We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal discretization. The formulation is a version of Dubos and Tort (2014, https://doi.org/10.1175/MWR-D-14-00069.1) rewritten in terms of primitive variables. It is valid for terrain following mass or height coordinates and for both Eulerian or vertically Lagrangian discretizations. The discretization relies on an extension to Simmons and Burridge (1981, https://doi.org/10.1175/1520-0493(1981)109<0758:AEAAMC>2.0.CO;2) vertical differencing, which we show obeys a discrete derivative product rule. This product rule allows us to simplify the treatment of the vertical transport terms. Energy conservation is obtained via a term-by-term balance in the kinetic, internal, and potential energy budgets, ensuring an energy-consistent discretization up to time truncation error with no spurious sources of energy. We demonstrate convergence with respect to time truncation error in a spectral element code with a horizontal explicit vertically implicit implicit-explicit time stepping algorithm.
Particle-in-cell (PIC) simulation methods are attractive for representing species distribution functions in plasmas. However, as a model, they introduce uncertain parameters, and for quantifying their prediction uncertainty it is useful to be able to assess the sensitivity of a quantity-of-interest (QoI) to these parameters. Such sensitivity information is likewise useful for optimization. However, computing sensitivity for PIC methods is challenging due to the chaotic particle dynamics, and sensitivity techniques remain underdeveloped compared to those for Eulerian discretizations. This challenge is examined from a dual particle–continuum perspective that motivates a new sensitivity discretization. Two routes to sensitivity computation are presented and compared: a direct fully-Lagrangian particle-exact approach provides sensitivities of each particle trajectory, and a new particle-pdf discretization, which is formulated from a continuum perspective but discretized by particles to take the advantages of the same type of Lagrangian particle description leveraged by PIC methods. Since the sensitivity particles in this approach are only indirectly linked to the plasma-PIC particles, they can be positioned and weighted independently for efficiency and accuracy. The corresponding numerical algorithms are presented in mathematical detail. The advantage of the particle-pdf approach in avoiding the spurious chaotic sensitivity of the particle-exact approach is demonstrated for Debye shielding and sheath configurations. In essence, the continuum perspective makes implicit the distinctness of the particles, which circumvents the Lyapunov instability of the N-body PIC system. The cost of the particle-pdf approach is comparable to the baseline PIC simulation.
Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional complexity, namely, uncertain parameters in the PDEs. Uncertainty quantification (UQ) is necessary to characterize, prioritize, and study the influence of these uncertain parameters. Sensitivity analysis, a classical tool in UQ, is frequently used to study the sensitivity of a model to uncertain parameters. In this article, we introduce "hyper-differential sensitivity analysis" which considers the sensitivity of the solution of a PDE-constrained optimization problem to uncertain parameters. Our approach is a goal-oriented analysis which may be viewed as a tool to complement other UQ methods in the service of decision making and robust design. We formally define hyper-differential sensitivity indices and highlight their relationship to the existing optimization and sensitivity analysis literatures. Assuming the presence of low rank structure in the parameter space, computational efficiency is achieved by leveraging a generalized singular value decomposition in conjunction with a randomized solver which converts the computational bottleneck of the algorithm into an embarrassingly parallel loop. Two multi-physics examples, consisting of nonlinear steady state control and transient linear inversion, demonstrate efficient identification of the uncertain parameters which have the greatest influence on the optimal solution.
This article describes a parallel implementation of a two-level overlapping Schwarz preconditioner with the GDSW (Generalized Dryja–Smith–Widlund) coarse space described in previous work [12, 10, 15] into the Trilinos framework; cf. [16]. The software is a significant improvement of a previous implementation [12]; see Sec. 4 for results on the improved performance.
