11,237 research outputs found
Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part I: template-based generic programming
An approach for incorporating embedded simulation and analysis capabilities
in complex simulation codes through template-based generic programming is
presented. This approach relies on templating and operator overloading within
the C++ language to transform a given calculation into one that can compute a
variety of additional quantities that are necessary for many state-of-the-art
simulation and analysis algorithms. An approach for incorporating these ideas
into complex simulation codes through general graph-based assembly is also
presented. These ideas have been implemented within a set of packages in the
Trilinos framework and are demonstrated on a simple problem from chemical
engineering
An Algebraic Framework for the Real-Time Solution of Inverse Problems on Embedded Systems
This article presents a new approach to the real-time solution of inverse
problems on embedded systems. The class of problems addressed corresponds to
ordinary differential equations (ODEs) with generalized linear constraints,
whereby the data from an array of sensors forms the forcing function. The
solution of the equation is formulated as a least squares (LS) problem with
linear constraints. The LS approach makes the method suitable for the explicit
solution of inverse problems where the forcing function is perturbed by noise.
The algebraic computation is partitioned into a initial preparatory step, which
precomputes the matrices required for the run-time computation; and the cyclic
run-time computation, which is repeated with each acquisition of sensor data.
The cyclic computation consists of a single matrix-vector multiplication, in
this manner computation complexity is known a-priori, fulfilling the definition
of a real-time computation. Numerical testing of the new method is presented on
perturbed as well as unperturbed problems; the results are compared with known
analytic solutions and solutions acquired from state-of-the-art implicit
solvers. The solution is implemented with model based design and uses only
fundamental linear algebra; consequently, this approach supports automatic code
generation for deployment on embedded systems. The targeting concept was tested
via software- and processor-in-the-loop verification on two systems with
different processor architectures. Finally, the method was tested on a
laboratory prototype with real measurement data for the monitoring of flexible
structures. The problem solved is: the real-time overconstrained reconstruction
of a curve from measured gradients. Such systems are commonly encountered in
the monitoring of structures and/or ground subsidence.Comment: 24 pages, journal articl
Automatic Differentiation Variational Inference
Probabilistic modeling is iterative. A scientist posits a simple model, fits
it to her data, refines it according to her analysis, and repeats. However,
fitting complex models to large data is a bottleneck in this process. Deriving
algorithms for new models can be both mathematically and computationally
challenging, which makes it difficult to efficiently cycle through the steps.
To this end, we develop automatic differentiation variational inference (ADVI).
Using our method, the scientist only provides a probabilistic model and a
dataset, nothing else. ADVI automatically derives an efficient variational
inference algorithm, freeing the scientist to refine and explore many models.
ADVI supports a broad class of models-no conjugacy assumptions are required. We
study ADVI across ten different models and apply it to a dataset with millions
of observations. ADVI is integrated into Stan, a probabilistic programming
system; it is available for immediate use
Numerical Analysis
Acknowledgements: This article will appear in the forthcoming Princeton Companion to Mathematics, edited by Timothy Gowers with June Barrow-Green, to be published by Princeton University Press.\ud
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In preparing this essay I have benefitted from the advice of many colleagues who corrected a number of errors of fact and emphasis. I have not always followed their advice, however, preferring as one friend put it, to "put my head above the parapet". So I must take full responsibility for errors and omissions here.\ud
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With thanks to: Aurelio Arranz, Alexander Barnett, Carl de Boor, David Bindel, Jean-Marc Blanc, Mike Bochev, Folkmar Bornemann, Richard Brent, Martin Campbell-Kelly, Sam Clark, Tim Davis, Iain Duff, Stan Eisenstat, Don Estep, Janice Giudice, Gene Golub, Nick Gould, Tim Gowers, Anne Greenbaum, Leslie Greengard, Martin Gutknecht, Raphael Hauser, Des Higham, Nick Higham, Ilse Ipsen, Arieh Iserles, David Kincaid, Louis Komzsik, David Knezevic, Dirk Laurie, Randy LeVeque, Bill Morton, John C Nash, Michael Overton, Yoshio Oyanagi, Beresford Parlett, Linda Petzold, Bill Phillips, Mike Powell, Alex Prideaux, Siegfried Rump, Thomas Schmelzer, Thomas Sonar, Hans Stetter, Gil Strang, Endre Süli, Defeng Sun, Mike Sussman, Daniel Szyld, Garry Tee, Dmitry Vasilyev, Andy Wathen, Margaret Wright and Steve Wright
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