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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 271 records · Page 15

Stabilization and Attenuation of Bounded Perturbations in Discrete Control Systems

Necessary and sufficient conditions for the static output feedback stabilization of linear discrete-time control systems are formulated in the form of a matrix inequality. It is shown that the algorithms of stabilization based on these conditions are applicable to a certain class of nonlinear discrete-time control systems. We propose the procedure of construction of the regularities of control guaranteeing the required estimation of the weighted level of attenuation of input signals and initial perturbations, as well as the robust stability of the equilibrium state of the controlled system. A numerical example of the discretetime system of stabilization of a pendulum on a moving platform is presented.

97 MATHEMATICS AND COMPUTING↗

Giving Research Software Engineers a Larger Stage Through the Better Scientific Software Fellowship

The Better Scientific Software Fellowship (BSSwF) was launched in 2018 to foster and promote practices, processes, and tools to improve developer productivity and software sustainability of scientific codes. The BSSwF’s vision is to grow the community with practitioners, leaders, mentors, and consultants to increase the visibility of scientific software. Over the last five years, many fellowship recipients and honorable mentions have identified as research software engineers (RSEs). Furthermore, case studies from several of the program’s participants illustrate the diverse ways the BSSwF has benefited both the RSE and scientific communities. In an environment where the contributions of RSEs are too often undervalued, we believe that programs such as the BSSwF can help recognize and encourage community members to step outside of their regular commitments and expand on their work, collaborations, and ideas for a larger audience.

97 MATHEMATICS AND COMPUTING↗

Eco-PiNN: A Physics-informed Neural Network for Eco-toll Estimation

The eco-toll estimation problem quantifies the expected environmental cost (e.g., energy consumption, exhaust emissions) for a vehicle to travel along a path. This problem is important for societal applications such as eco-routing, which aims to find paths with the lowest exhaust emissions or energy need. The challenges of this problem are threefold: (1) the dependence of a vehicle's eco-toll on its physical parameters; (2) the lack of access to data with eco-toll information; and (3) the influence of contextual information (i.e. the connections of adjacent segments in the path) on the eco-toll of road segments. Prior work on eco-toll estimation has mostly relied on pure data-driven approaches and has high estimation errors given the limited training data. To address these limitations, we propose a novel Eco-toll estimation Physics-informed Neural Network framework (Eco-PiNN) using three novel ideas, namely, (1) a physics-informed decoder that integrates the physical laws governing vehicle dynamics into the network, (2) an attention-based contextual information encoder, and (3) a physics-informed regularization to reduce overfitting. Experiments on real-world heavy-duty truck data show that the proposed method can greatly improve the accuracy of eco-toll estimation compared with state-of-the-art methods.

97 MATHEMATICS AND COMPUTING↗

A Discrete Nonlinear Schrödinger-Type Hierarchy, Its Finite-Dimensional Reduction Analysis, and the Numerical Integration Scheme

We investigate the procedures of discretization of the integrable nonlinear Schrödinger dynamical system, well known as the Ablowitz–Ladik equation, the corresponding symplectic structures, and the finite-dimensional invariant reductions. We develop an efficient scheme of invariant reduction of the corresponding infinite system of ordinary differential equations to an equivalent finite system of ordinary differential equations with respect to the evolution parameter. We construct a finite set of recurrence algebraic regular relations that allows one to generate solutions of the discrete nonlinear Schrödinger dynamical system and discuss the related functional spaces of solutions. Finally, we analyze the Fourier-transform approach to the study of the set of solutions of the discrete nonlinear Schrödinger dynamical system and its functional-analytic aspects.

97 MATHEMATICS AND COMPUTING↗

Physically interpretable approximations of many-body spectral functions

The rational function approximation provides a natural and interpretable representation of response functions such as the many-body spectral functions. We apply the vector fitting (VFIT) algorithm to fit a variety of spectral functions calculated from the Holstein model of electron-phonon interactions. We show that the resulting rational functions are highly efficient in their fitting of sharp features in the spectral functions, and could provide a means to infer physically relevant information from a spectral data set. The position of the peaks in the approximated spectral function are determined by the location of poles in the complex plane. Additionally, we developed a variant of VFIT that incorporates regularization to improve the quality of fits. With this procedure, we demonstrate it is possible to achieve accurate spectral function fits that vary smoothly as a function of physical conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach

Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg–de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditions to test the robustness of the proposed approach.

