In this LDRD we investigated the application of machine learning methods to understand dimensionality reduction and evolution of the Rayleigh-Taylor instability (RTI). As part of the project, we undertook a significant literature review to understand current analytical theory and machine learning based methods to treat evolution of this instability. We note that we chose to refocus on assessing the hydrodynamic RTI as opposed to the magneto-Rayleigh-Taylor instability originally proposed. This choice enabled utilizing a wealth of analytic test cases and working with relatively fast running open-source simulations of single-mode RTI. This greatly facilitated external collaboration with URA summer fellowship student, Theodore Broeren. In this project we studied the application of methods from dynamical systems learning and traditional regression methods to recover behavior of RTI ranging from the fully nonlinear to weakly nonlinear (wNL) regimes. Here we report on two of the tested methods SINDy and a more traditional regression-based approach inspired by analytic wNL theory with which we had the most success. We conclude with a discussion of potential future extensions to this work that may improve our understanding from both theoretical and phenomenological perspectives.
Significant variety is observed in spherical crystal x-ray imager (SCXI) data for the stagnated fuel–liner system created in Magnetized Liner Inertial Fusion (MagLIF) experiments conducted at the Sandia National Laboratories Z-facility. As a result, image analysis tasks involving, e.g., region-of-interest selection (i.e. segmentation), background subtraction and image registration have generally required tedious manual treatment leading to increased risk of irreproducibility, lack of uncertainty quantification and smaller-scale studies using only a fraction of available data. We present a convolutional neural network (CNN)-based pipeline to automate much of the image processing workflow. This tool enabled batch preprocessing of an ensemble of Nscans = 139 SCXI images across Nexp = 67 different experiments for subsequent study. The pipeline begins by segmenting images into the stagnated fuel and background using a CNN trained on synthetic images generated from a geometric model of a physical three-dimensional plasma. The resulting segmentation allows for a rules-based registration. Our approach flexibly handles rarely occurring artifacts through minimal user input and avoids the need for extensive hand labelling and augmentation of our experimental dataset that would be needed to train an end-to-end pipeline. Here we also fit background pixels using low-degree polynomials, and perform a statistical assessment of the background and noise properties over the entire image database. Our results provide a guide for choices made in statistical inference models using stagnation image data and can be applied in the generation of synthetic datasets with realistic choices of noise statistics and background models used for machine learning tasks in MagLIF data analysis. We anticipate that the method may be readily extended to automate other MagLIF stagnation imaging applications.
Making reliable predictions in the presence of uncertainty is critical to high-consequence modeling and simulation activities, such as those encountered at Sandia National Laboratories. Surrogate or reduced-order models are often used to mitigate the expense of performing quality uncertainty analyses with high-fidelity, physics-based codes. However, phenomenological surrogate models do not always adhere to important physics and system properties. This project develops surrogate models that integrate physical theory with experimental data through a maximally-informative framework that accounts for the many uncertainties present in computational modeling problems. Correlations between relevant outputs are preserved through the use of multi-output or co-predictive surrogate models; known physical properties (specifically monotoncity) are also preserved; and unknown physics and phenomena are detected using a causal analysis. By endowing surrogate models with key properties of the physical system being studied, their predictive power is arguably enhanced, allowing for reliable simulations and analyses at a reduced computational cost.
Fuel magnetization in magneto-inertial fusion (MIF) experiments improves charged burn product confinement, reducing requirements on fuel areal density and pressure to achieve self-heating. By elongating the path length of 1.01 MeV tritons produced in a pure deuterium fusion plasma, magnetization enhances the probability for deuterium-tritium reactions producing 11.8−17.1 MeV neutrons. Nuclear diagnostics thus enable a sensitive probe of magnetization. Characterization of magnetization, including uncertainty quantification, is crucial for understanding the physics governing target performance in MIF platforms, such as magnetized liner inertial fusion (MagLIF) experiments conducted at Sandia National Laboratories, Z-facility. We demonstrate a deep-learned surrogate of a physics-based model of nuclear measurements. A single model evaluation is reduced from CPU hours on a high-performance computing cluster down to ms on a laptop. This enables a Bayesian inference of magnetization, rigorously accounting for uncertainties from surrogate modeling and noisy nuclear measurements. The approach is validated by testing on synthetic data and comparing with a previous study. We analyze a series of MagLIF experiments systematically varying preheat, resulting in the first ever systematic experimental study of magnetic confinement properties of the fuel plasma as a function of fundamental inputs on any neutron-producing MIF platform. We demonstrate that magnetization decreases from B ∼0.5 to B MG cm as laser preheat energy deposited increases from preheat ∼460 J to E preheat ∼1.4 kJ. This trend is consistent with 2D LASNEX simulations showing Nernst advection of the magnetic field out of the hot fuel and diffusion into the target liner.
The morphology of the stagnated plasma resulting from Magnetized Liner Inertial Fusion (MagLIF) is measured by imaging the self-emission x-rays coming from the multi-keV plasma, and the evolution of the imploding liner is measured by radiographs. Equivalent diagnostic response can be derived from integrated rad-MHD simulations from programs such as Hydra and Gorgon. There have been only limited quantitative ways to compare the image mor- phology, that is the texture, of simulations and experiments. We have developed a metric of image morphology based on the Mallat Scattering Transformation (MST), a transformation that has proved to be effective at distinguishing textures, sounds, and written characters. This metric has demonstrated excellent performance in classifying ensembles of synthetic stagnation images. We use this metric to quantitatively compare simulations to experimen- tal images, cross experimental images, and to estimate the parameters of the images with uncertainty via a linear regression of the synthetic images to the parameter used to generate them. This coordinate space has proved very adept at doing a sophisticated relative back- ground subtraction in the MST space. This was needed to compare the experimental self emission images to the rad-MHD simulation images. We have also developed theory that connects the transformation to the causal dynamics of physical systems. This has been done from the classical kinetic perspective and from the field theory perspective, where the MST is the generalized Green's function, or S-matrix of the field theory in the scale basis. From both perspectives the first order MST is the current state of the system, and the second order MST are the transition rates from one state to another. . An efficient, GPU accelerated, Python implementation of the MST was developed. Future applications are discussed.