A sustainable burn platform through inertial confinement fusion (ICF) has been an ongoing challenge for over 50 years. Mitigating engineering limitations and improving the current design involves an understanding of the complex coupling of physical processes. While sophisticated simulations codes are used to model ICF implosions, these tools contain necessary numerical approximation but miss physical processes that limit predictive capability. Identification of relationships between controllable design inputs to ICF experiments and measurable outcomes (e.g. yield, shape) from performed experiments can help guide the future design of experiments and development of simulation codes, to potentially improve the accuracy of the computational models used to simulate ICF experiments. We use sparse matrix decomposition methods to identify clusters of a few related design variables. Sparse principal component analysis (SPCA) identifies groupings that are related to the physical origin of the variables (laser, hohlraum, and capsule). A variable importance analysis finds that in addition to variables highly correlated with neutron yield such as picket power and laser energy, variables that represent a dramatic change of the ICF design such as number of pulse steps are also very important. The obtained sparse components are then used to train a random forest (RF) surrogate for predicting total yield. The RF performance on the training and testing data compares with the performance of the RF surrogate trained using all design variables considered. This work is intended to inform design changes in future ICF experiments by augmenting the expert intuition and simulations results.

We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems, including history matching. The developed technique is based on principal component analysis (PCA) but modifies a purely data-driven basis of principal components considering objective function behavior. To define an efficient encoding, Gradient-Sensitive PCA uses an objective function gradient with respect to model parameters. We propose computationally efficient implementations of the technique, and two of them are based on stationary perturbation theory (SPT). Optimality, correctness, and low computational costs of the new encoding approach are tested, verified, and discussed. Three algorithms for optimal parameter decomposition are presented and applied to an objective of 2D synthetic history matching. The results demonstrate improvements in encoding quality regarding objective function minimization and distributional patterns of the desired field. Possible applications and extensions are proposed.

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works have proposed a probabilistic approach able to infer the number of significant components. To this purpose, this paper introduces a Bayesian nonparametric principal component analysis (BNP-PCA). The proposed model projects observations onto a random orthogonal basis which is assigned a prior distribution defined on the Stiefel manifold. The prior on factor scores involves an Indian buffet process to model the uncertainty related to the number of components. The parameters of interest as well as the nuisance parameters are finally inferred within a fully Bayesian framework via Monte Carlo sampling. A study of the (in-)consistence of the marginal maximum a posteriori estimator of the latent dimension is carried out. A new estimator of the subspace dimension is proposed. Moreover, for sake of statistical significance, a Kolmogorov-Smirnov test based on the posterior distribution of the principal components is used to refine this estimate. The behaviour of the algorithm is first studied on various synthetic examples. Finally, the proposed BNP dimension reduction approach is shown to be easily yet efficiently coupled with clustering or latent factor models within a unique framework.

Surrogate models provide a low computational cost alternative to evaluating expensive functions. The construction of accurate surrogate models with large numbers of independent variables is currently prohibitive because it requires a large number of function evaluations. Gradient-enhanced kriging has the potential to reduce the number of function evaluations for the desired accuracy when efficient gradient computation, such as an adjoint method, is available. However, current gradient-enhanced kriging methods do not scale well with the number of sampling points due to the rapid growth in the size of the correlation matrix where new information is added for each sampling point in each direction of the design space. They do not scale well with the number of independent variables either due to the increase in the number of hyperparameters that needs to be estimated. To address this issue, we develop a new gradient-enhanced surrogate model approach that drastically reduced the number of hyperparameters through the use of the partial-least squares method that maintains accuracy. In addition, this method is able to control the size of the correlation matrix by adding only relevant points defined through the information provided by the partial-least squares method. To validate our method, we compare the global accuracy of the proposed method with conventional kriging surrogate models on two analytic functions with up to 100 dimensions, as well as engineering problems of varied complexity with up to 15 dimensions. We show that the proposed method requires fewer sampling points than conventional methods to obtain the desired accuracy, or provides more accuracy for a fixed budget of sampling points. In some cases, we get over 3 times more accurate models than a bench of surrogate models from the literature, and also over 3200 times faster than standard gradient-enhanced kriging models.