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At least 1,441 records · Page 80

Bayesian probability of predictive agreement for comparing the outcome of two separate regressions

The concept of a Bayesian probability of agreement was recently introduced to give the posterior probabilities that the response surfaces for two different groups are within δ of one another. For example, a difference of less than δ in the mean response at fixed levels of the predictor variables might be thought to be practically unimportant. In such a case, we would say that the mean responses are in agreement. The posterior probability of this is called the Bayesian probability of agreement. In this article, we quantify the probability that new response observations from two groups will be within δ for a continuous response, and the probability that the two responses agree completely for categorical cases such as logistic regression and Poisson regression. We call these Bayesian comparative predictive probabilities, with the former being the predictive probability of agreement. We use Markov chain Monte Carlo simulation to estimate the posterior distribution of the model parameters and then the predictive probability of agreement. Here, we illustrate the use of this methodology with three examples and provide a freely available R Shiny app that automates the computation and estimation associated with the methodology.

97 MATHEMATICS AND COMPUTING↗

Expanded Capabilities and Opportunities for Virtual Beamline Code

In the 25 years since LLNL broke ground on the National Ignition Facility (NIF) - a cornerstone of the National Nuclear Security Administration’s Stockpile Stewardship Program - the NIF and Photon Science (NIF&PS) Directorate has steadily pushed the boundaries of laser physics, nonlinear optics, and photonics in service of inertial confinement fusion experiments, and advanced photon sources development. Beyond the 192 beamlines of the primary laser facility with its world-record energy and fusion yields, NIF&PS capabilities have expanded to include chirped-pulse amplification, kilojoule petawatt-class short-pulse systems to generate hard x-ray radiographic probes, high-average power lasers as secondary sources for generation or wake field particle acceleration along directed energy applications, and other scientific pursuits. The Computing Directorate partners with NIF&PS on numerous projects and technologies from diagnostic measurements and high performance control systems to data analysis, information technology infrastructure, and scientific simulation code development. “This strong collaboration enables cutting-edge science, particularly with regard to physics-based modeling and simulation,” says physicist Jean-Michel Di Nicola. One crucial capability for NIF&PS is the Virtual Beamline (VBL) laser simulation code. It can model all the major laser physics and technology involved in the design optimization, commissioning, and operations of advanced laser architectures from tabletop to NIF-scale. VBL provides researchers with high-fidelity models and high-resolution calculations of laser performance predictions—including for the entire NIF laser system, the Advanced Radiographic Capability, parts of the High Repetition-Rate Advanced Petawatt Laser System laser delivered to the Czech Republic, and the Optical Science Laser. After more than two decades of experimentally verified physics and computing enhancements, this unique workhorse code is wrapping up another major milestone: migration from Java to C++ with a flurry of user interface and optimization features, as well as laser physics and high-resolution enhancements thanks to parallel execution on Livermore Computing platforms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Computer simulation studies in fluid and calcium regulation and orthostatic intolerance

The systems analysis approach to physiological research uses mathematical models and computer simulation. Major areas of concern during prolonged space flight discussed include fluid and blood volume regulation; cardiovascular response during shuttle reentry; countermeasures for orthostatic intolerance; and calcium regulation and bone atrophy. Potential contributions of physiologic math models to future flight experiments are examined.

Source record↗

Complex optimization for big computational and experimental neutron datasets

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, and refine first principles calculations to better describe the experimental data.

36 MATERIALS SCIENCE↗

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗

Data-Conforming Data-Driven Control: Avoiding Premature Generalizations Beyond Data

Data-driven and adaptive control approaches face the problem of introducing sudden distributional shifts beyond the distribution of data encountered during learning. Therefore, they are prone to invalidating the very assumptions used in their own construction. This is due to the linearity of the underlying system, inherently assumed and formulated in most data-driven control approaches, which may falsely generalize the behavior of the system beyond the behavior experienced in the data. This article seeks to mitigate these problems by enforcing consistency of the newly designed closed-loop systems with data and slowing down any distributional shifts in the joint state-input space. This is achieved through incorporating affine regularization terms and linear matrix inequality constraints to data-driven approaches, resulting in convex semi-definite programs that can be efficiently solved by standard software packages. We discuss the optimality conditions of these programs and then conclude this article with a numerical example that further highlights the problem of premature generalization beyond data and shows the effectiveness of our proposed approaches in enhancing the safety of data-driven control methods.

