Nga T. T. Nguyen

Bradley T. Wolfe, Michael J. Falato, Xinhua Zhang et al.

In many inertial confinement fusion experiments, the neutron yield and other parameters cannot be completely accounted for with one and two dimensional models. This discrepancy suggests that there are three dimensional effects which may be significant. Sources of these effects include defects in the shells and shell interfaces, the fill tube of the capsule, and the joint feature in double shell targets. Due to their ability to penetrate materials, X-rays are used to capture the internal structure of objects. Methods such as Computational Tomography use X-ray radiographs from hundreds of projections in order to reconstruct a three dimensional model of the object. In experimental environments, such as the National Ignition Facility and Omega-60, the availability of these views is scarce and in many cases only consist of a single line of sight. Mathematical reconstruction of a 3D object from sparse views is an ill-posed inverse problem. These types of problems are typically solved by utilizing prior information. Neural networks have been used for the task of 3D reconstruction as they are capable of encoding and leveraging this prior information. We utilize half a dozen different convolutional neural networks to produce different 3D representations of ICF implosions from the experimental data. We utilize deep supervision to train a neural network to produce high resolution reconstructions. We use these representations to track 3D features of the capsules such as the ablator, inner shell, and the joint between shell hemispheres. Machine learning, supplemented by different priors, is a promising method for 3D reconstructions in ICF and X-ray radiography in general.

Nga T. T. Nguyen-Fotiadis, Robert Chiodi, Michael McKerns et al.

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by numerical discretization in under-resolved simulations is to use a flux limiter. A wide range of flux limiters has been studied in the literature, with recent interest in their optimization via machine learning methods trained on high-resolution datasets. The common use of flux limiters in numerical codes as plug-and-play blackbox components makes them key targets for design improvement. Moreover, while aleatoric (inherent randomness) and epistemic (lack of knowledge) uncertainty is commonplace in fluid dynamical systems, these effects are generally ignored in the design of flux limiters. Even for deterministic dynamical models, numerical uncertainty is introduced via coarse-graining required by insufficient computational power to solve all scales of motion. Here, we introduce a conceptually distinct type of flux limiter that is designed to handle the effects of randomness in the model and uncertainty in model parameters. This new, {\it probabilistic flux limiter}, learned with high-resolution data, consists of a set of flux limiting functions with associated probabilities, which define the frequencies of selection for their use. Using the example of Burgers' equation, we show that a machine learned, probabilistic flux limiter may be used in a shock capturing code to more accurately capture shock profiles. In particular, we show that our probabilistic flux limiter outperforms standard limiters, and can be successively improved upon (up to a point) by expanding the set of probabilistically chosen flux limiting functions.

Boram Yoon, Chia Cheng Chang, Garrett T. Kenyon et al.

We present regression and compression algorithms for lattice QCD data utilizing the efficient binary optimization ability of quantum annealers. In the regression algorithm, we encode the correlation between the input and output variables into a sparse coding machine learning algorithm. The trained correlation pattern is used to predict lattice QCD observables of unseen lattice configurations from other observables measured on the lattice. In the compression algorithm, we define a mapping from lattice QCD data of floating-point numbers to the binary coefficients that closely reconstruct the input data from a set of basis vectors. Since the reconstruction is not exact, the mapping defines a lossy compression, but, a reasonably small number of binary coefficients are able to reconstruct the input vector of lattice QCD data with the reconstruction error much smaller than the statistical fluctuation. In both applications, we use D-Wave quantum annealers to solve the NP-hard binary optimization problems of the machine learning algorithms.

Boram Yoon, Nga T. T. Nguyen, Chia Cheng Chang et al.

We present a new lossy compression algorithm for statistical floating-point data through a representation learning with binary variables. The algorithm finds a set of basis vectors and their binary coefficients that precisely reconstruct the original data. The optimization for the basis vectors is performed classically, while binary coefficients are retrieved through both simulated and quantum annealing for comparison. A bias correction procedure is also presented to estimate and eliminate the error and bias introduced from the inexact reconstruction of the lossy compression for statistical data analyses. The compression algorithm is demonstrated on two different datasets of lattice quantum chromodynamics simulations. The results obtained using simulated annealing show 3.5 times better compression performance than the algorithms based on a neural-network autoencoder and principal component analysis. Calculations using quantum annealing also show promising results, but performance is limited by the integrated control error of the quantum processing unit, which yields large uncertainties in the biases and coupling parameters. Hardware comparison is further studied between the previous generation D-Wave 2000Q and the current D-Wave Advantage system. Our study shows that the Advantage system is more likely to obtain low-energy solutions for the problems than the 2000Q.

Nga T. T. Nguyen, Garrett T. Kenyon

We use a quantum annealing D-Wave 2X computer to obtain solutions to NP-hard sparse coding problems. To reduce the dimensionality of the sparse coding problem to fit on the quantum D-Wave 2X hardware, we passed downsampled MNIST images through a bottleneck autoencoder. To establish a benchmark for classification performance on this reduced dimensional data set, we used an AlexNet-like architecture implemented in TensorFlow, obtaining a classification score of $94.54 \pm 0.7 \%$. As a control, we showed that the same AlexNet-like architecture produced near-state-of-the-art classification performance $(\sim 99\%)$ on the original MNIST images. To obtain a set of optimized features for inferring sparse representations of the reduced dimensional MNIST dataset, we imprinted on a random set of $47$ image patches followed by an off-line unsupervised learning algorithm using stochastic gradient descent to optimize for sparse coding. Our single-layer of sparse coding matched the stride and patch size of the first convolutional layer of the AlexNet-like deep neural network and contained $47$ fully-connected features, $47$ being the maximum number of dictionary elements that could be embedded onto the D-Wave $2$X hardware. Recent work suggests that the optimal level of sparsity corresponds to a critical value of the trade-off parameter associated with a putative second order phase transition, an observation supported by a free energy analysis of D-Wave energy states. When the sparse representations inferred by the D-Wave $2$X were passed to a linear support vector machine, we obtained a classification score of $95.68\%$. Thus, on this problem, we find that a single-layer of quantum inference is able to outperform a standard deep neural network architecture.