Interval Arithmetic and Automatic Differentiation on GPU Using OpenCL
This paper investigates efficient and powerful approach to the Gradient and the Hessian evaluation for complex functions. The idea is to apply the parallel GPU architecture and the Automatic Differentiation methods. In order to achieve better accuracy, the interval arithmetic is used. Considerations are based on sequential and parallel authors’ implementation. In this solution, both the AD methods: Forward and Reverse modes are employed. Computational experiments include analysis of performance and are studied on the generated test functions with a given complexity.
Keywordsinterval computations automatic differentiation GPGPU OpenCL
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- 1.C-XSC interval library, http://www.xsc.de.
- 2.CUDA homepage: http://www.nvidia.com/object/cuda_home.html
- 3.OpenCL homepage: http://www.khronos.org/opencl.
- 4.Bücker, M.: Automatic Differentiation: Applications, Theory and Implementation. Springer (1981)Google Scholar
- 5.Collange, S., Florez, J., Defour, D.: A GPU interval library based on Boost interval (2008)Google Scholar
- 7.Jastrzebski, K., Szczap, L.: Different parallelism approaches to interval computations. Master’s thesis, Faculty of Electronics and Information Technology, WUT (2009)Google Scholar
- 9.Kearfott, R.B., Nakao, M.T., Neumaier, A., Rump, S.M., Shary, S.P., van Hentenryck, P.:Standardized notation in interval analysis (2002) http://www.mat.univie.ac.at/~neum/software/int/notation.ps.gz
- 10.Kamran, K., Neil, G., Firas, H.: A Performance Comparision of CUDA and OpenCL (2011), http://arxiv.org/abs/1005.2581
- 11.Kozikowski, G.: Implementation of automatic differentiation library using the OpenCL technology. BEng thesis, Faculty of Electronics and Information Technology, WUT (2011)Google Scholar
- 12.Werbos, P.: Backpropagation Through Time: What It Does and How to Do ItGoogle Scholar