By returning to the topological basics of fusion target design, Generative Artificial Intelligence (genAI) is used to specify how to initially configure and drive the optimally entangled topological state, and stabilize that topological state from disruption. This can be applied to all methods; including tokamaks, laser-driven schemes, and pulsed-power driven schemes. The result is practical, room temperature targets that can yield up to 10 GJ of energy, driven by as little as 3 MJ of absorbed energy. The genAI is based on the concept of Ubuntu that replaces the Deep Convolutional Neural Network approximation of a functional, with the formula for the generating functional of a canonical transformation from the domain of the canonical field momentums and fields, to the domain of the canonical momentums and coordinates, that is the Reduced Order Model. This formula is a logical process of renormalization, enabling Heisenberg's canonical approach to field theory, via calculation of the S-matrix, given observation of the fields. This can be viewed as topological characterization and control of collective, that is complex, systems.

A Machine and Deep Learning (MLDL) methodology is developed and applied to give a high fidelity, fast surrogate for 2D resistive MagnetoHydroDynamic (MHD) simulations of Magnetic Liner Inertial Fusion (MagLIF) implosions. The resistive MHD code GORGON is used to generate an ensemble of implosions with different liner aspect ratios, initial gas preheat temperatures (that is, different adiabats), and different liner perturbations. The liner density and magnetic field as functions of x, y, and z were generated. The Mallat Scattering Transformation (MST) is taken of the logarithm of both fields and a Principal Components Analysis (PCA) is done on the logarithm of the MST of both fields. The fields are projected onto the PCA vectors and a small number of these PCA vector components are kept. Singular Value Decompositions of the cross correlation of the input parameters to the output logarithm of the MST of the fields, and of the cross correlation of the SVD vector components to the PCA vector components are done. This allows the identification of the PCA vectors vis-a-vis the input parameters. Finally, a Multi Layer Perceptron (MLP) neural network with ReLU activation and a simple three layer encoder/decoder architecture is trained on this dataset to predict the PCA vector components of the fields as a function of time. Details of the implosion, stagnation, and the disassembly are well captured. Examination of the PCA vectors and a permutation importance analysis of the MLP show definitive evidence of an inverse turbulent cascade into a dipole emergent behavior. The orientation of the dipole is set by the initial liner perturbation. The analysis is repeated with a version of the MST which includes phase, called Wavelet Phase Harmonics (WPH). While WPH do not give the physical insight of the MST, they can and are inverted to give field configurations as a function of time, including field-to-field correlations.

Computational simulation allows scientists to explore, observe, and test physical regimes thought to be unattainable. Validation and uncertainty quantification play crucial roles in extrapolating the use of physics-based models. Bayesian analysis provides a natural framework for incorporating the uncertainties that undeniably exist in computational modeling. However, the ability to perform quality Bayesian and uncertainty analyses is often limited by the computational expense of first-principles physics models. In the absence of a reliable low-fidelity physics model, phenomenological surrogate or machine learned models can be used to mitigate this expense; however, these data-driven models may not adhere to known physics or properties. Furthermore, the interactions of complex physics in high-fidelity codes lead to dependencies between quantities of interest (QoIs) that are difficult to quantify and capture when individual surrogates are used for each observable. Although this is not always problematic, predicting multiple QoIs with a single surrogate preserves valuable insights regarding the correlated behavior of the target observables and maximizes the information gained from available data. A method of constructing a Gaussian Process (GP) that emulates multiple QoIs simultaneously is presented. As an exemplar, we consider Magnetized Liner Inertial Fusion, a fusion concept that relies on the direct compression of magnetized, laser-heated fuel by a metal liner to achieve thermonuclear ignition. Magneto-hydrodynamics (MHD) codes calculate diagnostics to infer the state of the fuel during experiments, which cannot be measured directly. The calibration of these diagnostic metrics is complicated by sparse experimental data and the expense of high-fidelity neutron transport models. The development of an appropriate surrogate raises long-standing issues in modeling and simulation, including calibration, validation, and uncertainty quantification. The performance of the proposed multi-output GP surrogate model, which preserves correlations between QoIs, is compared to the standard single-output GP for a 1D realization of the MagLIF experiment.

