., 555 N. Kensington Avenue, La Grange Park, Illinois 60526 (United States)
• OSTI ID: 22105784
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
97 MATHEMATICS AND COMPUTING
APPROXIMATIONS
COMPUTER CODES
COMPUTERIZED SIMULATION
RANDOMNESS
SODIUM COOLED REACTORS