An Investigation Into Bayesian Networks for Modeling National Ignition Facility Capsule Implosions

Summary form only given. Radiation environments characteristic of those encountered during the low-temperature foot pulse and subsequent higher-temperature early-step pulses required for indirect-drive ICF ignition on the National Ignition Facility (NIF) are desired in order to provide a platform to better understand the dynamics of NIF hohlraums and capsules prior to NIF completion. In this paper, we show that an axial hohlraum using the static-wall-hohlraum geometry heated by X-rays from a Z-pinch on the Z generator is capable of providing environments for such pre-NIF studies as well as for diagnostic applications.

The interface between the capsule ablator and fuel ice layer is susceptible to hydrodynamic instabilities. The subsequent mixing of hot ablator material into the ice reduces fuel compression at stagnation and is a candidate for reduced capsule performance. The ability to diagnose ice–ablator mix is critical to understanding and improving stability at this interface. Combining the crystal backlighter imager with the single line of sight camera on the National Ignition Facility (NIF) allows direct measurement of ice–ablator mix by providing multiple quasi-monochromatic radiographs of layered capsule implosions per experiment with high spatial (∼12 μm) and temporal (∼35 ps) resolution. The narrow bandwidth of this diagnostic platform allows radiography of the inner edge of the capsule limb close to stagnation without capsule self-emission contaminating the data and removes opacity uncertainties typically associated with the spectral content of the radiograph. Analysis of radiographic data via a parameterized forward-fitting Abel inversion technique provides measurements of the distribution of mix mass inwards from the ice–ablator interface. The sensitivity of this mix measurement technique was demonstrated by applying it to layered experiments in which the stability of the ice–ablator interface was expected to vary significantly. Additional experiments suggest that high-density carbon capsules that employ a buried-layer dopant profile suffer from mixing at the innermost doped–undoped interface. Data from these experiments suggest that opacity models used in hydrodynamic simulations of NIF experiments can potentially over-predict the opacity of doped capsules. LLNL-JRNL-850535-DRAFT.

We report on the first layered deuterium-tritium (DT) capsule implosions indirectly driven by a "high-foot" laser pulse that were fielded in depleted uranium hohlraums at the National Ignition Facility. Recently, high-foot implosions have demonstrated improved resistance to ablation-front Rayleigh-Taylor instability induced mixing of ablator material into the DT hot spot [Hurricane etal., Nature (London) 506, 343 (2014)]. Uranium hohlraums provide a higher albedo and thus an increased drive equivalent to an additional 25TW laser power at the peak of the drive compared to standard gold hohlraums leading to higher implosion velocity. Additionally, we observe an improved hot-spot shape closer to round which indicates enhanced drive from the waist. In contrast to findings in the National Ignition Campaign, now all of our highest performing experiments have been done in uranium hohlraums and achieved total yields approaching 10^{16} neutrons where more than 50% of the yield was due to additional heating of alpha particles stopping in the DT fuel.

The Crystal Backlighter Imager (CBI) is a quasi-monochromatic, near-normal incidence, spherically bent crystal imager developed for the National Ignition Facility (NIF), which will allow inertial confinement fusion capsule implosions to be radiographed close to stagnation. This is not possible using the standard pinhole-based area-backlighter configuration, as the self-emission from the capsule hotspot overwhelms the backlighter signal in the final stages of the implosion. The CBI mitigates the broadband self-emission from the capsule hot spot by using the extremely narrow bandwidth inherent to near-normal-incidence Bragg diffraction. Implementing a backlighter system based on near-normal reflection in the NIF chamber presents unique challenges, requiring the CBI to adopt novel engineering and operational strategies. The CBI currently operates with an 11.6 keV backlighter, making it the highest energy radiography diagnostic based on spherically bent crystals to date. For a given velocity, Doppler shift is proportional to the emitted photon energy. At 11.6 keV, the ablation velocity of the backlighter plasma results in a Doppler shift that is significant compared to the bandwidth of the instrument and the width of the atomic line, requiring that the shift be measured to high accuracy and the optics aligned accordingly to compensate. Experiments will be presented that used the CBI itself to measure the backlighter Doppler shift to an accuracy of better than 1 eV. These experiments also measured the spatial resolution of CBI radiographs at 7.0 μm, close to theoretical predictions. Finally, results will be presented from an experiment in which the CBI radiographed a capsule implosion driven by a 1 MJ NIF laser pulse, demonstrating a significant (>100) improvement in the backlighter to self-emission ratio compared to the pinhole-based area-backlighter configuration.

