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The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the(More)
Solution of statistical inverse problems via the frequentist or Bayesian approaches described in earlier chapters can be a computationally intensive endeavor, particularly when faced with large-scale forward models characteristic of many engineering and science applications. High computational cost arises in several ways. First, thousands or millions of(More)
Process variations can significantly degrade device performance and chip yield in silicon photonics. In order to reduce the design and production costs, it is highly desirable to predict the statistical behavior of a device before the final fabrication. Monte Carlo is the mainstream computational technique used to estimate the uncertainties caused by(More)
Changes in ow strain and mixture composition on the order of a ame time scale are characteristic of many practical combustion processes. Accurately predicting the unsteady reponse of burning to these changes requires detailed modeling of species transport and chemical kinetics. This thesis formulates a detailed one-dimensional computational model for(More)
Autocorrelation of a double-exposed image, unlike cross-correlation between two images, produces a correlation function that is symmetric about the origin. Thus, while it is possible to calculate the speed and direction of tracer particles in a particle image velocimetry (PIV) image using autocorrela-tion, it is impossible to tell whether the velocity is in(More)