Publications

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Uncertainty quantification is recognized as a fundamental task to obtain predictive numerical simulations. However, many realistic engineering applications require complex and computationally expensive high-fidelity numerical simulations for the accurate characterization of the system responses. Moreover, complex physical models and extreme operative conditions can easily lead to hundreds of uncertain parameters that need to be propagated through high-fidelity codes. Under these circumstances, a single fidelity approach, i.e. a workflow that only uses high-fidelity simulations to perform the uncertainty quantification task, is unfeasible due to the prohibitive overall computational cost. In recent years, multifidelity strategies have been introduced to overcome this issue. The core idea of this family of methods is to combine simulations with varying levels of fidelity/accuracy in order to obtain the multifidelity estimators or surrogates with the same accuracy of their single fidelity counterparts at a much lower computational cost. This goal is usually accomplished by defining a prioria sequence of discretization levels or physical modeling assumptions that can be used to decrease the complexity of a numerical realization and thus its computational cost. However ,less attention has been dedicated to low-fidelity models that can be built directly from the small number of high-fidelity simulations available. In this work we focus our attention on Reduced-Order Models that can be considered a particular class of data-driven approaches. Our main goal is to explore the combination of multifidelity uncertainty quantification and reduced-order models to obtain an efficient framework for propagating uncertainties through expensive numerical codes.

This report summarizes the accomplishments and challenges of a two year LDRD effort focused on improving design-to-simulation agility. The central bottleneck in most solid mechanics simulations is the process of taking CAD geometry and creating a discretization of suitable quality, i.e., the "meshing" effort. This report revisits meshfree methods and documents some key advancements that allow their use on problems with complex geometries, low quality meshes, nearly incompressible materials or that involve fracture. The resulting capability was demonstrated to be an effective part of an agile simulation process by enabling rapid discretization techniques without increasing the time to obtain a solution of a given accuracy. The first enhancement addressed boundary-related challenges associated with meshfree methods. When using point clouds and Euclidean metrics to construct approximation spaces, the boundary information is lost, which results in low accuracy solutions for non-convex geometries and mate rial interfaces. This also complicates the application of essential boundary conditions. The solution involved the development of conforming window functions which use graph and boundary information to directly incorporate boundaries into the approximation space.

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Dragonflies are known to be highly successful hunters (achieving 90-95% success rate in nature) that implement a guidance law like proportional navigation to intercept their prey. This project tested the hypothesis that dragonflies are able to implement proportional navigation using prey-image translation on their eyes. The model dragonfly presented here calculates changes in pitch and yaw to maintain the prey's image at a designated location (the fovea) on a two-dimensional screen (the model's eyes ). When the model also uses self-knowledge of its own maneuvers as an error signal to adjust the location of the fovea, its interception trajectory becomes equivalent to proportional navigation. I also show that this model can also be applied successfully (in a limited number of scenarios) against maneuvering prey. My results provide a proof-of-concept demonstration of the potential of using the dragonfly nervous system to design a robust interception algorithm for implementation on a man-made system.

In stochastic optimization, probabilities naturally arise as cost functionals and chance constraints. Unfortunately, these functions are difficult to handle both theoretically and computationally. The buffered probability of failure and its subsequent extensions were developed as numerically tractable, conservative surrogates for probabilistic computations. In this manuscript, we introduce the higher-moment buffered probability. Whereas the buffered probability is defined using the conditional value-at-risk, the higher-moment buffered probability is defined using higher-moment coherent risk measures. In this way, the higher-moment buffered probability encodes information about the magnitude of tail moments, not simply the tail average. We prove that the higher-moment buffered probability is closed, monotonic, quasi-convex and can be computed by solving a smooth one-dimensional convex optimization problem. These properties enable smooth reformulations of both higher-moment buffered probability cost functionals and constraints.