We present the calculations and preliminary results from experiments on the Omega laser facility using d-(3)He filled plastic capsule implosions in gold Hohlraums. These experiments aim to develop a technique to measure shell rho r and capsule unablated mass with proton spectroscopy and will be applied to future National Ignition Facility (NIF) experiments with ignition scale capsules. The Omega Hohlraums are 1900 microm length x 1200 microm diameter and have a 70% laser entrance hole. This is approximately a 0.2 NIF scale ignition Hohlraum and reaches temperatures of 265-275 eV similar to those during the peak of the NIF drive. These capsules can be used as a diagnostic of shell rho r, since the d-(3)He gas fill produces 14.7 MeV protons in the implosion, which escape through the shell and produce a proton spectrum that depends on the integrated rho r of the remaining shell mass. The neutron yield, proton yield, and spectra change with capsule shell thickness as the unablated mass or remaining capsule rho r changes. Proton stopping models are used to infer shell unablated mass and shell rho r from the proton spectra measured with different filter thicknesses. The experiment is well modeled with respect to Hohlraum energetics, neutron yields, and x-ray imploded core image size, but there are discrepancies between the observed and simulated proton spectra.

Bayesian networks (BNs) model problems that involve uncertainty. A BN is a directed graph, whose nodes are the uncertain variables and whose edges are the causal or influential links between the variables. Associated with each node is a set of conditional probability functions that model the uncertain relationship between the node and its parents. The benefits of using BNs to model uncertain domains are well known, especially since the recent breakthroughs in algorithms and tools to implement them. However, there have been serious problems for practitioners trying to use BNs to solve realistic problems. This is because, although the tools make it possible to execute large-scale BNs efficiently, there have been no guidelines on building BNs. Specifically, practitioners face two significant barriers. The first barrier is that of specifying the graph structure such that it is a sensible model of the types of reasoning being applied. The second barrier is that of eliciting the conditional probability values. In this paper we concentrate on this first problem. Our solution is based on the notion of generally applicable “building blocks”, called idioms, which serve solution patterns. These can then in turn be combined into larger BNs, using simple combination rules and by exploiting recent ideas on modular and object oriented BNs (OOBNs). This approach, which has been implemented in a BN tool, can be applied in many problem domains. We use examples to illustrate how it has been applied to build large-scale BNs for predicting software safety. In the paper we review related research from the knowledge and software engineering literature. This provides some context to the work and supports our argument that BN knowledge engineers require the same types of processes, methods and strategies enjoyed by systems and software engineers if they are to succeed in producing timely, quality and cost-effective BN decision support solutions.

The National Ignition Facility (NIF) provides a unique opportunity to study implosion physics with nuclear yield. The use of polar direct drive (PDD) [A. M. Cok, R. S. Craxton, and P. W. McKenty, Phys. Plasmas 15, 082705 (2008)] provides a simple platform for the experimental studies without expensive optics upgrades to NIF. To determine the optimum PDD laser pointing geometry on NIF and provide a baseline for validating inertial confinement fusion codes against experiments for symmetric and asymmetric implosions, computer simulations using the 3D radiation-hydrodynamics code hydra [M. M. Marinak, R. E. Tipton, O. L. Landen, T. J. Murphy, P. Amendt, S. W. Haan, S. P. Hatchett, C. J. Keane, R. McEachern, and R. Wallace, Phys. Plasmas 3, 2070 (1996)] were preformed. The upper hemisphere of a DT-filled CH capsule was imploded by 96 NIF beams in a PDD configuration. Asymmetries in both polar and equatorial directions around the capsule were observed, with the former dominating the latter. Analysis of the simulation results indicates that the lack of symmetry in the initial power density profile (during the first 200 ps of the implosion) is a primary cause of late-time asymmetry in the implosion as well as decreased yield. By adjusting the laser pointings, the symmetry and total neutron yield were improved. Simulations with dropped quads (four of the NIF laser system’s 192 beamlines) without repointing worsen the overall symmetry by a factor of 10 (with respect to rms radial variation around the capsule) and reduce neutron yield by a factor of 2. Both of these degraded implosion characteristics are restored by azimuthal repointing of the remaining quads.

Reflections on the use of Bayesian belief networks for adaptive management

When learning Bayesian networks from data, in many real circumstances, experts of domains could give the relationships between the classes of variables. In this paper, the problem of `learning Bayesian networks based on ordering of sets' is formulated. To solve this problem, we propose a partitioned greedy search algorithm for learning structures of Bayesian networks based on the ordering of sets. The results of experiments show that, with the ordering of sets, compared with traditional greedy DAG search algorithm, the score of the structure obtained by our algorithm is improved, and the search time is greatly reduced

Bayesian networks (BNs) are being studied in recent years for system diagnosis, reliability analysis, and design of complex engineered systems. In several practical applications, BNs need to be learned from available data before being used for design or other purposes. Current BN learning algorithms are mainly developed for networks with only discrete variables. Engineering design problems often consist of both discrete and continuous variables. This paper develops a framework to handle continuous variables in BN learning by integrating learning algorithms of discrete BNs with Gaussian mixture models (GMMs). We first make the topology learning more robust by optimizing the number of Gaussian components in the univariate GMMs currently available in the literature. Based on the BN topology learning, a new multivariate Gaussian mixture (MGM) strategy is developed to improve the accuracy of conditional probability learning in the BN. A method is proposed to address this difficulty of MGM modeling with data of mixed discrete and continuous variables by mapping the data for discrete variables into data for a standard normal variable. The proposed framework is capable of learning BNs without discretizing the continuous variables or making assumptions about their conditional probability densities (CPDs). The applications of the learned BN to uncertainty quantification and model calibration are also investigated. The results of a mathematical example and an engineering application example demonstrate the effectiveness of the proposed framework.

Capsule performance optimization campaigns will be conducted at the National Ignition Facility [G. H. Miller, E. I. Moses, and C. R. Wuest, Nucl. Fusion 44, 228 (2004)] to substantially increase the probability of ignition. The campaigns will experimentally correct for residual uncertainties in the implosion and hohlraum physics used in our radiation-hydrodynamic computational models using a variety of ignition capsule surrogates before proceeding to cryogenic-layered implosions and ignition experiments. The quantitative goals and technique options and down selections for the tuning campaigns are first explained. The computationally derived sensitivities to key laser and target parameters are compared to simple analytic models to gain further insight into the physics of the tuning techniques. The results of the validation of the tuning techniques at the OMEGA facility [J. M. Soures et al., Phys. Plasmas 3, 2108 (1996)] under scaled hohlraum and capsule conditions relevant to the ignition design are shown to meet the required sensitivity and accuracy. A roll-up of all expected random and systematic uncertainties in setting the key ignition laser and target parameters due to residual measurement, calibration, cross-coupling, surrogacy, and scale-up errors has been derived that meets the required budget. Finally, we show how the tuning precision will be improved after a number of shots and iterations to meet an acceptable level of residual uncertainty.

We present a probabilistic logic programming framework that allows the representation of conditional probabilities. While conditional probabilities are the most commonly used method for representing uncertainty in probabilistic expert systems, they have been largely neglected by work in quantitative logic programming. We define a fixpoint theory, declarative semantics, and proof procedure for the new class of probabilistic logic programs. Compared to other approaches to quantitative logic programming, we provide a true probabilistic framework with potential applications in probabilistic expert systems and decision support systems. We also discuss the relationship between such programs and Bayesian networks, thus moving toward a unification of two major approaches to automated reasoning.

Bayesian networks can be used to model gene regulatory networks because of its capability of capturing causal relationships between genes. However, learning Bayesian network is an NP-hard problem. Hill climbing methods are used in BN learning, in which K2 is a frequently used greedy search algorithm. But the performance of K2 algorithm is greatly affected by a prior ordering of input nodes and relatively low accuracy of the learned structures may be observed. To solve these problems, we propose a new algorithm (BPSOBN) to explore the use of Binary Particle Swarm Optimization (BPSO) algorithms for learning Bayesian networks. The result of experiments show that our BPSO based algorithm can obtain better networks than hill climbing methods. BPSOBN also shows the effectiveness for network reconstruction to gene expression data measured during the yeast cell cycle.