97 MATHEMATICS AND COMPUTING↗

Elviz – exploration of metagenome assemblies with an interactive visualization tool

Metagenomics, the sequencing of DNA collected from an entire microbial community, enables the study of natural microbial consortia in their native habitats. Metagenomics studies produce huge volumes of data, including both the sequences themselves and metadata describing their abundance, assembly, predicted functional characteristics and environmental parameters. The ability to explore these data visually is critically important to meaningful biological interpretation. Current genomics applications cannot effectively integrate sequence data, assembly metadata, and annotation to support both genome and community-level inquiry. Elviz (Environmental Laboratory Visualization) is an interactive web-based tool for the visual exploration of assembled metagenomes and their complex metadata. Elviz allows scientists to navigate metagenome assemblies across multiple dimensions and scales, plotting parameters such as GC content, relative abundance, phylogenetic affiliation and assembled contig length. Furthermore Elviz enables interactive exploration using real-time plot navigation, search, filters, axis selection, and the ability to drill from a whole-community profile down to individual gene annotations. Thus scientists engage in a rapid feedback loop of visual pattern identification, hypothesis generation, and hypothesis testing. Compared to the current alternative of generating a succession of static figures, Elviz can greatly accelerate the speed of metagenome analysis. Elviz can be used to explore both user-submitted datasets and numerous metagenome studies publicly available at the Joint Genome Institute (JGI). Elviz is freely available at http://genome.jgi.doe.gov/viz and runs on most current web-browsers.

59 BASIC BIOLOGICAL SCIENCES↗

Spectral Mesh-Free Quadrature for Planar Regions Bounded by Rational Parametric Curves

This article presents spectral, mesh-free, Green’s theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find intermediate quadrature rules for line integrals along the region’s boundary curves corresponding to Green’s theorem. (2) We then use a high-order quadrature rule to compute the numerical antiderivative of the integrand along a coordinate axis, which is used to evaluate the Green’s theorem line integral. We present two methods to compute the intermediate quadrature rule. The first is spectrally accurate (it converges faster than any algebraic order with respect to number of quadrature points) and is relatively easy to implement, but has no guarantee of polynomial exactness. The second guarantees exactness for polynomial integrands up to a pre-specified degree with an a priori-known number of quadrature points and retains the convergence properties of the first, but is slightly more complicated. The quadrature schemes have applications to computation of geometric moments, immersogeometric analysis, conservative field transfer between high-order meshes, and initialization of multi-material simulations with rational geometry. We compare the quadrature schemes produced using our method to other methods in the literature and show that they are much more efficient both in terms of number of quadrature points and computational time. We provide an open-source implementation of the algorithm in MATLAB.

97 MATHEMATICS AND COMPUTING↗

A new approach for simulating inhomogeneous chemical kinetics

Abstract In this paper, inhomogeneous chemical kinetics are simulated by describing the concentrations of interacting chemical species by a linear expansion of basis functions in such a manner that the coupled reaction and diffusion processes are propagated through time efficiently by tailor-made numerical methods. The approach is illustrated through modelling $$\alpha$$ α - and $$\gamma$$ γ -radiolysis in thin layers of water and at their solid interfaces from the start of the chemical phase until equilibrium was established. The method’s efficiency is such that hundreds of such systems can be modelled in a few hours using a single core of a typical laptop, allowing the investigation of the effects of the underlying parameter space. Illustrative calculations showing the effects of changing dose-rate and water-layer thickness are presented. Other simulations are presented which show the approach’s capability to solve problems with spherical symmetry (an approximation to an isolated radiolytic spur), where the hollowing out of an initial Gaussian distribution is observed, in line with previous calculations. These illustrative simulations show the generality and the computational efficiency of this approach to solving reaction-diffusion problems. Furthermore, these example simulations illustrate the method’s suitability for simulating solid-fluid interfaces, which have received a lot of experimental attention in contrast to the lack of computational studies.