We present a general method for optimizing the configuration of an experimental diagnostic to minimize uncertainty and bias in inferred quantities from experimental data. The method relies on Bayesian inference to sample the posterior using a physical model of the experiment and instrument. The mean squared error (MSE) of posterior samples relative to true values obtained from a high fidelity model (HFM) across multiple configurations is used as the optimization metric. The method is demonstrated on a common problem in dense plasma research, the use of radiation detectors to estimate physical properties of the plasma. We optimize a set of filtered photoconducting diamond detectors to minimize the MSE in the inferred X-ray spectrum, from which we can derive quantities like the electron temperature. In the optimization we self-consistently account for uncertainties in the instrument response with appropriate prior probabilities. We also develop a penalty term, acting as a soft constraint on the optimization, to produce results that avoid negative instrumental effects. We show results of the optimization and compare with two other reference instrument configurations to demonstrate the improvement. The MSE with respect to the total inferred X-ray spectrum is reduced by more than an order of magnitude using our optimized configuration compared with the two reference cases. We also extract multiple other quantities from the inference and compare with the HFM, showing an overall improvement in multiple inferred quantities like the electron temperature, the peak in the X-ray spectrum and the total radiated energy.

Laser propagation experiments using four beams of the National Ignition Facility to deliver up to 35 kJ of laser energy at 351 nm laser wavelength to heat magnetized liner inertial fusion-scale (1 cm-long), hydrocarbon-filled gas pipe targets to ∼keV electron temperatures have demonstrated energy coupling >20 kJ with essentially no backscatter in 15% critical electron density gas fills with 0–19 T applied axial magnetic fields. The energy coupling is also investigated for an electron density of 11.5% critical and for applied field strengths up to 24 T at both densities. This spans a range of Hall parameters 0 < ωceτei≲2, where a Hall parameter of 0.5 is expected to reduce electron thermal conduction across the field lines by a factor of 4–5 for the conditions of these experiments. At sufficiently high applied field strength (and therefore Hall parameter), the measured laser propagation speed through the targets increases in the measurements, consistent with reduced perpendicular electron thermal transport; this reduces the coupled energy to the target once the laser burns through the gas pipe. The results compare well with a 1D analytic propagation model for inverse Bremsstrahlung absorption.

Limited-angle X-ray tomography reconstruction is an ill-conditioned inverse problem in general. Especially when the projection angles are limited and the measurements are taken in a photon-limited condition, reconstructions from classical algorithms such as filtered backprojection may lose fidelity and acquire artifacts due to the missing-cone problem. To obtain satisfactory reconstruction results, prior assumptions, such as total variation minimization and nonlocal image similarity, are usually incorporated within the reconstruction algorithm. In this work, we introduce deep neural networks to determine and apply a prior distribution in the reconstruction process. Our neural networks learn the prior directly from synthetic training samples. The neural nets thus obtain a prior distribution that is specific to the class of objects we are interested in reconstructing. In particular, we used deep generative models with 3D convolutional layers and 3D attention layers which are trained on 3D synthetic integrated circuit (IC) data from a model dubbed CircuitFaker. We demonstrate that, when the projection angles and photon budgets are limited, the priors from our deep generative models can dramatically improve the IC reconstruction quality on synthetic data compared with maximum likelihood estimation. Training the deep generative models with synthetic IC data from CircuitFaker illustrates the capabilities of the learned prior from machine learning. We expect that if the process were reproduced with experimental data, the advantage of the machine learning would persist. The advantages of machine learning in limited angle X-ray tomography may further enable applications in low-photon nanoscale imaging.

