6 research outputs found
Data-scarce surrogate modeling of shock-induced pore collapse process
Understanding the mechanisms of shock-induced pore collapse is of great
interest in various disciplines in sciences and engineering, including
materials science, biological sciences, and geophysics. However, numerical
modeling of the complex pore collapse processes can be costly. To this end, a
strong need exists to develop surrogate models for generating economic
predictions of pore collapse processes. In this work, we study the use of a
data-driven reduced order model, namely dynamic mode decomposition, and a deep
generative model, namely conditional generative adversarial networks, to
resemble the numerical simulations of the pore collapse process at
representative training shock pressures. Since the simulations are expensive,
the training data are scarce, which makes training an accurate surrogate model
challenging. To overcome the difficulties posed by the complex physics
phenomena, we make several crucial treatments to the plain original form of the
methods to increase the capability of approximating and predicting the
dynamics. In particular, physics information is used as indicators or
conditional inputs to guide the prediction. In realizing these methods, the
training of each dynamic mode composition model takes only around 30 seconds on
CPU. In contrast, training a generative adversarial network model takes 8 hours
on GPU. Moreover, using dynamic mode decomposition, the final-time relative
error is around 0.3% in the reproductive cases. We also demonstrate the
predictive power of the methods at unseen testing shock pressures, where the
error ranges from 1.3% to 5% in the interpolatory cases and 8% to 9% in
extrapolatory cases
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal