Publications

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Nonlocal models naturally handle a range of physics of interest to SNL, but discretization of their underlying integral operators poses mathematical challenges to realize the accuracy and robustness commonplace in discretization of local counterparts. This project focuses on the concept of asymptotic compatibility, namely preservation of the limit of the discrete nonlocal model to a corresponding well-understood local solution. We address challenges that have traditionally troubled nonlocal mechanics models primarily related to consistency guarantees and boundary conditions. For simple problems such as diffusion and linear elasticity we have developed complete error analysis theory providing consistency guarantees. We then take these foundational tools to develop new state-of-the-art capabilities for: lithiation-induced failure in batteries, ductile failure of problems driven by contact, blast-on-structure induced failure, brittle/ductile failure of thin structures. We also summarize ongoing efforts using these frameworks in data-driven modeling contexts. This report provides a high-level summary of all publications which followed from these efforts.

The quantum k-Local Hamiltonian problem is a natural generalization of classical constraint satisfaction problems (k-CSP) and is complete for QMA, a quantum analog of NP. Although the complexity of k-Local Hamiltonian problems has been well studied, only a handful of approximation results are known. For Max 2-Local Hamiltonian where each term is a rank 3 projector, a natural quantum generalization of classical Max 2-SAT, the best known approximation algorithm was the trivial random assignment, yielding a 0.75-approximation. We present the first approximation algorithm beating this bound, a classical polynomial-time 0.764-approximation. For strictly quadratic instances, which are maximally entangled instances, we provide a 0.801 approximation algorithm, and numerically demonstrate that our algorithm is likely a 0.821-approximation. We conjecture these are the hardest instances to approximate. We also give improved approximations for quantum generalizations of other related classical 2-CSPs. Finally, we exploit quantum connections to a generalization of the Grothendieck problem to obtain a classical constant-factor approximation for the physically relevant special case of strictly quadratic traceless 2-Local Hamiltonians on bipartite interaction graphs, where a inverse logarithmic approximation was the best previously known (for general interaction graphs). Our work employs recently developed techniques for analyzing classical approximations of CSPs and is intended to be accessible to both quantum information scientists and classical computer scientists.

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Hole spin qubits confined to lithographically - defined lateral quantum dots in Ge/SiGe heterostructures show great promise. On reason for this is the intrinsic spin - orbit coupling that allows all - electric control of the qubit. That same feature can be exploited as a coupling mechanism to coherently link spin qubits to a photon field in a superconducting resonator, which could, in principle, be used as a quantum bus to distribute quantum information. The work reported here advances the knowledge and technology required for such a demonstration. We discuss the device fabrication and characterization of different quantum dot designs and the demonstration of single hole occupation in multiple devices. Superconductor resonators fabricated using an outside vendor were found to have adequate performance and a path toward flip-chip integration with quantum devices is discussed. The results of an optical study exploring aspects of using implanted Ga as quantum memory in a Ge system are presented.

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Nonlocal models use integral operators that embed length-scales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials' behavior, we propose a learning framework to extract, from MD data, an optimal nonlocal model as a surrogate for MD displacements. Our framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. The efficacy of this approach is demonstrated with several numerical tests for single layer graphene both in the case of perfect crystal and in the presence of thermal noise.