We present an overview of the magneto-inertial fusion (MIF) concept Magnetized Liner Inertial Fusion (MagLIF) pursued at Sandia National Laboratories and review some of the most prominent results since the initial experiments in 2013. In MagLIF, a centimeter-scale beryllium tube or ‘liner’ is filled with a fusion fuel, axially pre-magnetized, laser pre-heated, and finally imploded using up to 20 MA from the Z machine. All of these elements are necessary to generate a thermonuclear plasma: laser preheating raises the initial temperature of the fuel, the electrical current implodes the liner and quasi-adiabatically compresses the fuel via the Lorentz force, and the axial magnetic field limits thermal conduction from the hot plasma to the cold liner walls during the implosion. MagLIF is the first MIF concept to demonstrate fusion relevant temperatures, significant fusion production (>1013 primary DD neutron yield), and magnetic trapping of charged fusion particles. On a 60 MA next-generation pulsed-power machine, two-dimensional simulations suggest that MagLIF has the potential to generate multi-MJ yields with significant self-heating, a long-term goal of the US Stockpile Stewardship Program. At currents exceeding 65 MA, the high gains required for fusion energy could be achievable.

We propose a noise-resilient deep reconstruction algorithm for X-ray tomography. Our approach shows strong noise resilience without obtaining noisy training examples. The advantages of our framework may further enable low-photon tomographic imaging.

X-ray tomography is capable of imaging the interior of objects in three dimensions non-invasively, with applications in biomedical imaging, materials science, electronic inspection, and other fields. The reconstruction process can be an ill-conditioned inverse problem, requiring regularization to obtain satisfactory results. Recently, deep learning has been adopted for tomographic reconstruction. Unlike iterative algorithms which require a distribution that is known a priori, deep reconstruction networks can learn a prior distribution through sampling the training distributions. In this work, we develop a Physics-assisted Generative Adversarial Network (PGAN), a two-step algorithm for tomographic reconstruction. In contrast to previous efforts, our PGAN utilizes maximum-likelihood estimates derived from the measurements to regularize the reconstruction with both known physics and the learned prior. Compared with methods with less physics assisting in training, PGAN can reduce the photon requirement with limited projection angles to achieve a given error rate. The advantages of using a physics-assisted learned prior in X-ray tomography may further enable low-photon nanoscale imaging.

the intensity level which provided correct total ventricular volume. Cast cross sections were quantitatively well represented by these borders. This ventricular border definition algorithm forms the basis for applications of the technique in animals and humans.

Laser Powder Bed Fusion has become a widely adopted method for metal Additive Manufacturing (AM) due to its ability to mass produce complex parts with increased local control. However, AM produced parts can be subject to undesirable porosity, negatively influencing the properties of printed components. Thus, controlling porosity is integral for creating effective parts. A precise understanding of the porosity distribution is crucial for accurately simulating potential fatigue and failure zones. Previous research on generating synthetic porous microstructures have succeeded in generating parts with high density, isotropic porosity distributions but are often inapplicable to cases with sparser, boundary-dependent pore distributions. Our work bridges this gap by providing a method that considers these constraints by deconstructing the generation problem into its constitutive parts. A framework is introduced that combines Generative Adversarial Networks with Mallat Scattering Transform-based autocorrelation methods to construct novel realizations of the individual pore geometries and surface roughness, then stochastically reconstruct them to form realizations of a porous printed part. The generated parts are compared to the existing experimental porosity distributions based on statistical and dimensional metrics, such as nearest neighbor distances, pore volumes, pore anisotropies and scattering transform based auto-correlations.