97 MATHEMATICS AND COMPUTING↗

Simulation of Dynamics of a Flexible Miniature Airplane

A short report discusses selected aspects of the development of the University of Florida micro-aerial vehicle (UFMAV) basically, a miniature airplane that has a flexible wing and is representative of a new class of airplanes that would operate autonomously or under remote control and be used for surveillance and/or scientific observation. The flexibility of the wing is to be optimized such that passive deformation of the wing in the presence of aerodynamic disturbances would reduce the overall response of the airplane to disturbances, thereby rendering the airplane more stable as an observation platform. The aspect of the development emphasized in the report is that of computational simulation of dynamics of the UFMAV in flight, for the purpose of generating mathematical models for use in designing control systems for the airplane. The simulations are performed by use of data from a wind-tunnel test of the airplane in combination with commercial software, in which are codified a standard set of equations of motion of an airplane, and a set of mathematical routines to compute trim conditions and extract linear state space models.

Waszak, Martin R.↗

Transforming Energy Through Computational Excellence: Artificial Intelligence and Machine Learning

The National Renewable Energy Laboratory's (NREL's) expertise accelerates a decarbonized energy economy through the most advanced computational techniques, including artificial intelligence (AI) and Machine Learning (ML). AI is the simulation of human intelligence processes by machines, while ML encompasses the study of computer algorithms to imitate the way humans learn.

97 MATHEMATICS AND COMPUTING↗

Modeling Fluid Flow in Domains Containing Moving Interfaces

Numerical simulations of fluid flow in domains containing moving rigid objects or boundaries are still challenging when meshes have to be adapted and periodically regenerated. A numerical strategy that falls into the general category of Arbitrary Lagrangian - Eulerian (ALE) methods is being developed. The method is based on a fixed mesh that is locally modified both in space and time to describe the moving interfaces which are allowed to move independently of the mesh. This results in a fully robust formulation capable of calculating in irregular meshes containing moving devises of complex geometry and free of mesh entanglement problems. The present work constitutes the first stage in the development of a three-dimensional model to interface with the new KIVA-hpFE simulator. The method’s accuracy has been assessed in two dimensions using a case that has an analytical solution.

02 PETROLEUM↗

Comparing Mitigations under Uncertainty in Simulated Influenza Outbreak [Slides]

Consequences of an influenza outbreak and effects of factors determining mitigation strategies were studied by computer simulation using statistical design and analysis of experiments methods. Twelve input variables that specify differing degrees of disease mitigation were selected to be evaluated within the context of nine uncertain inputs that characterize influenza expression, e. g., reproductive number, case mortality rate, duration of infective period. Variables were characterized with probability distributions based on assessments of low, high, and typical values from expert opinion and literature review. An approach to experiment design called dispersion array based experiment was developed that incorporates orthogonal array based Latin hypercube sampling. The simulation experiment consisted of 128 combinations of mitigation factors each evaluated over 16 distinct disease characterizations and allowed a quick assessment of simulation results, particularly mitigation efficacy. Sensitivity evaluation of the mitigation factors showed effectiveness against the range of influenza expressions with little stress on the health care system.

60 APPLIED LIFE SCIENCES↗

Hydrocode Development on the Ncube and the Connection Machine Hypercubes [Book Chapter]

Hydrocode simulations constitute an important tool at Sandia National Laboratories and elsewhere for analyzing complex two- and three-dimensional systems. However, current vector supercomputers do not provide a growth path to enable fast, routine, and cost-effective simulations of large problems. Future, massively-parallel computers will provide a solution. Sandia has already developed simplified versions of the production hydrocode CTH for the Connection Machine and the nCUBE massively-parallel supercomputers. The parallel versions solve problems in two-dimensional, multi-fluid, shock-wave physics. Code development strategy, coding methodology, visualization techniques and performance results for this work are described.

640410 -- Fluid Physics-- General Fluid Dynamics↗