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GPU-Based Parallel Integration of Large Numbers of Independent ODE Systems [chapter]

Kyle E. Niemeyer, Chih-Jen Sung
2014 Numerical Computations with GPUs  
The task of integrating a large number of independent ODE systems arises in various scientific and engineering areas.  ...  In this chapter, we present the mathematical background, implementation details, and source code for the RKCK and RKC algorithms for use integrating large numbers of independent systems of ODEs on GPUs  ...  Conclusions In this chapter, we presented two explicit algorithms appropriate for integrating large numbers of independent ODE systems on GPUs.  ... 
doi:10.1007/978-3-319-06548-9_8 fatcat:ubyfgbp2izehlaujt5bfu56zny

A methodology for the integration of stiff chemical kinetics on GPUs

Fabian Sewerin, Stelios Rigopoulos
2015 Combustion and Flame  
An in-depth evaluation is based upon runtime measurements of the CPU and the GPU implementation on a user level and a high-end CPU/GPU for an increasing number of ODE systems, reduced and detailed reaction  ...  Recently, researchers have begun to explore the highly parallel structure of graphics processing units (GPUs) in order to accelerate integration schemes for these ODE systems.  ...  For this, each ODE 60 system was assigned a degree of stiffness based upon the number of integration steps which the ODE system required in the previous global time step.  ... 
doi:10.1016/j.combustflame.2014.11.003 fatcat:52omgvifozadlcysuw66o6l6du

Accelerating finite-rate chemical kinetics with coprocessors: Comparing vectorization methods on GPUs, MICs, and CPUs

Christopher P. Stone, Andrew T. Alferman, Kyle E. Niemeyer
2018 Computer Physics Communications  
Analysis showed that the wider vector width of the GPU incurs a higher level of divergence than the narrower Sandy Bridge or Xeon Phi.  ...  Two runtime benchmarks were conducted to clearly determine any performance advantage offered by either method: evaluating the right-hand-side source terms in parallel, and integrating a series of constant-pressure  ...  Acknowledgements This material is based upon work supported, in part, by the National Science Foundation under grant ACI-1535065.  ... 
doi:10.1016/j.cpc.2018.01.015 fatcat:x2ilsi2nsbal3ccgbno7nhxvzy

FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks

Andrea Tangherloni, Marco S. Nobile, Paolo Cazzaniga, Giulia Capitoli, Simone Spolaor, Leonardo Rundo, Giancarlo Mauri, Daniela Besozzi, Dina Schneidman-Duhovny
2021 PLoS Computational Biology  
On the other hand, the computational analysis of a model typically requires the execution of a large number of simulations for its calibration or to test the effect of perturbations.  ...  In particular, FiCoS exploits two different integration methods, namely, the Dormand–Prince and the Radau IIA, to efficiently solve both non-stiff and stiff systems of coupled Ordinary Differential Equations  ...  batches of independent simulations in parallel.  ... 
doi:10.1371/journal.pcbi.1009410 pmid:34499658 pmcid:PMC8476010 fatcat:vyuizpu5wrcrfben4qzafapjxq

GPU code generation for ODE-based applications with phased shared-data access patterns

Andrei Hagiescu, Bing Liu, R. Ramanathan, Sucheendra K. Palaniappan, Zheng Cui, Bipasa Chattopadhyay, P. S. Thiagarajan, Weng-Fai Wong
2013 ACM Transactions on Architecture and Code Optimization (TACO)  
These results suggest how our scheme could be extended to deal with other applications involving systems of ODEs.  ...  This application consists of computing a Dynamic Bayesian Network (DBN) approximation of the dynamics of signalling pathways described as a system of Ordinary Differential Equations (ODEs).  ...  a system of ODEs.  ... 
doi:10.1145/2541228.2555311 fatcat:nlizmwcii5dfvmfs7m5qzaoq2e

GPU code generation for ODE-based applications with phased shared-data access patterns

Andrei Hagiescu, Bing Liu, R. Ramanathan, Sucheendra K. Palaniappan, Zheng Cui, Bipasa Chattopadhyay, P. S. Thiagarajan, Weng-Fai Wong
2013 ACM Transactions on Architecture and Code Optimization (TACO)  
These results suggest how our scheme could be extended to deal with other applications involving systems of ODEs.  ...  This application consists of computing a Dynamic Bayesian Network (DBN) approximation of the dynamics of signalling pathways described as a system of Ordinary Differential Equations (ODEs).  ...  a system of ODEs.  ... 
doi:10.1145/2555289.2555311 fatcat:5malqytdlrdtflqekx2d4ij2ji

Accelerating Cardiac Bidomain Simulations Using Graphics Processing Units

A. Neic, M. Liebmann, E. Hoetzl, L. Mitchell, E. J. Vigmond, G. Haase, G. Plank
2012 IEEE Transactions on Biomedical Engineering  
Details on the GPU-based ODE solver have been described previously [14] . 2) GPU Implementation of the PDE Solvers-Solving sparse linear systems on GPUs efficiently is a more involved endeavor.  ...  until the local systems were linearly independent.  ... 
doi:10.1109/tbme.2012.2202661 pmid:22692867 pmcid:PMC3696513 fatcat:xp6noyvupndhjmkrxogkzornqm

FiCoS: a fine- and coarse-grained GPU-powered deterministic simulator for biochemical networks [article]