Concern about memory errors has been widespread in high-performance computing (HPC) for decades. These concerns have led to significant research on detecting and correcting memory errors to improve performance and provide strong guarantees about the correctness of the memory contents of scientific simulations. However, power concerns and changes in memory architectures threaten the viability of current approaches to protecting memory (e.g., Chipkill). Returning to less protective error-correcting codes (ECC), e.g., single-error correction, double-error detection (SECDED), may increase the frequency of memory errors, including silent data corruption (SDC). SDC has the potential to silently cause applications to produce incorrect results and mislead domain scientists. We propose an approach for exploiting unnecessary bits in pointer values to support encoding the pointer with a Reed-Solomon code. Encoding the pointer allows us to provides strong capabilities for correcting and detecting corruption of pointer values. In this paper, we provide a detailed description of how we can exploit unnecessary pointer bits to store Reed-Solomon parity symbols. We evaluate the performance impacts of this approach and examine the effectiveness of the approach against corruption. Our results demonstrate that encoding and decoding is fast (less than 45 per event) and that the protection it provides is robust (the rate of miscorrection is less than 5% even for significant corruption). The data and analysis presented in this paper demonstrates the power of our approach. It is fast, tunable, requires no additional per-pointer storage resources, and provides robust protection against pointer corruption.
Truly predictive numerical simulations can only be obtained by performing Uncertainty Quantification. However, many realistic engineering applications require extremely complex and computationally expensive high-fidelity numerical simulations for their accurate performance characterization. Very often the combination of 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 uncertainty quantification approach, i.e. a workflow that only uses high-fidelity simulations, is unfeasible due to its prohibitive overall computational cost. To overcome this difficulty, in recent years multifidelity strategies emerged and gained popularity. Their core idea is to combine simulations with varying levels of fidelity/accuracy in order to obtain estimators or surrogates that can yield the same accuracy of their single fidelity counterparts at a much lower computational cost. This goal is usually accomplished by defining a priori a sequence of discretization levels or physical modeling assumptions that can be used to decrease the complexity of a numerical model realization and thus its computational cost. Less attention has been dedicated to low-fidelity models that can be built directly from a small number of available high-fidelity simulations. In this work we focus our attention on reduced order models (ROMs). Our main goal in this work is to investigate the combination of multifidelity uncertainty quantification and ROMs in order to evaluate the possibility to obtain an efficient framework for propagating uncertainties through expensive numerical codes. We focus our attention on sampling-based multifidelity approaches, like the multifidelity control variate, and we consider several scenarios for a numerical test problem, namely the Kuramoto-Sivashinsky equation, for which the efficiency of the multifidelity-ROM estimator is compared to the standard (single-fidelity) Monte Carlo approach.
Bayesian optimization (BO) is an efficient and flexible global optimization framework that is applicable to a very wide range of engineering applications. To leverage the capability of the classical BO, many extensions, including multi-objective, multi-fidelity, parallelization, and latent-variable modeling, have been proposed to address the limitations of the classical BO framework. In this work, we propose a novel multi-objective (MO) extension, called srMOBO-3GP, to solve the MO optimization problems in a sequential setting. Three different Gaussian processes (GPs) are stacked together, where each of the GP is assigned with a different task: the first GP is used to approximate a single-objective computed from the MO definition, the second GP is used to learn the unknown constraints, and the third GP is used to learn the uncertain Pareto frontier. At each iteration, a MO augmented Tchebycheff function converting MO to single-objective is adopted and extended with a regularized ridge term, where the regularization is introduced to smooth the single-objective function. Finally, we couple the third GP along with the classical BO framework to explore the richness and diversity of the Pareto frontier by the exploitation and exploration acquisition function. The proposed framework is demonstrated using several numerical benchmark functions, as well as a thermomechanical finite element model for flip-chip package design optimization.
Lecture Notes in Computational Science and Engineering
Maljaars, Jakob M.; Labeur, Robert J.; Trask, Nathaniel A.; Sulsky, Deborah L.