The principal approach to ignition on the National Ignition Facility (NIF) is indirect drive. A schematic of an ignition target is shown in Figure 1. The laser beams are focused through laser entrance holes at each end of a high-Z cylindrical case, or hohlraum. The lasers irradiate the hohlraum walls producing x-rays that ablate and compress the fuel capsule in the center of the hohlraum. The hohlraum is made of Au, U, or other high-Z material. For ignition targets, the hohlraum is {approx}0.5 cm diameter by {approx}1 cm in length. The hohlraum absorbs the incident laser energy producing x-rays for symmetrically imploding the capsule. The fuel capsule is a {approx}2-mm-diameter spherical shell of CH, Be, or C filled with DT fuel. The DT fuel is in the form of a cryogenic layer on the inside of the capsule. X-rays ablate the outside of the capsule, producing a spherical implosion. The imploding shell stagnates in the center, igniting the DT fuel. NIC has overseen installation of all of the hardware for performing ignition experiments, including commissioning of approximately 50 diagnostic systems in NIF. The diagnostics measure scattered optical light, x-rays from the hohlraum over the energy range from 100 eV to 500 keV, and x-rays, neutrons, and charged particles from the implosion. An example of a diagnostic is the Magnetic Recoil Spectrometer (MRS) built by a collaboration of scientists from MIT, UR-LLE, and LLNL shown in Figure 2. MRS measures the neutron spectrum from the implosion, providing information on the neutron yield and areal density that are metrics of the quality of the implosion. Experiments on NIF extend ICF research to unexplored regimes in target physics. NIF can produce more than 50 times the laser energy and more than 20 times the power of any previous ICF facility. Ignition scale hohlraum targets are three to four times larger than targets used at smaller facilities, and the ignition drive pulses are two to five times longer. The larger targets and longer pulse lengths produce unique plasma conditions for laser-plasma instabilities that could reduce hohlraum coupling efficiency. Initial experiments have demonstrated efficient coupling of laser energy to x-rays. X-ray drive greater than 300 eV has been measured in gas-filled ignition hohlraum and shows the expected scaling with laser energy and hohlraum scale size. Experiments are now optimizing capsule implosions for ignition. Ignition conditions require assembling the fuel with sufficient density and temperature for thermonuclear burn. X-rays ablate the outside of the capsule, accelerating and spherically compressing the capsule for assembling the fuel. The implosion stagnates, heating the central core and producing a hot spot that ignites and burns the surrounding fuel. The four main characteristics of the implosion are shell velocity, central hot spot shape, fuel adiabat, and mix. Experiments studying these four characteristics of implosions are used to optimize the implosion. Integrated experiments using cryogenic fuel layer experiments demonstrate the quality of the implosion as the optimization experiments progress. The final compressed fuel conditions are diagnosed by measuring the x-ray emission from the hot core and the neutrons and charged particles produced in the fusion reactions. Metrics of the quality of the implosion are the neutron yield and the shell areal density, as well as the size and shape of the core. The yield depends on the amount of fuel in the hot core and its temperature and is a gauge of the energy coupling to the fuel. The areal density, the density of the fuel times its thickness, diagnoses the fuel assembly, which is measured using the fraction of neutrons that are down scattered passing through the dense shell. The yield and fraction of down scattered neutrons, or shell rho-r, from the cryogenic layered implosions are shown in Figure 3. The different sets of data represent results after a series of implosion optimization experiments. Both yield and areal density show significant increases as a result of the optimization. The experimental Ignition Threshold Factor (ITFX) is a measure of the progress toward ignition. ITFX is analogous to the Lawson Criterion in Magnetic Fusion. Implosions have improved by over a factor of 50 since the first cryogenic layered experiments were done in September 2010. This increase is a measure of the progress made toward the ignition goal in the past year. Optimization experiments are planned in the coming year for continued improvement in implosion performance to achieve the ignition goal. In summary, NIF has made significant progress toward ignition in the 30 months since project completion. Diagnostics and all of the supporting equipment are in place for ignition experiments. The Ignition Campaign is under way as a national collaborative effort of all the National Nuclear Security Administration (NNSA) science laboratories as well as international partners.

EXP’s IC3D system classifies SAR or LiDAR derived 3D point clouds using a deep representation learning approach, producing as output a vector of categorical posterior probabilities of target classifications. Such posterior probabilities are suitable observational inputs to a Bayesian belief network (BBN), such as the EXP Shadow Compass system. In concert with conditional probabilities of intermediate events depending on the observation states, the Bayesian network computes posterior probabilities for events conditionally dependent on those intermediate event states. We demonstrate this approach by computing posterior event probabilities for sample analyst scenarios with intermediate event conditional probabilities specified by analysts. Future work could include extending the Bayesian network approach to discovery of the network topology from analyst data.