Publications

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We generalize the theory of underlying one-step methods to strictly stable general linear methods (GLMs) solving nonautonomous ordinary differential equations (ODEs) that satisfy a global Lipschitz condition. We combine this theory with the Lyapunov and Sacker-Sell spectral stability theory for one-step methods developed in [34, 35, 36] to analyze the stability of a strictly stable GLM solving a nonautonomous linear ODE. These results are applied to develop a stability diagnostic for the solution of nonautonomous linear ODEs by strictly stable GLMs.

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There has been much interest in leveraging the topological order of materials for quantum information processing. Among the various solid-state systems, one-dimensional topological superconductors made out of strongly spin-orbit-coupled nanowires have been shown to be the most promising material platform. In this project, we investigated the feasibility of turning silicon, which is a non-topological semiconductor and has weak spin-orbit coupling, into a one-dimensional topological superconductor. Our theoretical analysis showed that it is indeed possible to create a sizable effective spin-orbit gap in the energy spectrum of a ballistic one-dimensional electron channel in silicon with the help of nano-magnet arrays. Experimentally, we developed magnetic materials needed for fabricating such nano-magnets, characterized the magnetic behavior at low temperatures, and successfully demonstrated the required magnetization configuration for opening the spin-orbit gap. Our results pave the way toward a practical topological quantum computing platform using silicon, one of the most technologically mature electronic materials.

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We present a preliminary investigation of the use of Multi-Layer Perceptrons (MLP) and Recurrent Neural Networks (RNNs) as surrogates of parameter-to-prediction maps of computational expensive dynamical models. In particular, we target the approximation of Quantities of Interest (QoIs) derived from the solution of a Partial Differential Equations (PDEs) at different time instants. In order to limit the scope of our study while targeting a relevant application, we focus on the problem of computing variations in the ice sheets mass (our QoI), which is a proxy for global mean sea-level changes. We present a number of neural network formulations and compare their performance with that of Polynomial Chaos Expansions (PCE) constructed on the same data.

This SAND report fulfills the final report requirement for the Born Qualified Grand Challenge LDRD. Born Qualified was funded from FY16-FY18 with a total budget of ~$13M over the 3 years of funding. Overall 70+ staff, Post Docs, and students supported this project over its lifetime. The driver for Born Qualified was using Additive Manufacturing (AM) to change the qualification paradigm for low volume, high value, high consequence, complex parts that are common in high-risk industries such as ND, defense, energy, aerospace, and medical. AM offers the opportunity to transform design, manufacturing, and qualification with its unique capabilities. AM is a disruptive technology, allowing the capability to simultaneously create part and material while tightly controlling and monitoring the manufacturing process at the voxel level, with the inherent flexibility and agility in printing layer-by-layer. AM enables the possibility of measuring critical material and part parameters during manufacturing, thus changing the way we collect data, assess performance, and accept or qualify parts. It provides an opportunity to shift from the current iterative design-build-test qualification paradigm using traditional manufacturing processes to design-by-predictivity where requirements are addressed concurrently and rapidly. The new qualification paradigm driven by AM provides the opportunity to predict performance probabilistically, to optimally control the manufacturing process, and to implement accelerated cycles of learning. Exploiting these capabilities to realize a new uncertainty quantification-driven qualification that is rapid, flexible, and practical is the focus of this effort.

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The Vanguard program informally began in January 2017 with the submission of a white paper entitled "Sandia's Vision for a 2019 Arm Testbed" to NNSA headquarters. The program proceeded in earnest in May 2017 with an announcement by Doug Wade (Director, Office of Advanced Simulation and Computing and Institutional R&D at NNSA) that Sandia National Laboratories (Sandia) would host the first Advanced Architecture Prototype platform based on the Arm architecture. In August 2017, Sandia formed a Tri-lab team chartered to develop a robust HPC software stack for Astra to support the Vanguard program goal of demonstrating the viability of Arm in supporting ASC production computing workloads.

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