14,320 research outputs found
Theano: new features and speed improvements
Theano is a linear algebra compiler that optimizes a user's
symbolically-specified mathematical computations to produce efficient low-level
implementations. In this paper, we present new features and efficiency
improvements to Theano, and benchmarks demonstrating Theano's performance
relative to Torch7, a recently introduced machine learning library, and to
RNNLM, a C++ library targeted at recurrent neural networks.Comment: Presented at the Deep Learning Workshop, NIPS 201
Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations
We present a suite of Mathematica-based computer-algebra packages, termed
"Kranc", which comprise a toolbox to convert (tensorial) systems of partial
differential evolution equations to parallelized C or Fortran code. Kranc can
be used as a "rapid prototyping" system for physicists or mathematicians
handling very complicated systems of partial differential equations, but
through integration into the Cactus computational toolkit we can also produce
efficient parallelized production codes. Our work is motivated by the field of
numerical relativity, where Kranc is used as a research tool by the authors. In
this paper we describe the design and implementation of both the Mathematica
packages and the resulting code, we discuss some example applications, and
provide results on the performance of an example numerical code for the
Einstein equations.Comment: 24 pages, 1 figure. Corresponds to journal versio
Research and Education in Computational Science and Engineering
Over the past two decades the field of computational science and engineering
(CSE) has penetrated both basic and applied research in academia, industry, and
laboratories to advance discovery, optimize systems, support decision-makers,
and educate the scientific and engineering workforce. Informed by centuries of
theory and experiment, CSE performs computational experiments to answer
questions that neither theory nor experiment alone is equipped to answer. CSE
provides scientists and engineers of all persuasions with algorithmic
inventions and software systems that transcend disciplines and scales. Carried
on a wave of digital technology, CSE brings the power of parallelism to bear on
troves of data. Mathematics-based advanced computing has become a prevalent
means of discovery and innovation in essentially all areas of science,
engineering, technology, and society; and the CSE community is at the core of
this transformation. However, a combination of disruptive
developments---including the architectural complexity of extreme-scale
computing, the data revolution that engulfs the planet, and the specialization
required to follow the applications to new frontiers---is redefining the scope
and reach of the CSE endeavor. This report describes the rapid expansion of CSE
and the challenges to sustaining its bold advances. The report also presents
strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie
CALLABLE SWAPS, SNOWBALLS AND VIDEOGAMES
Although economically more meaningful than the alternatives, short rate models have been dismissed for financial engineering applications in favor of market models as the latter are more flexible and best suited to cluster computing implementations. In this paper, we argue that the paradigm shift toward GPU architectures currently taking place in the high performance computing world can potentially change the situation and tilt the balance back in favor of a new generation of short rate models. We find that operator methods provide a natural mathematical framework for the implementation of realistic short rate models that match features of the historical process such as stochastic monetary policy, calibrate well to liquid derivatives and provide new insights on complex structures. In this paper, we show that callable swaps, callable range accruals, target redemption notes (TARNs) and various flavors of snowballs and snowblades can be priced with methods numerically as precise, fast and stable as the ones based on analytic closed form solutions by means of BLAS level-3 methods on massively parallel GPU architectures.Interest Rate Derivatives; stochastic monetary policy; callable swaps; snowballs; GPU programming; operator methods
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