42 ENGINEERING↗

Optimization-based control using input convex neural networks

Input convex neural networks (ICNNs) are a family of deep learning models where the outputs are constructed to be convex functions of the inputs. By parameterizing system models using ICNNs, optimization-based control problems can be solved as convex optimization problems, leading to improved performance and robustness. This work proposes a novel framework where the control objective function and constraints are modelled using ICNNs. A case study of optimization-based control with output constraints is conducted on a process with input multiplicity and nonminimum phase behavior. The simulation results demonstrate improved economic yield compared with normal neural networks. Additionally, the input convexity formulation is compared with simple regularization techniques, and unique benefits such as improved data efficiency and robustness of the proposed formulation are shown. Finally, by explicitly incorporating prior knowledge about convexity, this framework provides a good balance between the universal approximation power of deep learning and computational feasibility required by control.

42 ENGINEERING↗

A Code to Code Benchmark for HTGR Fuel Element Depletion

The current lack of well-qualified experimental measurements for spent HGTR fuel elements limits the validation of advanced doubly heterogeneous depletion methods. Because of this shortage of data, a benchmark was developed as the first, simplest phase in a planned series of increasingly complex set of code-to-code benchmarks. The intent of this benchmark was to encourage submission of a wide range of computational results for depletion calculations in a set of basic fuel cell models. Comparison of results using independent methods and data should provide insight into potential limitations in various modeling approximations. The benchmark seeks to provide the simplest possible models, in order to minimize the effect of competing and potentially offsetting phenomena that might mask weaknesses in given methods. Twenty-one sets of results were submitted by twelve participants internationally. Various approaches were used for the treatment of microscopic grains dispersed in fuel elements in the second and third parts of the benchmark, including explicit treatment of grains distributed within a regular lattice, a randomized distribution of explicit grains, reactivity-equivalent physical transformation and a two-pass homogenization with disadvantage factors. The broad agreement appears to validate each of the double heterogeneity treatments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

RAJA Performance Suite

The RAJA Performance Suite is designed to evaluate performance of the RAJA performance portability library on a wide variety of important high performance computing (HPC) algorithmic lulmels. These kernels assess compiler optimizations and various parallel programming model backends accessible through RAJA, such as OpenMP, CUDA, etc. The Initial version of the suite contains 25 computational kernels, each of which appears in 6 variants: Baseline SequcntiaJ, RAJA SequentiaJ, Baseline OpenMP, RAJA OpenMP, Baseline CUDA, RAJA CUDA. All variants of each kernel perform essentially the same mathematical operations and the loop body code for each kernel is identical across all variants. There are a few kernels, such as those that contain reduction operations, that require CUDA-specific coding for their CUDA variants. ActuaJ computer instructions executed and how they run in parallel differs depending on the parallel programming model backend used and which optimizations are perfonned by the compiler used to build the Perfonnance Suite executable. The Suite will be used primarily by RAJA developers to perform regular assessments of RAJA performance across a range of hardware platforms and compilers as RAJA features are being developed. It will also be used by LLNL hardware and software vendor panners for new defining requirements for future computing platform procurements and acceptance testing. In particular, the RAJA Performance Suite will be used for compiler acceptance testing of the upcoming CORAUSierra machine {initial LLNL delivery expected in late-2017/early 2018) and the CORAL-2 procurement. The Suite will aJso be used to generate concise source code reproducers of compiler and runtime issues we uncover so that we may provide them to relevant vendors to be fixed.

Hornung, RichardD.↗

Support for Reactor Operators in Case of Cyber-Security Threats (NEUP Final Report)

