Ryan G. McClarren

Michael D. Vander Wal, Ryan G. McClarren, Kelli D. Humbird

Simulations of high energy density physics are expensive, largely in part for the need to produce non-local thermodynamic equilibrium opacities. High-fidelity spectra may reveal new physics in the simulations not seen with low-fidelity spectra, but the cost of these simulations also scale with the level of fidelity of the opacities being used. Neural networks are capable of reproducing these spectra, but neural networks need data to to train them which limits the level of fidelity of the training data. This paper demonstrates that it is possible to reproduce high-fidelity spectra with median errors in the realm of 3\% to 4\% using as few as 50 samples of high-fidelity Krypton data by performing transfer learning on a neural network trained on many times more low-fidelity data.

Michael D. Vander Wal, Ryan G. McClarren, Kelli D. Humbird

Simulations of high-energy density physics often need non-local thermodynamic equilibrium (NLTE) opacity data. This data, however, is expensive to produce at relatively low-fidelity. It is even more so at high-fidelity such that the opacity calculations can contribute ninety-five percent of the total computation time. This proportion can even reach large proportions. Neural networks can be used to replace the standard calculations of low-fidelity data, and the neural networks can be trained to reproduce artificial, high-fidelity opacity spectra. In this work, it is demonstrated that a novel neural network architecture trained to reproduce high-fidelity krypton spectra through transfer learning can be used in simulations. Further, it is demonstrated that this can be done while achieving a relative percent error of the peak radiative temperature of the hohlraum of approximately 1\% to 4\% while achieving a 19.4x speed up.

William Bennett, Ryan G. McClarren, Ethan Smith et al.

Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The standard formulation of DMD is subject to strict assumptions concerning the time-spacing of the snapshots and is biased by measurement noise. Variations on the method have been developed to address these shortcomings, but the problem is still open. Motivated by the effectiveness of Galerkin methods in the field of model discovery, a weak formulation of DMD is presented, weak-DMD. Weak-DMD precludes timestep considerations and also filters noise. Results for two nuclear engineering applications and the flow of fluid past a cylinder are given and compared with a state of the art DMD algorithm.

Joseph Farmer, Ethan Smith, William Bennett et al.

Radiative heat transfer is a fundamental process in high energy density physics and inertial fusion. Accurately predicting the behavior of Marshak waves across a wide range of material properties and drive conditions is crucial for design and analysis of these systems. Conventional numerical solvers and analytical approximations often face challenges in terms of accuracy and computational efficiency. In this work, we propose a novel approach to model Marshak waves using Fourier Neural Operators (FNO). We develop two FNO-based models: (1) a base model that learns the mapping between the drive condition and material properties to a solution approximation based on the widely used analytic model by Hammer & Rosen (2003), and (2) a model that corrects the inaccuracies of the analytic approximation by learning the mapping to a more accurate numerical solution. Our results demonstrate the strong generalization capabilities of the FNOs and show significant improvements in prediction accuracy compared to the base analytic model.

Jichuan Tang, Patrick T. Brewick, Ryan G. McClarren et al.

Spatio-temporal data, which consists of responses or measurements gathered at different times and positions, is ubiquitous across diverse applications of civil infrastructure. While SciML methods have made significant progress in tackling the issue of response prediction for individual time histories, creating a full spatial-temporal surrogate remains a challenge. This study proposes a novel variant of deep operator networks (DeepONets), namely the full-field Extended DeepONet (FExD), to serve as a spatial-temporal surrogate that provides multi-output response predictions for dynamical systems. The proposed FExD surrogate model effectively learns the full solution operator across multiple degrees of freedom by enhancing the expressiveness of the branch network and expanding the predictive capabilities of the trunk network. The proposed FExD surrogate is deployed to simultaneously capture the dynamics at several sensing locations along a testbed model of a cable-stayed bridge subjected to stochastic ground motions. The ensuing response predictions from the FExD are comprehensively compared against both a vanilla DeepONet and a modified spatio-temporal Extended DeepONet. The results demonstrate the proposed FExD can achieve both superior accuracy and computational efficiency, representing a significant advancement in operator learning for structural dynamics applications.