A particle-mesh strategy is presented for scalar transport problems which provides diffusion-free advection, conserves mass locally (i.e. cellwise) and exhibits optimal convergence on arbitrary polyhedral meshes. This is achieved by expressing the convective field naturally located on the Lagrangian particles as a mesh quantity by formulating a dedicated particle-mesh projection based via a PDE-constrained optimization problem. Optimal convergence and local conservation are demonstrated for a benchmark test, and the application of the scheme to mass conservative density tracking is illustrated for the Rayleigh–Taylor instability.
American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM
Laros, James H.; Visintainer, Robert; Furlan, John; Pagalthivarthi, Krishnan V.; Garman, Mohamed; Cutright, Aaron; Wang, Yan
Wear prediction is important in designing reliable machinery for slurry industry. It usually relies on multi-phase computational fluid dynamics, which is accurate but computationally expensive. Each run of the simulations can take hours or days even on a high-performance computing platform. The high computational cost prohibits a large number of simulations in the process of design optimization. In contrast to physics-based simulations, data-driven approaches such as machine learning are capable of providing accurate wear predictions at a small fraction of computational costs, if the models are trained properly. In this paper, a recently developed WearGP framework [1] is extended to predict the global wear quantities of interest by constructing Gaussian process surrogates. The effects of different operating conditions are investigated. The advantages of the WearGP framework are demonstrated by its high accuracy and low computational cost in predicting wear rates.
Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
As the mean time between failures on the future high-performance computing platforms is expected to decrease to just a few minutes, the development of “smart”, property-preserving checkpointing schemes becomes imperative to avoid dramatic decreases in application utilization. In this paper we formulate a generic optimization-based approach for fault-tolerant computations, which separates property preservation from the compression and recovery stages of the checkpointing processes. We then specialize the approach to obtain a fault recovery procedure for a model scalar transport equation, which preserves local solution bounds and total mass. Numerical examples showing solution recovery from a corrupted application state for three different failure modes illustrate the potential of the approach.
The data from the multi-modal transportation test conducted in 2017 demonstrated that the inputs from the shock events during all transport modes (truck, rail, and ship) were amplified from the cask to the spent commercial nuclear fuel surrogate assemblies. These data do not support common assumption that the cask content experiences the same accelerations as the cask itself. This was one of the motivations for conducting 30 cm drop tests. The goal of the 30 cm drop test is to measure accelerations and strains on the surrogate spent nuclear fuel assembly and to determine whether the fuel rods can maintain their integrity inside a transportation cask when dropped from a height of 30 cm. The 30 cm drop is the remaining NRC normal conditions of transportation regulatory requirement (10 CFR 71.71) for which there are no data on the actual surrogate fuel. Because the full-scale cask and impact limiters were not available (and their cost was prohibitive), it was proposed to achieve this goal by conducting three separate tests. This report describes the first two tests — the 30 cm drop test of the 1/3 scale cask (conducted in December 2018) and the 30 cm drop of the full-scale dummy assembly (conducted in June 2019). The dummy assembly represents the mass of a real spent nuclear fuel assembly. The third test (to be conducted in the spring of 2020) will be the 30 cm drop of the full-scale surrogate assembly. The surrogate assembly represents a real full-scale assembly in physical, material, and mechanical characteristics, as well as in mass.
Trusting simulation output is crucial for Sandia’s mission objectives. Here, we rely on these simulations to perform our high-consequence mission tasks given national treaty obligations. Other science and modeling applications, while they may have high-consequence results, still require the strongest levels of trust to enable using the result as the foundation for both practical applications and future research. To this end, the computing community has developed workflow and provenance systems to aid in both automating simulation and modeling execution as well as determining exactly how was some output was created so that conclusions can be drawn from the data. Current approaches for workflows and provenance systems are all at the user level and have little to no system level support making them fragile, difficult to use, and incomplete solutions. The introduction of container technology is a first step towards encapsulating and tracking artifacts used in creating data and resulting insights, but their current implementation is focused solely on making it easy to deploy an application in an isolated “sandbox” and maintaining a strictly read-only mode to avoid any potential changes to the application. All storage activities are still using the system-level shared storage. This project explores extending the container concept to include storage as a new container type we call data pallets. Data Pallets are potentially writeable, auto generated by the system based on IO activities, and usable as a way to link the contained data back to the application and input deck used to create it.