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The emergence of deep learning as a leading computational workload for machine learning tasks on large-scale cloud infrastructure installations has led to plethora of accelerator hardware releases. However, the reduced precision and range of the floating-point numbers on these new platforms makes it a non-trivial task to leverage these unprecedented advances in computational power for numerical linear algebra operations that come with a guarantee of robust error bounds. In order to address these concerns, we present a number of strategies that can be used to increase the accuracy of limited-precision iterative refinement. By limited precision, we mean 16-bit floating-point formats implemented in modern hardware accelerators and are not necessarily compliant with the IEEE half-precision specification. We include the explanation of a broader context and connections to established IEEE floating-point standards and existing high-performance computing (HPC) benchmarks. We also present a new formulation of LU factorization that we call signed square root LU which produces more numerically balanced L and U factors which directly address the problems of limited range of the low-precision storage formats. The experimental results indicate that it is possible to recover substantial amounts of the accuracy in the system solution that would otherwise be lost. Previously, this could only be achieved by using iterative refinement based on single-precision floating-point arithmetic. The discussion will also explore the numerical stability issues that are important for robust linear solvers on these new hardware platforms.

Data-driven tools for finding structure–property (S–P) relations, such as the Materials Knowledge System (MKS) framework, can accelerate materials design, once the costly and technical calibration process has been completed. A three-model method is proposed to reduce the expense of S–P relation model calibration: (1) direct simulations are performed as per (2) a Gaussian process-based data collection model, to calibrate (3) an MKS homogenization model in an application to α-Ti. The new methods are compared favorably with expert texture selection on the performance of the so-calibrated MKS models. Benefits for the development of new and improved materials are discussed.

This report presents the code verification of EMPIRE-PIC to the analytic solution to a cold diode which was first derived by Jaffe. The cold diode was simulated using EMPIRE-PIC and the error norms were computed based on the Jaffe solution. The diode geometry is one-dimensional and uses the EMPIRE electrostatic field solver. After a transient start-up phase as the electrons first cross the anode-cathode gap, the simulations reach an equilibrium where the electric potential and electric field are approximately steady. The expected spatial order of convergence for potential, electric field and particle velocity are observed.

We present a new, distributed-memory parallel algorithm for detection of degenerate mesh features that can cause singularities in ice sheet mesh simulations. Identifying and removing mesh features such as disconnected components (icebergs) or hinge vertices (peninsulas of ice detached from the land) can significantly improve the convergence of iterative solvers. Because the ice sheet evolves during the course of a simulation, it is important that the detection algorithm can run in situ with the simulation - - running in parallel and taking a negligible amount of computation time - - so that degenerate features (e.g., calving icebergs) can be detected as they develop. We present a distributed memory, BFS-based label-propagation approach to degenerate feature detection that is efficient enough to be called at each step of an ice sheet simulation, while correctly identifying all degenerate features of an ice sheet mesh. Our method finds all degenerate features in a mesh with 13 million vertices in 0.0561 seconds on 1536 cores in the MPAS Albany Land Ice (MALI) model. Compared to the previously used serial pre-processing approach, we observe a 46,000x speedup for our algorithm, and provide additional capability to do dynamic detection of degenerate features in the simulation.

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Use of insensitive high explosives (IHEs) has significantly improved ammunition safety because of their remarkable insensitivity to violent cook-off, shock and impact. Triamino-trinitrobenzene (TATB) is the IHE used in many modern munitions. Previously, lightning simulations in different test configurations have shown that the required detonation threshold for standard density TATB at ambient and elevated temperatures (250 C) has a sufficient margin over the shock caused by an arc from the most severe lightning. In this paper, the Braginskii model with Lee-More channel conductivity prescription is used to demonstrate how electrical arcs from lightning could cause detonation in TATB. The steep rise and slow decay in typical lightning pulse are used in demonstrating that the shock pressure from an electrical arc, after reaching the peak, falls off faster than the inverse of the arc radius. For detonation to occur, two necessary detonation conditions must be met: the Pop-Plot criterion and minimum spot size requirement. The relevant Pop-Plot for TATB at 250 C was converted into an empirical detonation criterion, which is applicable to explosives subject to shocks of variable pressure. The arc cross-section was required to meet the minimum detonation spot size reported in the literature. One caveat is that when the shock pressure exceeds the detonation pressure the Pop-Plot may not be applicable, and the minimum spot size requirement may be smaller.

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