Solving Large Nonlinear Systems of First-Order Ordinary Differential Equations With Hierarchical Structure Using Multi-GPGPUs and an Adaptive Runge Kutta ODE Solver
The adaptive Runge-Kutta (ARK) method on multi-general-purpose graphical processing units (GPUs) is used for solving large nonlinear systems of first-order ordinary differential equations (ODEs) with over ~ 10 000 variables describing a large genetic network in systems biology for the biological clo...
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| Format: | Article |
| Language: | English |
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IEEE
2013-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/6662399/ |
| _version_ | 1818457966058143744 |
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| author | Ahmad Al-Omari Jonathan Arnold Thiab Taha Heinz-Bernd Schuttler |
| author_facet | Ahmad Al-Omari Jonathan Arnold Thiab Taha Heinz-Bernd Schuttler |
| author_sort | Ahmad Al-Omari |
| collection | DOAJ |
| description | The adaptive Runge-Kutta (ARK) method on multi-general-purpose graphical processing units (GPUs) is used for solving large nonlinear systems of first-order ordinary differential equations (ODEs) with over ~ 10 000 variables describing a large genetic network in systems biology for the biological clock. To carry out the computation of the trajectory of the system, a hierarchical structure of the ODEs is exploited, and an ARK solver is implemented in compute unified device architecture/C++ (CUDA/C++) on GPUs. The result is a 75-fold speedup for calculations of 2436 independent modules within the genetic network describing clock function relative to a comparable CPU architecture. These 2436 modules span one-quarter of the entire genome of a model fungal system, Neurospora crassa. The power of a GPU can in principle be harnessed by using warp-level parallelism, instruction level parallelism or both of them. Since the ARK ODE solver is entirely sequential, we propose a new parallel processing algorithm using warp-level parallelism for solving ~ 10 000 ODEs that belong to a large genetic network describing clock genome-level dynamics. A video is attached illustrating the general idea of the method on GPUs that can be used to provide new insights into the biological clock through single cell measurements on the clock. |
| first_indexed | 2024-12-14T22:50:57Z |
| format | Article |
| id | doaj.art-416ec5843597402da8d6e377a9795289 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-14T22:50:57Z |
| publishDate | 2013-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-416ec5843597402da8d6e377a97952892022-12-21T22:44:44ZengIEEEIEEE Access2169-35362013-01-01177077710.1109/ACCESS.2013.22906236662399Solving Large Nonlinear Systems of First-Order Ordinary Differential Equations With Hierarchical Structure Using Multi-GPGPUs and an Adaptive Runge Kutta ODE SolverAhmad Al-Omari0Jonathan Arnold1Thiab Taha2Heinz-Bernd Schuttler3Institute of Bioinformatics, University of Georgia, Athens, GA, USADepartment of Genetics, University of Georgia, Athens, GA, USADepartment of Computer Science, University of Georgia, Athens, GA, USADepartment of Physics and Astronomy, University of Georgia, Athens, GA, USAThe adaptive Runge-Kutta (ARK) method on multi-general-purpose graphical processing units (GPUs) is used for solving large nonlinear systems of first-order ordinary differential equations (ODEs) with over ~ 10 000 variables describing a large genetic network in systems biology for the biological clock. To carry out the computation of the trajectory of the system, a hierarchical structure of the ODEs is exploited, and an ARK solver is implemented in compute unified device architecture/C++ (CUDA/C++) on GPUs. The result is a 75-fold speedup for calculations of 2436 independent modules within the genetic network describing clock function relative to a comparable CPU architecture. These 2436 modules span one-quarter of the entire genome of a model fungal system, Neurospora crassa. The power of a GPU can in principle be harnessed by using warp-level parallelism, instruction level parallelism or both of them. Since the ARK ODE solver is entirely sequential, we propose a new parallel processing algorithm using warp-level parallelism for solving ~ 10 000 ODEs that belong to a large genetic network describing clock genome-level dynamics. A video is attached illustrating the general idea of the method on GPUs that can be used to provide new insights into the biological clock through single cell measurements on the clock.https://ieeexplore.ieee.org/document/6662399/Bioinformaticsbiological clockgeneral-purpose graphical processing unitfinite element methodordinary differential equationadaptive Runge–Kutta integration |
| spellingShingle | Ahmad Al-Omari Jonathan Arnold Thiab Taha Heinz-Bernd Schuttler Solving Large Nonlinear Systems of First-Order Ordinary Differential Equations With Hierarchical Structure Using Multi-GPGPUs and an Adaptive Runge Kutta ODE Solver IEEE Access Bioinformatics biological clock general-purpose graphical processing unit finite element method ordinary differential equation adaptive Runge–Kutta integration |
| title | Solving Large Nonlinear Systems of First-Order Ordinary Differential Equations With Hierarchical Structure Using Multi-GPGPUs and an Adaptive Runge Kutta ODE Solver |
| title_full | Solving Large Nonlinear Systems of First-Order Ordinary Differential Equations With Hierarchical Structure Using Multi-GPGPUs and an Adaptive Runge Kutta ODE Solver |
| title_fullStr | Solving Large Nonlinear Systems of First-Order Ordinary Differential Equations With Hierarchical Structure Using Multi-GPGPUs and an Adaptive Runge Kutta ODE Solver |
| title_full_unstemmed | Solving Large Nonlinear Systems of First-Order Ordinary Differential Equations With Hierarchical Structure Using Multi-GPGPUs and an Adaptive Runge Kutta ODE Solver |
| title_short | Solving Large Nonlinear Systems of First-Order Ordinary Differential Equations With Hierarchical Structure Using Multi-GPGPUs and an Adaptive Runge Kutta ODE Solver |
| title_sort | solving large nonlinear systems of first order ordinary differential equations with hierarchical structure using multi gpgpus and an adaptive runge kutta ode solver |
| topic | Bioinformatics biological clock general-purpose graphical processing unit finite element method ordinary differential equation adaptive Runge–Kutta integration |
| url | https://ieeexplore.ieee.org/document/6662399/ |
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