A key problem in social network analysis is to identify nonhuman interactions. State-of-the-art bot-detection systems like Botometer train machine-learning models on user-specific data. Unfortunately, these methods do not work on data sets in which only topological information is available. In this paper, we propose a new, purely topological approach. Our method removes edges that connect nodes exhibiting strong evidence of non-human activity from publicly available electronic-social-network datasets, including, for example, those in the Stanford Network Analysis Project repository (SNAP). Our methodology is inspired by classic work in evolutionary psychology by Dunbar that posits upper bounds on the total strength of the set of social connections in which a single human can be engaged. We model edge strength with Easley and Kleinberg's topological estimate; label nodes as “violators” if the sum of these edge strengths exceeds a Dunbar-inspired bound; and then remove the violator-to-violator edges. We run our algorithm on multiple social networks and show that our Dunbar-inspired bound appears to hold for social networks, but not for nonsocial networks. Our cleaning process classifies 0.04% of the nodes of the Twitter-2010 followers graph as violators, and we find that more than 80% of these violator nodes have Botometer scores of 0.5 or greater. Furthermore, after we remove the roughly 15 million violator-violator edges from the 1.2-billion-edge Twitter-2010 follower graph, 34% of the violator nodes experience a factor-of-two decrease in PageRank. PageRank is a key component of many graph algorithms such as node/edge ranking and graph sparsification. Thus, this artificial inflation would bias algorithmic output, and result in some incorrect decisions based on this output.
Flame detectors provide an important layer of protection for personnel in petrochemical plants, but effective placement can be challenging. A mixed-integer nonlinear programming formulation is proposed for optimal placement of flame detectors while considering non-uniform probabilities of detection failure. We show that this approach allows for the placement of fire detectors using a fixed sensor budget and outperforms models that do not account for imperfect detection. We develop a linear relaxation to the formulation and an efficient solution algorithm that achieves global optimality with reasonable computational effort. We integrate this problem formulation into the Python package, Chama, and demonstrate the effectiveness of this formulation on a small test case and on two real-world case studies using the fire and gas mapping software, Kenexis Effigy.
Knowledge graph embedding (KGE) learns latent vector representations of named entities (i.e., vertices) and relations (i.e., edge labels) of knowledge graphs. Herein, we address two problems in KGE. First, relations may belong to one or multiple categories, such as functional, symmetric, transitive, reflexive, and so forth; thus, relation categories are not exclusive. Some relation categories cause non-trivial challenges for KGE. Second, we found that zero gradients happen frequently in many translation based embedding methods such as TransE and its variations. To solve these problems, we propose i) converting a knowledge graph into a bipartite graph, although we do not physically convert the graph but rather use an equivalent trick; ii) using multiple vector representations for a relation; and iii) using a new hinge loss based on energy ratio(rather than energy gap) that does not cause zero gradients. We show that our method significantly improves the quality of embedding.
Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (e.g., radiation effects) into an existing model is not trivial and may require redevelopment from scratch. Machine Learning (ML) techniques have the potential to automate and significantly speed up the development of compact models. In addition, ML provides a range of modeling options that can be used to develop hierarchies of compact models tailored to specific circuit design stages. In this paper, we explore three such options: (1) table-based interpolation, (2) Generalized Moving Least-Squares, and (3) feedforward Deep Neural Networks, to develop compact models for a p-n junction diode. We evaluate the performance of these "data-driven" compact models by (1) comparing their voltage-current characteristics against laboratory data, and (2) building a bridge rectifier circuit using these devices, predicting the circuit's behavior using SPICE-like circuit simulations, and then comparing these predictions against laboratory measurements of the same circuit.