85,480 research outputs found
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
Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography
This work addresses the inverse problem of electrocardiography from a new
perspective, by combining electrical and mechanical measurements. Our strategy
relies on the defini-tion of a model of the electromechanical contraction which
is registered on ECG data but also on measured mechanical displacements of the
heart tissue typically extracted from medical images. In this respect, we
establish in this work the convergence of a sequential estimator which combines
for such coupled problems various state of the art sequential data assimilation
methods in a unified consistent and efficient framework. Indeed we ag-gregate a
Luenberger observer for the mechanical state and a Reduced Order Unscented
Kalman Filter applied on the parameters to be identified and a POD projection
of the electrical state. Then using synthetic data we show the benefits of our
approach for the estimation of the electrical state of the ventricles along the
heart beat compared with more classical strategies which only consider an
electrophysiological model with ECG measurements. Our numerical results
actually show that the mechanical measurements improve the identifiability of
the electrical problem allowing to reconstruct the electrical state of the
coupled system more precisely. Therefore, this work is intended to be a first
proof of concept, with theoretical justifications and numerical investigations,
of the ad-vantage of using available multi-modal observations for the
estimation and identification of an electromechanical model of the heart
TMB: Automatic Differentiation and Laplace Approximation
TMB is an open source R package that enables quick implementation of complex
nonlinear random effect (latent variable) models in a manner similar to the
established AD Model Builder package (ADMB, admb-project.org). In addition, it
offers easy access to parallel computations. The user defines the joint
likelihood for the data and the random effects as a C++ template function,
while all the other operations are done in R; e.g., reading in the data. The
package evaluates and maximizes the Laplace approximation of the marginal
likelihood where the random effects are automatically integrated out. This
approximation, and its derivatives, are obtained using automatic
differentiation (up to order three) of the joint likelihood. The computations
are designed to be fast for problems with many random effects (~10^6) and
parameters (~10^3). Computation times using ADMB and TMB are compared on a
suite of examples ranging from simple models to large spatial models where the
random effects are a Gaussian random field. Speedups ranging from 1.5 to about
100 are obtained with increasing gains for large problems. The package and
examples are available at http://tmb-project.org
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