Analysis and Understanding of Drawings using Deep Learning and Graphs
Abstract not provided.
97 MATHEMATICS AND COMPUTING↗
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Results for “Mathematical Computing”
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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Nonlinear Optimization and the Modeling of Energy Systems [Slides]
Energy delivery systems are critical for the function of modern society. (Up to) continental-scale engineered systems move energy from source points to consumers. These systems are increasingly complex and interconnected.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Machine Learning meets Algebraic Combinatorics: A Suite of Benchmark Datasets to Accelerate AI for Mathematics Research
The use of benchmark datasets has become an important engine of progress in machine learning (ML) over the past 15 years. Recently there has been growing interest in utilizing machine learning to drive advances in research-level mathematics. However, off-the-shelf solutions often fail to deliver the types of insights required by mathematicians. This suggests the need for new ML methods specifically designed with mathematics in mind. The question then is: what benchmarks should the community use to evaluate these? On the one hand, toy problems such as learning the multiplicative structure of small finite groups have become popular in the mechanistic interpretability community whose perspective on explainability aligns well with the needs of mathematicians. While toy datasets are a useful benchmark for initial work, they lack the scale, complexity, and sophistication of many of the principal objects of study in modern mathematics. To address this, we introduce a new collection of benchmark datasets, Algebraic Combinatorics Benchmarks (ACBench), representing either classic or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. After describing the datasets, we discuss the challenges involved in constructing “good” mathematics benchmarks, describe baseline model performance, and discuss some of the insights these datasets can provide that may be of interest even to those who are not interested in mathematics research itself.
97 MATHEMATICS AND COMPUTING↗
Developing Capabilities in Physical and Computational Sciences
The Physical and Computational Sciences Directorate (PCSD) performs fundamental research in support of the science missions of Offices of Basic Energy Sciences (BES), Advanced Scientific Computing Research (ASCR), High Energy Physics (HEP), Nuclear Physics (NP), and Fusion Energy Sciences (FES), and others within the domains of the chemical, materials, computational sciences, mathematics, and physics. This LDRD project aims to provide funding to develop/demonstrate research capabilities for proposals and publications to support these science missions. Staff will propose small research tasks/projects to be performed under this overall project.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Position Papers for Inverse Methods for Complex Systems under Uncertainty Workshop
The ability to solve inverse problems – inferring unknown parameters, structures, or states of a system from observed data – is essential for advancing scientific discovery and innovation capabilities for the DOE mission. Basic research needs and challenges are particularly acute in emerging areas such as the interactive, data-driven, modeling and simulation of digital twins; decision support for experiments at DOE scientific user facilities; and for other complex systems and workflows. Inverse problems are at the heart of understanding and controlling complex systems due to factors such as observational data with varying modalities and fidelities, inherent uncertainties in physical measurements and numerical models, and the computational demands of rapid and high-fidelity simulations. The convergence of recent scientific computing trends – scientific machine learning, artificial intelligence, and computing advances such as exascale computing – is creating unprecedented opportunities. These advancements offer the potential to revolutionize how we approach inverse problems to extract actionable insights with the required level of accuracy and computational efficiency. This workshop and the Call for Position Papers are vital steps in bringing together experts to collectively explore and identify the new computational and mathematical directions needed in inverse methods for complex systems under uncertainty.
97 MATHEMATICS AND COMPUTING↗
HyLiPoD: Parallel Particle Advection via a Hybrid of Lifeline Scheduling and Parallelization-Over-Data
Performance characteristics of parallel particle advection algorithms can vary greatly based on workload.With this short paper, we build a new algorithm based on results from a previous bake-off study which evaluated the performance of four algorithms on a variety of workloads. Our algorithm, called HyLiPoD, is a ''meta-algorithm,'' i.e., it considers the desired workload to choose from existing algorithms to maximize performance. To demonstrate HyliPoD's benefit, we analyze results from 162 tests including concurrencies of up to 8192 cores, meshes as large as 34 billion cells, and particle counts as large as 300 million. Our findings demonstrate that HyLiPoD's adaptive approach allows it to match the best performance of existing algorithms across diverse workloads.