Increasing use of digital technology in nuclear power plants (NPPs) poses cyber-security as a crucial threat to public safety and to continuous energy production. Cyber-security risks are comprised of complex known and unknown interactions between various entities, system vulnerabilities, network protocols, human users and malicious attacks. There is little understanding or research geared towards plant operators’ response under cyber-security threats and operational procedures to cope with such threats. This is particularly critical when a cyber-security event masquerades as a safety incident or an evolving accident. Instead of leading operators to the remediation of the accident, the masked cyber event may lead them to circumvent the safety mechanisms of the plant. Given these challenges, the objective of this project is to develop a tool to characterize abnormal NPP events as “cyber” or “safety” incidents, and to further develop this tool as a real-time operator aid to assist in response to the incident. This NEUP Final Report summarizes the research efforts towards the above goals and the results in the following three aspects. First, a methodology for classifying abnormal NPP events as cyber-attacks or safety incidents was developed. This provides the basis for responding to potential cyber-attacks. In this methodology, the causal relationships between various variables (i.e., physical variables, network variables, and control variables) for a nuclear system under consideration are modeled using dynamic Bayesian networks. Based on observations of certain variables (i.e., the evidence), inference is performed to identify the state of hidden variables, which helps indicate the occurrence of cyber-attacks or safety incidents. The proposed methodology was applied to the full scope NPP simulator system at The Ohio State University as a case study. The result shows that the proposed methodology is capable of distinguishing between cyber-attacks and safety incidents. Second, a game-theoretic approach for responding to cyber-attacks on nuclear power plants was developed. This is the second major goal of the project, and the method is used to recommend optimal responses to reactor operators in the case of cyber-attacks. We consider two cases in this research. In the first case, the interaction between the defender (i.e., the reactor operator) and the attacker is modeled as a two-player, nonzero-sum, Markov game with an infinite time horizon. In the second case, we consider a semi-Markov game between the defender and the attacker within a finite time horizon. The model in the second case enables us to consider the time sensitive response of the defender. In each case, the method for deriving the Nash equilibrium is developed. The Nash Equilibrium of the game provides the valid prediction of both players’ actions because no single player can benefit from unilaterally deviating from the equilibrium policy if the other player adheres to his/hers, hence it provides the best response of the defender to cyber-attacks. The proposed method in each case is demonstrated through a simplified benchmark digital feedwater control system. Third, a prototype display is developed to integrate the above information. The prototype display depicts the communication information to the operator and incorporates the cyber-security tool developed by the team into the interface. It consists of the regular display in current control rooms, as well as a panel used to indicate the occurrence of cyber-attacks or safety events and a panel used to guide the operator’s response to detected cyber-attacks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Positive Configuration Space

Abstract We define and study the totally nonnegative part of the Chow quotient of the Grassmannian, or more simply the nonnegative configuration space . This space has a natural stratification by positive Chow cells , and we show that nonnegative configuration space is homeomorphic to a polytope as a stratified space. We establish bijections between positive Chow cells and the following sets: (a) regular subdivisions of the hypersimplex into positroid polytopes, (b) the set of cones in the positive tropical Grassmannian, and (c) the set of cones in the positive Dressian. Our work is motivated by connections to super Yang–Mills scattering amplitudes, which will be discussed in a sequel.

Physics↗

Computational thermomechanics for crystalline rock. Part II: Chemo-damage-plasticity and healing in strongly anisotropic polycrystals

We present a thermal–mechanical–chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase field, and chemical concentration incrementally. In nuclear waste disposal in salt formation, brine inside the crystal salt may migrate along the grain boundary and cracks due to the gradient of interfacial energy and pressure. This migration has a significant implication on the permeability evolution, creep deformation, and crack healing within rock salt but is difficult to incorporate implicitly via effective medium theories compared with computational homogenization. As such, we introduce a thermodynamic framework and a corresponding computational implementation that explicitly captures the brine diffusion along the grain boundary and crack at the grain scale. Meanwhile, the anisotropic fracture and healing are captured via a high-order phase field that represents the regularized crack region in which a newly derived non-monotonic driving force is used to capture the fracture and healing due to the solution–precipitation. Numerical examples are presented to demonstrate the capacity of the thermodynamic framework to capture the multiphysics material behaviors of rock salt.

42 ENGINEERING↗

Sparsifying priors for Bayesian uncertainty quantification in model discovery

We propose a probabilistic model discovery method for identifying ordinary differential equations governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy) framework, where models are expressed as sparse linear combinations of pre-specified candidate functions. Promoting parsimony through sparsity leads to interpretable models that generalize to unknown data. Instead of targeting point estimates of the SINDy coefficients, we estimate these coefficients via sparse Bayesian inference. The resulting method, uncertainty quantification SINDy (UQ-SINDy), quantifies not only the uncertainty in the values of the SINDy coefficients due to observation errors and limited data, but also the probability of inclusion of each candidate function in the linear combination. UQ-SINDy promotes robustness against observation noise and limited data, interpretability (in terms of model selection and inclusion probabilities) and generalization capacity for out-of-sample forecast. Sparse inference for UQ-SINDy employs Markov chain Monte Carlo, and we explore two sparsifying priors: the spike and slab prior, and the regularized horseshoe prior. UQ-SINDy is shown to discover accurate models in the presence of noise and with orders-of-magnitude less data than current model discovery methods, thus providing a transformative method for real-world applications which have limited data.