Michael D. Vander Wal, Ryan G. McClarren, Kelli D. Humbird

Simulations of high energy density physics are expensive in terms of computational resources. In particular, the computation of opacities of plasmas in the non-local thermal equilibrium (NLTE) regime can consume as much as 90\% of the total computational time of radiation hydrodynamics simulations for high energy density physics applications. Previous work has demonstrated that a combination of fully-connected autoencoders and a deep jointly-informed neural network (DJINN) can successfully replace the standard NLTE calculations for the opacity of krypton. This work expands this idea to combining multiple elements into a single surrogate model with the focus here being on the autoencoder.

K. D. Humbird, J. L. Peterson, R. G. McClarren

Inertial confinement fusion (ICF) experiments are designed using computer simulations that are approximations of reality, and therefore must be calibrated to accurately predict experimental observations. In this work, we propose a novel nonlinear technique for calibrating from simulations to experiments, or from low fidelity simulations to high fidelity simulations, via "transfer learning". Transfer learning is a commonly used technique in the machine learning community, in which models trained on one task are partially retrained to solve a separate, but related task, for which there is a limited quantity of data. We introduce the idea of hierarchical transfer learning, in which neural networks trained on low fidelity models are calibrated to high fidelity models, then to experimental data. This technique essentially bootstraps the calibration process, enabling the creation of models which predict high fidelity simulations or experiments with minimal computational cost. We apply this technique to a database of ICF simulations and experiments carried out at the Omega laser facility. Transfer learning with deep neural networks enables the creation of models that are more predictive of Omega experiments than simulations alone. The calibrated models accurately predict future Omega experiments, and are used to search for new, optimal implosion designs.

K. D. Humbird, J. L. Peterson, R. G. McClarren

In this work, sequence-to-sequence (seq2seq) models, originally developed for language translation, are used to predict the temporal evolution of complex, multi-physics computer simulations. The predictive performance of seq2seq models is compared to state transition models for datasets generated with multi-physics codes with varying levels of complexity - from simple 1D diffusion calculations to simulations of inertial confinement fusion implosions. Seq2seq models demonstrate the ability to accurately emulate complex systems, enabling the rapid estimation of the evolution of quantities of interest in computationally expensive simulations.

Jonas Kusch, Ryan G. McClarren, Martin Frank

Uncertainty Quantification for nonlinear hyperbolic problems becomes a challenging task in the vicinity of shocks. Standard intrusive methods lead to oscillatory solutions and can result in non-hyperbolic moment systems. The intrusive polynomial moment (IPM) method guarantees hyperbolicity but comes at higher numerical costs. In this paper, we filter the gPC coefficients of the Stochastic Galerkin (SG) approximation, which allows a numerically cheap reduction of oscillations. The derived filter is based on Lasso regression which sets small gPC coefficients of high order to zero. We adaptively choose the filter strength to obtain a zero-valued highest order moment, which allows optimality of the corresponding optimization problem. The filtered SG method is tested for Burgers' and the Euler equations. Results show a reduction of oscillations at shocks, which leads to an improved approximation of expectation values and the variance compared to SG and IPM.

K. D. Humbird, J. L. Peterson, R. G. McClarren

In this work a novel, automated process for constructing and initializing deep feed-forward neural networks based on decision trees is presented. The proposed algorithm maps a collection of decision trees trained on the data into a collection of initialized neural networks, with the structures of the networks determined by the structures of the trees. The tree-informed initialization acts as a warm-start to the neural network training process, resulting in efficiently trained, accurate networks. These models, referred to as "deep jointly-informed neural networks" (DJINN), demonstrate high predictive performance for a variety of regression and classification datasets, and display comparable performance to Bayesian hyper-parameter optimization at a lower computational cost. By combining the user-friendly features of decision tree models with the flexibility and scalability of deep neural networks, DJINN is an attractive algorithm for training predictive models on a wide range of complex datasets.