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Authors:Antonios Alexos, Junze Liu, Akash Tiwari, Kshitij Bhardwaj, Sean Hayes, Pierre Baldi, Satish Bukkapatnam, Suhas Bhandarkar

Abstract:In Inertial Confinement Fusion (ICF) process, roughly a 2mm spherical shell made of high density carbon is used as target for laser beams, which compress and heat it to energy levels needed for high fusion yield. These shells are polished meticulously to meet the standards for a fusion shot. However, the polishing of these shells involves multiple stages, with each stage taking several hours. To make sure that the polishing process is advancing in the right direction, we are able to measure the shell surface roughness. This measurement, however, is very labor-intensive, time-consuming, and requires a human operator. We propose to use machine learning models that can predict surface roughness based on the data collected from a vibration sensor that is connected to the polisher. Such models can generate surface roughness of the shells in real-time, allowing the operator to make any necessary changes to the polishing for optimal result.

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Abstract:Changes in real-world dynamic processes are often described in terms of differences in energies $\textbf{E}(\underline{\alpha})$ of a set of spectral-bands $\underline{\alpha}$. Given continuous spectra of two classes $A$ and $B$, or in general, two stochastic processes $S^{(A)}(f)$ and $S^{(B)}(f)$, $f \in \mathbb{R}^+$, we address the ubiquitous problem of identifying a subset of intervals of $f$ called spectral-bands $\underline{\alpha} \subset \mathbb{R}^+$ such that the energies $\textbf{E}(\underline{\alpha})$ of these bands can optimally discriminate between the two classes. We introduce EGO-MDA, an unsupervised method to identify optimal spectral-bands $\underline{\alpha}^*$ for given samples of spectra from two classes. EGO-MDA employs a statistical approach that iteratively minimizes an adjusted multinomial log-likelihood (deviance) criterion $\mathcal{D}(\underline{\alpha},\mathcal{M})$. Here, Mixture Discriminant Analysis (MDA) aims to derive MLE of two GMM distribution parameters, i.e., $\mathcal{M}^* = \underset{\mathcal{M}}{\rm argmin}~\mathcal{D}(\underline{\alpha}, \mathcal{M})$ and identify a classifier that optimally discriminates between two classes for a given spectral representation. The Efficient Global Optimization (EGO) finds the spectral-bands $\underline{\alpha}^* = \underset{\underline{\alpha}}{\rm argmin}~\mathcal{D}(\underline{\alpha},\mathcal{M})$ for given GMM parameters $\mathcal{M}$. For pathological cases of low separation between mixtures and model misspecification, we discuss the effect of the sample size and the number of iterations on the estimates of parameters $\mathcal{M}$ and therefore the classifier performance. A case study on a synthetic data set is provided. In an engineering application of optimal spectral-banding for anomaly tracking, EGO-MDA achieved at least 70% improvement in the median deviance relative to other methods tested.

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