Search

This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and displacement fields. The proposed methodology develops a low-dimensional parametrization of these quantities of interest using space-time bases combining with machine learning methods. In particular, the space-time solutions are sought in a low-dimensional space-time linear trial subspace that can be obtained by computing tensor decompositions of usual state-snapshots data. The mapping between the input parameters and the basis expansion coefficients (or generalized coordinates) is approximated using four different machine learning techniques: multivariate polynomial regression, k-nearest-neighbors, random forest and neural network. The relative costs and effectiveness of the four machine learning techniques are explored through three engineering problems: steady heat conduction, unsteady heat conduction and unsteady advective-diffusive-reactive system. Numerical results demonstrate that the proposed method performs well in terms of both accuracy and computational cost, and highlight the important point that the amount of model training data available in an engineering setting is often much less than it is in other machine learning applications, making it essential to incorporate knowledge from physical models. In addition, simpler machine learning techniques are seen to perform better than more elaborate ones., Found significant issues with the manuscript

In this work, we provide a method for enhancing stochastic Galerkin moment calculations to the linear elliptic equation with random diffusivity using an ensemble of Monte Carlo solutions. This hybrid approach combines the accuracy of low-order stochastic Galerkin and the computational efficiency of Monte Carlo methods to provide statistical moment estimates which are significantly more accurate than performing each method individually. The hybrid approach involves computing a low-order stochastic Galerkin solution, after which Monte Carlo techniques are used to estimate the residual. We show that the combined stochastic Galerkin solution and residual is superior in both time and accuracy for a one-dimensional test problem and a more computational intensive two-dimensional linear elliptic problem for both the mean and variance quantities.

Many cloud microphysical processes occur on a much smaller scale than a typical numerical grid box can resolve. In such cases, a probability density function (PDF) can act as a proxy for subgrid variability in these microphysical processes. This method is known as the assumed PDF method. By placing a density on the microphysical fields, one can use samples from this density to estimate microphysics averages. In the assumed PDF method, the calculation of such microphysical averages has primarily been done using classical Monte Carlo methods and Latin hypercube sampling. Although these techniques are fairly easy to implement and ubiquitous in the literature, they suffer from slow convergence rates as a function of the number of samples. This paper proposes using deterministic quadrature methods instead of traditional random sampling approaches to compute the microphysics statistical moments for the assumed PDF method. For smooth functions, the quadrature-based methods can achieve much greater accuracy with fewer samples by choosing tailored quadrature points and weights instead of random samples. Moreover, these techniques are fairly easy to implement and conceptually similar to Monte Carlo–type methods. As a prototypical microphysical formula, Khairoutdinov and Kogan’s autoconversion and accretion formulas are used to illustrate the benefit of using quadrature instead of Monte Carlo or Latin hypercube sampling.

We consider the context of probabilistic inference of model parameters given error bars or confidence intervals on model output values, when the data is unavailable. We introduce a class of algorithms in a Bayesian framework, relying on maximum entropy arguments and approximate Bayesian computation methods, to generate consistent data with the given summary statistics. Once we obtain consistent data sets, we pool the respective posteriors, to arrive at a single, averaged density on the parameters. This approach allows us to perform accurate forward uncertainty propagation consistent with the reported statistics.

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all. The main tool used is the duality between risk-sensitive integrals and relative entropy, and we obtain explicit bounds on standard performance measures (variances, exceedance probabilities) over families of distributions whose distance from a nominal distribution is measured by relative entropy. The evaluation of the risk-sensitive expectations is based on polynomial chaos expansions, which help keep the computational aspects tractable.

A mechanical acceleration switch has been developed to synchronize instrumentation during a destructive acceleration test. The tests are of short durations and involve very high velocities and accelerations, and a destructive impact. Therefore, accurately synchronized instrumentation is critical. When the switch detects a desired acceleration time history, the switch closes to complete a circuit for instrument activation. Preliminary tests on the proposed switch have shown that switch-to-switch variations exist due to fabrication and assembly tolerances, and that combinations of variations may lead to a switch that does not respond properly. If the switch does not close at the proper time, improper data may be collected; or, at worst, no data may be collected before destructive impact. In this paper, a nonlinear model of the switch closing dynamics is developed in order to investigate the effect of uncertainty on its operation. In particular, the propagation of uncertainty from the switch parameters to the switch dynamics is quantified, and then the design is optimized such that the operation of the switch is insensitive to the variation and uncertainty. The results of the analysis elucidate the parameters that significantly impact switch operation, quantify the reliability of the existing switch design, and ultimately are used to recommend a design that could significantly improve reliability.Copyright © 2011 by ASME