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In data science applications, there are often many models that fit the data well. This phenomenon was called the Rashomon Effect by Leo Breiman. The set of good models is called the Rashomon Set, and the goal of this project is to locate, store, and study the Rashomon sets for classes of interpretable models, including decision trees and generalized additive models.
This paper reports on experiences gained and practices adopted when using the latest features of OpenMP to port a variety of HPC applications and mini-apps based on different computational motifs (BerkeleyGW, WDMApp/XGC, GAMESS, GESTS, and GridMini) to accelerator-based, leadership-class, high-performance supercomputer systems at the Department of Energy. As recent enhancements to OpenMP become available in implementations, there is a need to share the results of experimentation with them in order to better understand their behavior in practice, to identify pitfalls, and to learn how they can be effectively deployed in scientific codes. Additionally, we identify best practices from these experiences that we can share with the rest of the OpenMP community.
The application is discussed of illuminographic camera techniques to the measurement of radiative form factors for satellite modeling applications. The equation for the illuminographic mirror is derived, and the advantages of the method are discussed. Proximity error for the illuminographic mirror is defined, and estimates of this error as a function of the scale factor of the model are given, together with a method for halving this error. Designs for illuminographic mirrors are presented: the first provides a further threefold reduction in proximity error; the second permits the estimation of thermal radiation transfer coefficients to interior regions of otherwise inaccessible volumes. Finally, reflex Polaroid camera techniques appropriate to the relatively small size of the illuminographic mirror are described.
The purpose of this environmental calculation file (ECF) is to document predictions of flow and hydraulic head on the Central Plateau of the Hanford Site using the Plateau-to-River (P2R) Model (CP-57037, Model Package Report for the Plateau-to-River Model: Version 9.1). This calculation documents the simulation of the groundwater for the parent model domain of the P2R Model as a basis for use in other applications of the P2R Model. This application is unique from the standpoint that it will simulate all ensemble member models of the P2R Model whereas other applications may only utilize specific ensemble members. These simulations provide results that can be used in the process of selecting an appropriate subset of ensemble members for other applications.
In the standard picture of fully developed turbulence, highly intermittent hydrodynamic fields are nonlinearly coupled across scales, where local energy cascades from large scales into dissipative vortices and large density gradients. Microscopically, however, constituent fluid molecules are in constant thermal (Brownian) motion, but the role of molecular fluctuations in large-scale turbulence is largely unknown, and with rare exceptions, it has historically been considered irrelevant at scales larger than the molecular mean free path. Recent theoretical and computational investigations have shown that molecular fluctuations can impact energy cascade at Kolmogorov length scales. Here, we show that molecular fluctuations not only modify energy spectrum at wavelengths larger than the Kolmogorov length in compressible turbulence, but also significantly inhibit spatio-temporal intermittency across the entire dissipation range. Using large-scale direct numerical simulations of computational fluctuating hydrodynamics, we demonstrate that the extreme intermittency characteristic of turbulence models is replaced by nearly Gaussian statistics in the dissipation range. These results demonstrate that the compressible Navier–Stokes equations should be augmented with molecular fluctuations to accurately predict turbulence statistics across the dissipation range. Our findings have significant consequences for turbulence modelling in applications such as astrophysics, reactive flows and hypersonic aerodynamics, where dissipation-range turbulence is approximated by closure models.
Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024
Cosmic rays interact with mesoscale configurations of the interplanetary magnetic field. A technique is presented for calculating such configurations in the inner solar system, which are due to streams and source conditions near the sun, and maps of magnetic field are constructed for some plausible stream and source conditions. One effect of these mesoscale configurations on galactic cosmic rays is shown to be an out-of-the-ecliptic gradient drift sufficient to explain Forbush decreases. The effects on solar energetic particles include small polar drifts due to the field gradients and a possibly large modification of the time-intensity profiles and anisotropy characteristics due to the formation of mirror configurations in space. If a diffusion model is applicable to solar particles, the true diffusion coefficient will be masked by the effects of streams. A conceptual model which incorporates these ideas and those of several other models is presented.