We present a new analysis methodology that allows for the self-consistent integration of multiple diagnostics including nuclear measurements, x-ray imaging, and x-ray power detectors to determine the primary stagnation parameters, such as temperature, pressure, stagnation volume, and mix fraction in magnetized liner inertial fusion (MagLIF) experiments. The analysis uses a simplified model of the stagnation plasma in conjunction with a Bayesian inference framework to determine the most probable configuration that describes the experimental observations while simultaneously revealing the principal uncertainties in the analysis. We validate the approach by using a range of tests including analytic and three-dimensional MHD models. An ensemble of MagLIF experiments is analyzed, and the generalized Lawson criterion χ is estimated for all experiments.

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.

Gas-pipe experiments on the NIF have investigated MagLIF laser preheat at scales relevant to next-generation pulsed- power facilities. Experiments have been done into magnetized (up to 28 Tesla), room temperature, hydrocarbon and unmagnetized D2 gases of densities that span 1.6 mg/cc to 4.8 mg/cc (5% to 16% critical electron density). Up to 30 kJ of energy from one quad has been delivered into an oval spot of 1580 micron mean diameter over a time of about 11 ns with a power of 2 TW and an intensity of 2 x 10 14 W/cm 2 . A critical measurement in these experiments is the laser energy deposited though inverse Bremsstrahlung absorption in the gas. In this talk we describe line VISAR measurements taken in unmagnetized hydrocarbon-gas experiments. We show how the shock timing and velocity measured by line VISAR can be related to energy deposition over the 1 mm extent of the diagnostic view.

Physics-aware machine learning (PAML) has proven to be successful in re- trieving object in a low-photon imaging condition. In this study, we take an information theoretic approach to study maximum amount of information (i.e., the imaging capacity) that can be reliably retrieved under photon-starved imaging condition. We formulate a sim- ple problem to derive the imaging capacity using Monte Carlo approach: small integrated circuit objects (made out of two different type of materials) imaged with monochromatic x-rays. The simple problem is useful in that the entropies for priors and measurements can be explicitly computed. It is a simple version of the imaging system proposed in Ref. [3]. The constructed problem will help us understand the limit on photon budget, information gain associated with varying number of scan angles, and optimal PAML algorithm that can approach the theoretic imaging capacity.

Recent MagLIF experiments at the NIF have measured the energy coupling and propagation of a ~35 kJ laser pulse in 1 cm-long gas pipe targets with hydrocarbon gas fills and pre- imposed magnetic fields <25 T. The experiments explore the effects of gas density (n e = 0.12-0.16 n c ) and magnetic field strength (0-25 T) over the relevant design space. Temporally gated, spatially resolved x-ray imagers record the profile of the heated plasma throughout the laser propagation, showing evidence for modified electron transport when the magnetic field is applied. The time required for the laser to completely burn through the target is temporally resolved with an x-ray streak camera, and laser backscatter is measured during the entire interaction, allowing for accurate assessments of minimum energy coupling to the target. These emission profiles and burnthrough times are well reproduced in 2D Hydra simulations at electron densities of 12% critical and B=0, though there are discrepancies at higher density (16% critical) and with the magnetic field. Variation of the flux limiter choice alone is insufficient to bring the model into agreement with the data, so 3D simulations including additional MHD physics processes are now underway to better reproduce the measurements. The results show up to 30 kJ energy coupled into the gas which simulations suggest is close to optimal for MagLIF designs at 47 MA drive currents [1] .

In the MagLIF ICF scheme, a cylindrical gas volume is laser heated before the walls of the cylinder are driven radially inward to compress the heated gas. Exploring the effects of material from the walls and the laser entrance window mixing into the heated region are important considerations for MagLIF experiments 1 , 2 , 3 ,. The addition of these materials into the heated gas can potentially have detrimental effects, radiatively cooling the gas fill and degrading the yield 4 . The NIF has been used to drive gas-pipe experiments where a tracer element (Ti) is placed on the LEH window or where strips of Ti and Sc are attached to the wall. Spatially and temporally resolved spectroscopic measurements of the Ti and Sc emission indicate the spatial location of these materials at various times during the interaction, assisting future predictions and mitigations of their propagation into the gas-pipe.