1,508 research outputs found
Data Assimilation using a GPU Accelerated Path Integral Monte Carlo Approach
The answers to data assimilation questions can be expressed as path integrals
over all possible state and parameter histories. We show how these path
integrals can be evaluated numerically using a Markov Chain Monte Carlo method
designed to run in parallel on a Graphics Processing Unit (GPU). We demonstrate
the application of the method to an example with a transmembrane voltage time
series of a simulated neuron as an input, and using a Hodgkin-Huxley neuron
model. By taking advantage of GPU computing, we gain a parallel speedup factor
of up to about 300, compared to an equivalent serial computation on a CPU, with
performance increasing as the length of the observation time used for data
assimilation increases.Comment: 5 figures, submitted to Journal of Computational Physic
Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms
We present a mathematical framework for constructing and analyzing parallel
algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting
algorithms have the capacity to simulate a wide range of spatio-temporal scales
in spatially distributed, non-equilibrium physiochemical processes with complex
chemistry and transport micro-mechanisms. The algorithms can be tailored to
specific hierarchical parallel architectures such as multi-core processors or
clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms
are controlled-error approximations of kinetic Monte Carlo algorithms,
departing from the predominant paradigm of creating parallel KMC algorithms
with exactly the same master equation as the serial one.
Our methodology relies on a spatial decomposition of the Markov operator
underlying the KMC algorithm into a hierarchy of operators corresponding to the
processors' structure in the parallel architecture. Based on this operator
decomposition, we formulate Fractional Step Approximation schemes by employing
the Trotter Theorem and its random variants; these schemes, (a) determine the
communication schedule} between processors, and (b) are run independently on
each processor through a serial KMC simulation, called a kernel, on each
fractional step time-window.
Furthermore, the proposed mathematical framework allows us to rigorously
justify the numerical and statistical consistency of the proposed algorithms,
showing the convergence of our approximating schemes to the original serial
KMC. The approach also provides a systematic evaluation of different processor
communicating schedules.Comment: 34 pages, 9 figure
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