Two applications of mathematical modeling to aerodynamic problems are cussed. The first application is an investigation of the capacity of a nonlinear aerodynamic mathematical model to describe the aerodynamic reactions on an airfoil with a deflecting flap in transonic flow. Flow field computational methods are used to evaluate the nonlinear, unsteady aerodynamic data in terms of characteristic motions called for by the model. Histories of unconstrained motions of the flap are generated from the flap equations of motion, with the aerodynamic reactions specified by the mathematical model. In the second application wing rock is investigated. The most recent model accommodates experimental results wing rock by admitting the existence of aerodynamic hysteresis in the variation of the steady state rolling moment coefficient with roll angle is described.
The structure and composition of a new, emerging software application, which models and analyzes space exploration scenario options for feasibility based on technology development projections is presented. The software application consists of four main components: a scenario generator for designing and inputting scenario options and constraints; a processor which performs algorithmic coupling and options analyses of mission activity requirements and technology capabilities; a results display which graphically and textually shows coupling and options analysis results; and a data/knowledge base which contains information on a variety of mission activities and (power and propulsion) technology system capabilities. The general long-range study process used by NASA to support recent studies is briefly introduced to provide the primary basis for comparison for discussing the potential advantages to be gained from developing and applying this king of application. A hypothetical example of a scenario option to facilitate the best conceptual understanding of what the application is, how it works, or the operating methodology, and when it might be applied is presented.
This structure and composition of a new, emerging software application, which models and analyzes space exploration scenario options for feasibility based on technology development projections is presented. The software application consists of four main components: a scenario generator for designing and inputting scenario options and constraints; a processor which performs algorithmic coupling and options analyses of mission activity requirements and technology capabilities; a results display which graphically and textually shows coupling and options analysis results; and a data/knowledge base which contains information on a variety of mission activities and (power and propulsion) technology system capabilities. The general long-range study process used by NASA to support recent studies is briefly introduced to provide the primary basis for comparison for discussing the potential advantages to be gained from developing and applying this kind of application. A hypothetical example of a scenario option to facilitate the best conceptual understanding of what the application is, how it works, or the operating methodology, and when it might be applied is presented.
Over the last decade several new models for the sporadic interplanetary meteoroid flux have been developed. These include the Meteoroid Engineering Model (MEM), the Divine-Staubach model and the Interplanetary Meteoroid Engineering Model (IMEM). They typically cover mass ranges from 10-12 g (or lower) to 1 g and are applicable for model specific sun distance ranges between 0.2 A.U. and 10 A.U. Near 1 A.U. averaged fluxes (over direction and velocities) for all these models are tuned to the well established interplanetary model by Gr?n et. al. However, in many respects these models differ considerably. Examples are the velocity and directional distributions and the assumed meteoroid sources. In this paper flux predictions by the various models to Earth orbiting spacecraft are compared. Main differences are presented and analysed. The persisting differences even for near Earth space can be seen as surprising in view of the numerous ground based (optical, radar) and in-situ (captured IDPs, in-situ detectors and analysis of retrieved hardware) measurements and simulations. Remaining uncertainties and potential additional studies to overcome the existing model discrepancies are discussed.
This article presents the application of a recently developed statistical regression method to the controlled instrument calibration problem. The statistical method of Model Robust Regression (MRR), developed by Mays, Birch, and Starnes, is shown to improve instrument calibration by reducing the reliance of the calibration on a predetermined parametric (e.g. polynomial, exponential, logarithmic) model. This is accomplished by allowing fits from the predetermined parametric model to be augmented by a certain portion of a fit to the residuals from the initial regression using a nonparametric (locally parametric) regression technique. The method is demonstrated for the absolute scale calibration of silicon-based pressure transducers.
This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second.