97 MATHEMATICS AND COMPUTING↗

Design, analysis and numerical experiments for the virtual element p and hp approximations of elliptic eigenvalue problems

We discuss the p- and the hp-versions of the virtual element method for the approximation of the eigenvalues of elliptic operators with a potential term on polygonal meshes. An application of this model is provided by the Schr¨odinger equation with a pseudo-potential term. We present in details the analysis of the p-version of the method, proving the exponential convergence in the case of analytic eigenfunctions. The theoretical results are supplied with a wide set of experiments. We also show numerically that, in the case of eigenfunctions with finite Sobolev regularity, an exponential approximation of the eigenvalues in terms of the cubic root of the number of degrees of freedom can be obtained by employing hp-refinements. Importantly, the geometric flexibility of polygonal meshes is exploited in the construction of the hp-spaces.

97 MATHEMATICS AND COMPUTING↗

Effects of Jacobian Matrix Regularization on the Detectability of Adversarial Samples

The well-known vulnerability of Deep Neural Networks to adversarial samples has led to a rapid cycle of increasingly sophisticated attack algorithms and proposed defenses. While most contemporary defenses have been shown to be vulnerable to carefully configured attacks, methods based on gradient regularization and out-of-distribution detection have attracted much interest recently by demonstrating higher resilience to a broad range of attack algorithms. However, no study has yet investigated the effect of combining these techniques. In this paper, we consider the effect of Jacobian matrix regularization on the detectability of adversarial samples on the CIFAR-10 image benchmark dataset. We find that regularization has a significant effect on detectability, and in some cases can make an undetectable attack on a baseline model detectable. In addition, we give evidence that regularization may mitigate the known weaknesses of detectors to high-confidence adversarial samples. The defenses we consider here are highly generalizable, and we believe they will be useful for further investigations to transfer machine learning robustness to other data domains.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Optimization-based algorithms for nonlinear mechanics and frictional contact

An optimization-based strategy for solving nonlinear mechanics problems is proposed. In contrast to typical nonlinear equation solver algorithms that aim to find zeros in the residual force function, we minimize an energy (or energy-like) function to encourage solutions which are locally stable equilibria. These smooth and potentially non-convex objective functions are minimized using a preconditioned conjugate-gradient trust-region algorithm. Contact is formulated as an inequality constrained minimization problem, and is solved with an augmented Lagrangian algorithm. Friction is included in the approach via a regularized quasi-potential energy, and other dissipative behavior is included through the use of variational constitutive updates. Finally, to accelerate convergence rates for the Lagrange multipliers, we propose a novel multiplier update algorithm utilizing the Fischer-Burmeister function, and demonstrate super-linear solver convergence for some applications.

42 ENGINEERING↗

Application of transport-based metric for continuous interpolation between cryo-EM density maps

Cryogenic electron microscopy (cryo-EM) has become widely used for the past few years in structural biology, to collect single images of macromolecules "frozen in time". As this technique facilitates the identification of multiple conformational states adopted by the same molecule, a direct product of it is a set of 3D volumes, also called EM maps. To gain more insights on the possible mechanisms that govern transitions between different states, and hence the mode of action of a molecule, we recently introduced a bioinformatic tool that interpolates and generates morphing trajectories joining two given EM maps. This tool is based on recent advances made in optimal transport, that allow efficient evaluation of Wasserstein barycenters of 3D shapes. As the overall performance of the method depends on various key parameters, including the sensitivity of the regularization parameter, we performed various numerical experiments to demonstrate how MorphOT can be applied in different contexts and settings. Finally, we discuss current limitations and further potential connections between other optimal transport theories and the conformational heterogeneity problem inherent with cryo-EM data.

3D shapes↗

Restoration of the Initial Data in the Problem for a Diffusion Equation with Fractional Derivative with Respect to Time

We prove the correctness of the inverse problem of finding a pair of functions: the classical solution u(x,t) of the first boundary-value problem for a linear diffusion equation with regularized fractional derivative of order α ∈ (1, 2) with respect to time in a rectangular domain (0, ℓ) × (0, t{sub 0}] and unknown initial values of the function u(x,t) for the case of additionally given values of the function at a certain fixed time t{sub 0} .

97 MATHEMATICS AND COMPUTING↗