This report details the results of a three-fold investigation of sensitivity analysis (SA) for machine learning (ML) explainability (MLE): (1) the mathematical assessment of the fidelity of an explanation with respect to a learned ML model, (2) quantifying the trustworthiness of a prediction, and (3) the impact of MLE on the efficiency of end-users through multiple users studies. We focused on the cybersecurity domain as the data is inherently non-intuitive. As ML is being using in an increasing number of domains, including domains where being wrong can elicit high consequences, MLE has been proposed as a means of generating trust in a learned ML models by end users. However, little analysis has been performed to determine if the explanations accurately represent the target model and they themselves should be trusted beyond subjective inspection. Current state-of-the-art MLE techniques only provide a list of important features based on heuristic measures and/or make certain assumptions about the data and the model which are not representative of the real-world data and models. Further, most are designed without considering the usefulness by an end-user in a broader context. To address these issues, we present a notion of explanation fidelity based on Shapley values from cooperative game theory. We find that all of the investigated MLE explainability methods produce explanations that are incongruent with the ML model that is being explained. This is because they make critical assumptions about feature independence and linear feature interactions for computational reasons. We also find that in deployed, explanations are rarely used due to a variety of reason including that there are several other tools which are trusted more than the explanations and there is little incentive to use the explanations. In the cases when the explanations are used, we found that there is the danger that explanations persuade the end users to wrongly accept false positives and false negatives. However, ML model developers and maintainers find the explanations more useful to help ensure that the ML model does not have obvious biases. In light of these findings, we suggest a number of future directions including developing MLE methods that directly model non-linear model interactions and including design principles that take into account the usefulness of explanations to the end user. We also augment explanations with a set of trustworthiness measures that measure geometric aspects of the data to determine if the model output should be trusted.

Efficient modeling of low magnetic Reynolds number (low-Rm) magnetohydrodynamics is often challenging and requires the implementation of innovative techniques to avoid key barriers experienced with prior approaches. We detail a new paradigm for first-principles simulation of the solution to the low-Rm governing equations in complex geometries. As a result of a number of innovative numerical advances, the next-generation GPU (graphics processing unit) accelerated physics code LGR has been successfully applied to the modeling of exploding wire problems.

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The typical topology optimization workflow uses a design domain that does not change during the optimization process. Consequently, features of the design domain, such as the location of loads and constraints, must be determined in advance and are not optimizable. A method is proposed herein that allows the design domain to be optimized along with the topology. This approach uses topology and shape derivatives to guide nested optimizers to the optimal topology and design domain. The details of the method are discussed, and examples are provided that demonstrate the utility of this approach.

Constructing accurate statistical models of critical system responses typically requires an enormous amount of data from physical experiments or numerical simulations. Unfortunately, data generation is often expensive and time consuming. To streamline the data generation process, optimal experimental design determines the 'best' allocation of experiments with respect to a criterion that measures the ability to estimate some important aspect of an assumed statistical model. While optimal design has a vast literature, few researchers have developed design paradigms targeting tail statistics, such as quantiles. In this project, we tailored and extended traditional design paradigms to target distribution tails. Our approach included (i) the development of new optimality criteria to shape the distribution of prediction variances, (ii) the development of novel risk-adapted surrogate models that provably overestimate certain statistics including the probability of exceeding a threshold, and (iii) the asymptotic analysis of regression approaches that target tail statistics such as superquantile regression. To accompany our theoretical contributions, we released implementations of our methods for surrogate modeling and design of experiments in two complementary open source software packages, the ROL/OED Toolkit and PyApprox.

Ship tracks are quasi-linear cloud patterns produced from the interaction of ship emissions with low boundary layer clouds. They are visible throughout the diurnal cycle in satellite images from space-borne assets like the Advanced Baseline Imagers (ABI) aboard the National Oceanic and Atmospheric Administration Geostationary Operational Environmental Satellites (GOES-R). However, complex atmospheric dynamics often make it difficult to identify and characterize the formation and evolution of tracks. Ship tracks have the potential to increase a cloud's albedo and reduce the impact of global warming. Thus, it is important to study these patterns to better understand the complex atmospheric interactions between aerosols and clouds to improve our climate models, and examine the efficacy of climate interventions, such as marine cloud brightening. Over the course of this 3-year project, we have developed novel data-driven techniques that advance our ability to assess the effects of ship emissions on marine environments and the risks of future marine cloud brightening efforts. The three main innovative technical contributions we will document here are a method to track aerosol injections using optical flow, a stochastic simulation model for track formations and an automated detection algorithm for efficient identification of ship tracks in large datasets.

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