Semantic metadata models such as Brick, RealEstateCore, Project Haystack, and BOT promise to simplify and lower the cost of developing software for smart buildings, enabling the widespread deployment of energy efficiency applications. However, creating these models remains a challenge. Despite recent advances in creating models from existing digital representations like point labels and architectural models, there is still no feedback mechanism to ensure that the human input to these methods results in a model that can actually support the desired software. In this paper, we introduce the notion of semantic sufficiency, a practical principle for semantic metadata model creation that asserts that a model is "finished" when it contains the metadata necessary to support a given set of applications. To support semantic sufficiency, we design a standard representation for capturing application metadata requirements and a templating system for generating common metadata model components with limited user input. We then construct an iterative model creation workflow that integrates metadata requirements to direct the model creation effort, and present several novel optimizations that increase the model utility while minimizing the effort by a human operator. These new abstractions for model creation and validation lower model development costs and ensure the utility of the resulting model, thus facilitating the adoption of intelligent building applications.
An anisotropic creep model is formulated for metallic composites with strong fibers and low to moderate fiber volume percent (less than 40 percent). The idealization admits no creep in the local fiber direction and assumes equal creep strength in longitudinal and transverse shear. Identification of the matrix behavior with that of the isotropic limit of the theory permits characterization of the composite through uniaxial creep tests on the matrix material. Constant and step-wise creep tests are required as a data base. The model provides an upper bound on the transverse creep strength of a composite having strong fibers embedded in a particular matrix material. Comparison of the measured transverse strength with the upper bound gives an assessment of the integrity of the composite. Application is made to a Kanthal composite, a model high-temperature composite system. Predictions are made of the creep response of fiber reinforced Kanthal tubes under interior pressure.
This paper will address current NASA GRC research efforts utilizing the NASA Multiscale Analysis Tool (NASMAT) which address technical gaps in three of the Vision 2040 key discipline areas. NASMAT is a versatile platform for performing computationally efficient multiscale analyses of heterogeneous materials and is available free through the NASA software catalog. It offers the user flexibility to define an arbitrary number of length scales (levels) where a variety of micromechanics theories can be implemented at each level. Micromechanics theories can be selected to balance accuracy and computational efficiency and range from analytical (Mori-Tanaka) to several semi-analytical (method of cells) formulations. The resulting anisotropic, evolving nonlinear, thermomechanical constitutive model can also be coupled with external software and used to perform multiscale analyses of more complex structures. A recent application to model a complex, three-dimensional woven composite, with a particular emphasis placed on multiscale measurements utilized to enhance the quality of the multiscale analysis will be discussed. Since typical NASMAT analyses can be completed on the order of seconds to minutes, a second example will demonstrate the ability to generate large quantities of data useful for sensitivity analysis, uncertainty quantification, or machine learning applications. Current progress on implementing NASMAT within a multiscale digital thread/digital twin framework will also be addressed. These examples will demonstrate that NASMAT is an enabling platform for achieving the goals in Vision 2040.
Data relating to hydrologic and water resource systems and subsystems management are reported. Systems models, user application, and remote sensing technology are covered. Parameters governing water resources include evaportranspiration, vegetation, precipitation, streams and estuaries, reservoirs and lakes, and unsaturate and saturated soil zones.
A fault tolerant processor (FTP) plays a key role in many high performance, safety-critical control system applications. Realistic modeling of an FTP is crucial to gaining a high degree of confidence in the reliability and safety analysis of such a system. While fidelity is clearly a major consideration, a practical model must also be kept to a moderate size to allow its incorporation into the overall system model. This paper presents a systematic reduction technique that starts from a complex, detailed model of a triple, redundant FTP and produces a low order approximation of very high accuracy. The existence of two distinct time scales represents the key to the success of the technique. No eigenvalue solution or coordinate transformation are needed. The reduced model captures all the important features of the detailed model, is amenable to an analytical solution and provides insight into the reconfiguration behavior of an FTP.