Andrea Tangherloni, Marco S Nobile, Paolo Cazzaniga, Giulia Capitoli, Simone Spolaor, Leonardo Rundo, Giancarlo Mauri, Daniela Besozzi
2021 bioRxiv   pre-print
On the other hand, the computational analysis of a model typically requires the execution of a large number of simulations for its calibration or to test the effect of perturbations.  ...  In particular, FiCoS exploits two different integration methods, namely the Dormand-Prince and the Radau IIA, to efficiently solve both non-stiff and stiff systems of coupled Ordinary Differential Equations  ...  integrate the system of ODEs.  ... 
doi:10.1101/2021.01.15.426855 fatcat:p7gnp6tv6bb47b2pfc3kg6ck5u

Accelerating moderately stiff chemical kinetics in reactive-flow simulations using GPUs

Kyle E. Niemeyer, Chih-Jen Sung
2014 Journal of Computational Physics  
The GPU-based RKC implementation demonstrated an increase in performance of nearly 59 and 10 times, for problem sizes consisting of 262,144 ODEs and larger, than the single- and six-core CPU-based RKC  ...  The chemical kinetics ODEs arising from operator-split reactive-flow simulations were solved on GPUs using explicit integration algorithms.  ...  In the GPU-based algorithms, threads independently integrated each chemical kinetics ODE. The total number of threads then equaled the number of ODEs; blocks consisted of 64 threads each.  ... 
doi:10.1016/j.jcp.2013.09.025 fatcat:s6oop632vvf7jlnt7i6m7waaie

Solving Large Nonlinear Systems of First-Order Ordinary Differential Equations With Hierarchical Structure Using Multi-GPGPUs and an Adaptive Runge Kutta ODE Solver

Ahmad Al-Omari, Jonathan Arnold, Thiab Taha, Heinz-Bernd Schuttler
2013 IEEE Access  
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  ...  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  ...  DISCUSSION This new parallelization strategy for solving large systems of ODEs on GPUs opens up the possibility of simulating genome dynamics.  ... 
doi:10.1109/access.2013.2290623 fatcat:lkdr3yzh4fgw5iqsfnhlrw3h34

LASSIE: simulating large-scale models of biochemical systems on GPUs

Andrea Tangherloni, Marco S. Nobile, Daniela Besozzi, Giancarlo Mauri, Paolo Cazzaniga
2017 BMC Bioinformatics  
Conclusions: LASSIE adopts a novel fine-grained parallelization strategy to distribute on the GPU cores all the calculations required to solve the system of ODEs.  ...  Given a reaction-based model of a cellular process, LASSIE automatically generates the corresponding system of Ordinary Differential Equations (ODEs), assuming mass-action kinetics.  ...  Authors would like to thank the SYSBIO.IT Centre of Systems Biology for the support. Funding Not applicable.  ... 
doi:10.1186/s12859-017-1666-0 pmid:28486952 pmcid:PMC5424297 fatcat:n7eqd42xxrfr3cqv7g2nnmafii

Fast Parallel Unbiased Diffeomorphic Atlas Construction on Multi-Graphics Processing Units [article]

Linh K. Ha, Jens Krüger, P. Thomas Fletcher, Sarang Joshi, Claudio T. Silva
2009 Eurographics Symposium on Parallel Graphics and Visualization  
This paper presents an efficient implementation of unbiased diffeomorphic atlas construction on the new parallel processing architecture based on Multi-Graphics Processing Units (Multi-GPUs).  ...  Fortunately, the highly element-wise independence of the problem makes it well suited for parallel processing.  ...  . • Design of a scalable system that can handle large numbers of inputs and maintain the performance with different input sizes.  ... 
doi:10.2312/egpgv/egpgv09/041-048 fatcat:iric4eshtvazxfshsry4qgmrju

Parallel scalable simulations of biological neural networks using TensorFlow: A beginner's guide [article]

Rishika Mohanta, Collins Assisi
2022 arXiv   pre-print
equations using Python to solving a large system (1000's of differential equations) of coupled conductance-based neurons using a highly parallelized and scalable framework.  ...  Further, there is a high barrier of entry to developing flexible platform-independent general-purpose code that supports hardware acceleration on modern computing architectures such as GPUs/TPUs and Distributed  ...  TensorFlow GPU is much faster in (a) Matrix multiplication of N × N matrices and (b) RK4-based Numerical Integration of parallel ODEs for large systems and TensorFlow CPU is marginally better than NumPy  ... 
arXiv:1906.03958v2 fatcat:zz5bq7cgobbi3irppfjmh2j7m4

Parallel computation of transient processes on OpenCL framework

Marcin CEGIELSKI
2016 Przeglad Elektrotechniczny  
Parallel execution of calculation of transient analysis is based on a split-level model into sub-systems, which in certain time increments are calculated independently of each other.  ...  The process of implementing the calculation allows the use of parallel systems to calculations based on the use of the GPU, whose dynamic growth has been observed for several years.  ...  Introduction Computation of complex systems is always connected with necessity of making a large number of step by step toilsome calculations.  ... 
doi:10.15199/48.2016.07.16 fatcat:u5rwopcunvh63bk6a25ri2yr7a

GPU-powered model analysis with PySB/cupSODA

Leonard A Harris, Marco S Nobile, James C Pino, Alexander L R Lubbock, Daniela Besozzi, Giancarlo Mauri, Paolo Cazzaniga, Carlos F Lopez, Jonathan Wren
2017 Bioinformatics  
For three example models of varying size, we show that for large numbers of simulations PySB/cupSODA achieves orderof-magnitude speedups relative to a CPU-based ordinary differential equation integrator  ...  A major barrier to the practical utilization of large, complex models of biochemical systems is the lack of open-source computational tools to evaluate model behaviors over highdimensional parameter spaces  ...  Muhlich for useful feedback during the implementation of this work. Conflict of Interest: none declared.  ... 
doi:10.1093/bioinformatics/btx420 pmid:28666314 pmcid:PMC5860165 fatcat:zsmccq3f5naezkqesodrcqemt4
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