Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


dsfinal.pdf (1.14 MB)

ETD Abstract Container

Abstract Header

A Framework for Performance Optimization of Tensor Contraction Expressions

Lai, Pai-Wei
http://rave.ohiolink.edu/etdc/view?acc_num=osu1408968185

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Computer Science and Engineering.
Attaining high performance and productivity in the evaluation of scientific applications is a challenging task for computer scientists, and is often critical in the advancement of many scientific disciplines. In this dissertation, we focus on the development of high performance, scalable parallel programs for a class of scientific computations in quantum chemistry --- tensor contraction expressions. Tensor contraction expressions are generalized forms of multi-dimensional matrix-matrix operations, which form the fundamental computational constructs in electronic structure modeling. Tensors in these computations exhibit various types of symmetry and sparsity. Contractions on such tensors are highly irregular with significant computation and communication cost, if data locality is not considered in the implementation. Prior efforts have focused on implementing tensor contractions using block-sparse representation. Many parallel programs of tensor contractions have been successfully implemented, however, their performances are unsatisfactory on emerging computer systems. In this work, we investigate into several performance bottlenecks of previous approaches, and present responding techniques to optimize operations, parallelism, workload balance, and data locality. We exploit symmetric properties of tensors to minimize the operation count of tensor contraction expressions through algebraic transformation. Rules are formulated to discover symmetric properties of intermediate tensors; cost models and algorithms are developed to reduce operation counts. Our approaches result in significant operation count reduction, compared to many other state of the art computational chemistry softwares, using examples from real-world tensor contraction expressions from the coupled cluster methods. In order to achieve high performance and scalability, multiple programming models are often used in a single application. We design a domain-specific framework which utilizes the partitioned global address space programming model for data management and inter-node communication. We employ the task parallel execution model for dynamic load balancing. Tensor contraction expressions are decomposed into a collection of computational tasks operating on tensor tiles. We eliminate most of the synchronization steps by executing independent tensor contractions concurrently, and present mechanisms to improve their data locality. Our framework shows improved performance and scalability for tensor contraction expressions from representative coupled cluster methods.
P. Sadayappan (Advisor)
Gagan Agrawal (Committee Member)
Atanas Rountev (Committee Member)
170 p.
Computer Science
tensor contraction; operation minimization; dynamic load-balancing; caching

Recommended Citations

Citations

  • Lai, P.-W. (2014). A Framework for Performance Optimization of Tensor Contraction Expressions [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408968185

    APA Style (7th edition)

  • Lai, Pai-Wei. A Framework for Performance Optimization of Tensor Contraction Expressions. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1408968185.

    MLA Style (8th edition)

  • Lai, Pai-Wei. "A Framework for Performance Optimization of Tensor Contraction Expressions." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408968185

    Chicago Manual of Style (17th edition)

osu1408968185
740
© 2014, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.