Neural Algorithms for Low Power Implementation of Partial Differential Equations

Aimone, James Bradley; Hill, Aaron Jamison; Lehoucq, Richard B.; Parekh, Ojas D.; Reeder, Leah; Severa, William Mark

doi:10.2172/1474253

Title: Neural Algorithms for Low Power Implementation of Partial Differential Equations

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Abstract

The rise of low-power neuromorphic hardware has the potential to change high-performance computing; however much of the focus on brain-inspired hardware has been on machine learning applications. A low-power solution for solving partial differential equations could radically change how we approach large-scale computing in the future. The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking neuromorphic hardware. The first method tracks the positions of individual walkers independently by using a modular code inspired by grid cells in the brain. The second method tracks the densities of random walkers at each spatial location directly. We present the scaling complexity of each of these methods and illustrate their ability to model random walkers under different probabilistic conditions. Finally, we present implementations of these algorithms on neuromorphic hardware.

Authors:

Aimone, James Bradley ^[1]; Hill, Aaron Jamison ^[1]; Lehoucq, Richard B. ^[1]; Parekh, Ojas D. ^[1]; Reeder, Leah ^[1]; Severa, William Mark ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Sat Sep 01 00:00:00 EDT 2018

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1474253

Report Number(s):: SAND-2018-10553
668144

DOE Contract Number:: AC04-94AL85000

Resource Type:: Technical Report

Country of Publication:: United States

Language:: English

Citation Formats


                    Aimone, James Bradley, Hill, Aaron Jamison, Lehoucq, Richard B., Parekh, Ojas D., Reeder, Leah, and Severa, William Mark. Neural Algorithms for Low Power Implementation of Partial Differential Equations.  United States: N. p., 2018. 
        Web.  doi:10.2172/1474253.

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                    Aimone, James Bradley, Hill, Aaron Jamison, Lehoucq, Richard B., Parekh, Ojas D., Reeder, Leah, & Severa, William Mark. Neural Algorithms for Low Power Implementation of Partial Differential Equations.  United States.  https://doi.org/10.2172/1474253

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                    Aimone, James Bradley, Hill, Aaron Jamison, Lehoucq, Richard B., Parekh, Ojas D., Reeder, Leah, and Severa, William Mark. 2018.  
        "Neural Algorithms for Low Power Implementation of Partial Differential Equations".  United States.  https://doi.org/10.2172/1474253.  https://www.osti.gov/servlets/purl/1474253.

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@article{osti_1474253,

  title        = {Neural Algorithms for Low Power Implementation of Partial Differential Equations},

  author       = {Aimone, James Bradley and Hill, Aaron Jamison and Lehoucq, Richard B. and Parekh, Ojas D. and Reeder, Leah and Severa, William Mark},

  abstractNote = {The rise of low-power neuromorphic hardware has the potential to change high-performance computing; however much of the focus on brain-inspired hardware has been on machine learning applications. A low-power solution for solving partial differential equations could radically change how we approach large-scale computing in the future. The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking neuromorphic hardware. The first method tracks the positions of individual walkers independently by using a modular code inspired by grid cells in the brain. The second method tracks the densities of random walkers at each spatial location directly. We present the scaling complexity of each of these methods and illustrate their ability to model random walkers under different probabilistic conditions. Finally, we present implementations of these algorithms on neuromorphic hardware.},

  doi          = {10.2172/1474253},

  url          = {https://www.osti.gov/biblio/1474253},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Sat Sep 01 00:00:00 EDT 2018},

  month        = {Sat Sep 01 00:00:00 EDT 2018}

}

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