15,620 research outputs found
Massively parallel approximate Gaussian process regression
We explore how the big-three computing paradigms -- symmetric multi-processor
(SMC), graphical processing units (GPUs), and cluster computing -- can together
be brought to bare on large-data Gaussian processes (GP) regression problems
via a careful implementation of a newly developed local approximation scheme.
Our methodological contribution focuses primarily on GPU computation, as this
requires the most care and also provides the largest performance boost.
However, in our empirical work we study the relative merits of all three
paradigms to determine how best to combine them. The paper concludes with two
case studies. One is a real data fluid-dynamics computer experiment which
benefits from the local nature of our approximation; the second is a synthetic
data example designed to find the largest design for which (accurate) GP
emulation can performed on a commensurate predictive set under an hour.Comment: 24 pages, 6 figures, 1 tabl
Speeding up neighborhood search in local Gaussian process prediction
Recent implementations of local approximate Gaussian process models have
pushed computational boundaries for non-linear, non-parametric prediction
problems, particularly when deployed as emulators for computer experiments.
Their flavor of spatially independent computation accommodates massive
parallelization, meaning that they can handle designs two or more orders of
magnitude larger than previously. However, accomplishing that feat can still
require massive supercomputing resources. Here we aim to ease that burden. We
study how predictive variance is reduced as local designs are built up for
prediction. We then observe how the exhaustive and discrete nature of an
important search subroutine involved in building such local designs may be
overly conservative. Rather, we suggest that searching the space radially,
i.e., continuously along rays emanating from the predictive location of
interest, is a far thriftier alternative. Our empirical work demonstrates that
ray-based search yields predictors with accuracy comparable to exhaustive
search, but in a fraction of the time - bringing a supercomputer implementation
back onto the desktop.Comment: 24 pages, 5 figures, 4 table
High-performance solution of hierarchical equations of motions for studying energy-transfer in light-harvesting complexes
Excitonic models of light-harvesting complexes, where the vibrational degrees
of freedom are treated as a bath, are commonly used to describe the motion of
the electronic excitation through a molecule. Recent experiments point toward
the possibility of memory effects in this process and require to consider time
non-local propagation techniques. The hierarchical equations of motion (HEOM)
were proposed by Ishizaki and Fleming to describe the site-dependent
reorganization dynamics of protein environments (J. Chem. Phys., 130, p.
234111, 2009), which plays a significant role in photosynthetic electronic
energy transfer. HEOM are often used as a reference for other approximate
methods, but have been implemented only for small systems due to their adverse
computational scaling with the system size. Here, we show that HEOM are also
solvable for larger systems, since the underlying algorithm is ideally suited
for the usage of graphics processing units (GPU). The tremendous reduction in
computational time due to the GPU allows us to perform a systematic study of
the energy-transfer efficiency in the Fenna-Matthews-Olson (FMO)
light-harvesting complex at physiological temperature under full consideration
of memory-effects. We find that approximative methods differ qualitatively and
quantitatively from the HEOM results and discuss the importance of finite
temperature to achieve high energy-transfer efficiencies.Comment: 14 pages; Journal of Chemical Theory and Computation (2011
GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
This work presents an updated and extended guide on methods of a proper
acceleration of the Monte Carlo integration of stochastic differential
equations with the commonly available NVIDIA Graphics Processing Units using
the CUDA programming environment. We outline the general aspects of the
scientific computing on graphics cards and demonstrate them with two models of
a well known phenomenon of the noise induced transport of Brownian motors in
periodic structures. As a source of fluctuations in the considered systems we
selected the three most commonly occurring noises: the Gaussian white noise,
the white Poissonian noise and the dichotomous process also known as a random
telegraph signal. The detailed discussion on various aspects of the applied
numerical schemes is also presented. The measured speedup can be of the
astonishing order of about 3000 when compared to a typical CPU. This number
significantly expands the range of problems solvable by use of stochastic
simulations, allowing even an interactive research in some cases.Comment: 21 pages, 5 figures; Comput. Phys. Commun., accepted, 201
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