61 research outputs found
Model Reduction of Synchronized Lur'e Networks
In this talk, we investigate a model order reduction schemethat reduces the complexity of uncertain dynamical networks consisting of diffusively interconnected nonlinearLure subsystems. We aim to reduce the dimension ofeach subsystem and meanwhile preserve the synchronization property of the overall network. Using the upperbound of the Laplacian spectral radius, we first characterize the robust synchronization of the Lure network bya linear matrix equation (LMI), whose solutions can betreated as generalized Gramians of each subsystem, andthus the balanced truncation can be performed on the linear component of each Lure subsystem. As a result, thedimension of the each subsystem is reduced, and the dynamics of the network is simplified. It is verified that, withthe same communication topology, the resulting reducednetwork system is still robustly synchronized, and the apriori bound on the approximation error is guaranteed tocompare the behaviors of the full-order and reduced-orderLure subsyste
Programming Languages for Scientific Computing
Scientific computation is a discipline that combines numerical analysis,
physical understanding, algorithm development, and structured programming.
Several yottacycles per year on the world's largest computers are spent
simulating problems as diverse as weather prediction, the properties of
material composites, the behavior of biomolecules in solution, and the quantum
nature of chemical compounds. This article is intended to review specfic
languages features and their use in computational science. We will review the
strengths and weaknesses of different programming styles, with examples taken
from widely used scientific codes.Comment: 21 page
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
dPV: An End-to-End Differentiable Solar-Cell Simulator
We introduce dPV, an end-to-end differentiable photovoltaic (PV) cell
simulator based on the drift-diffusion model and Beer-Lambert law for optical
absorption. dPV is programmed in Python using JAX, an automatic differentiation
(AD) library for scientific computing. Using AD coupled with the implicit
function theorem, dPV computes the power conversion efficiency (PCE) of an
input PV design as well as the derivative of the PCE with respect to any input
parameters, all within comparable time of solving the forward problem. We show
an example of perovskite solar-cell optimization and multi-parameter discovery,
and compare results with random search and finite differences. The simulator
can be integrated with optimization algorithms and neural networks, opening up
possibilities for data-efficient optimization and parameter discovery
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