high performance computing↗
Developing a Vorticity-Velocity-Based Off-Body Solver to Perform Multifidelity Simulations of Wind Farms
Wind power has become a key player in satisfying the global energy needs. With increased market penetration, unanticipated unsteady loading induced failures, installation related reductions in power generation, and significant maintenance costs have underscored the need to predict the unsteady fluid-structure interactions related to turbine layout and off-design wind conditions. Contemporary turbine design tools are incapable of accounting for such loadings. As a result, researchers have started utilizing high-Performance-Computing (HPC) based Computational Fluid Dynamics (CFD) solvers, such as the U.S. Department of Energy sponsored ExaWind software package, to investigate these phenomena. Unfortunately, such HPC tools are computationally expensive for routine industrial use, often because of the sheer number of cells required to resolve the wake flowfield. This paper describes a preliminary effort to address this issue by developing a vorticity-velocity based CFD off-body solver, VorTran-M2-AMReX, that integrates directly with DOE's ExaWind wind turbine analysis system to perform accurate and reliable simulations of wind turbine/farm at a lower computational cost than ExaWind alone. This article summarizes work undertaken to date concerning the assembly of the proposed analysis tool, and provides preliminary validation and verification of the VorTran-M2-AMReX off-body solver.
adaptive mesh refinement↗
Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities
Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 10 6 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.
79 ASTRONOMY AND ASTROPHYSICS↗
Logarithm-Based Methods for Interpolating Quaternion Time Series
In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C 2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive interpolation, i.e., interpolating an arbitrary quaternion time series. To accomplish this, we provide a robust method of taking the logarithm of a quaternion time series such that the variables $\theta$ and $\hat{n}$ have a consistent and continuous axis-angle representation. We then demonstrate how logarithmic quaternion interpolation out-performs Renormalized Quaternion Bezier interpolation by orders of magnitude.
97 MATHEMATICS AND COMPUTING↗
Dynamic Optimal Dispatch of Energy Systems with Intermittent Renewables and Damage Model
With the increasing penetration of intermittent renewable energy sources into the grid, there is a growing need for process systems-based strategies that integrate dispatchable and variable energy systems for supplying the demand while maintaining grid reliability. The proposed framework corresponds to a dynamic mixed-integer linear programming optimization approach that integrates coal-fired and natural gas-fired power plants, NaS batteries for energy storage, and solar/wind energy to supply the demand. This optimization approach considers an economic goal and constraints to provide power balance while maintaining the overall damage of the natural gas combined cycle (NGCC) power plant drum under a maximum stress as well as avoiding the overheating of the NGCC superheater and reheater. Renewable curtailment levels are also retained at minimum levels. Case studies are analyzed considering different loads and renewable penetration levels. The results show that the demand was met for all cases. Grid flexibility was mostly provided by the NGCC, while the batteries were used sparingly. In addition, considering a CO 2 equivalent analysis, the environmental performance was intrinsically connected to grid flexibility and the level of renewable penetration. Stress analysis results reinforced the necessity for an equipment health-related constraint.
97 MATHEMATICS AND COMPUTING↗
A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem
The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. Finally, we numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular meshes, where the method coincides with the $\mathbb{P}_1$ – $\mathbb{P}_0$ Scott-Vogelius scheme, and on square meshes, which are situations that are well-known to be unstable.
97 MATHEMATICS AND COMPUTING↗
Spectral convergence of the stochastic galerkin approximation to the boltzmann equation with multiple scales and large random perturbation in the collision kernel
In a 2018 article, spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation with random inputs in the initial data and collision kernel for hard potentials and Maxwellian molecules under Grad's angular cutoff were established using the hypocoercive properties of the collisional kinetic model. One assumption for the random perturbation of the collision kernel is that the perturbation is in the order of the Knudsen number, which can be very small in the fluid dynamical regime. In this article, we remove this smallness assumption, and establish the same results but now for random perturbations of the collision kernel that can be of order one. The new analysis relies on the establishment of a spectral gap for the numerical collision operator.
97 MATHEMATICS AND COMPUTING↗
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↗
QP Statistics Spotlight: Practical versus Statistical Priorities
Randomization during data collection in a designed experiment is an effective strategy for reducing system bias and ensuring independent observations1, but at what cost should it be fully implemented? We recently encountered a scenario that highlights an important aspect of collaboration2 between statisticians, scientists and engineers – the idea of compromise for the sake of achieving wins for all team members. In a multi-million-dollar experiment with a fixed amount of time on the test equipment, each experimental run involved resetting the input values and then waiting for the continuous process to reach a new equilibrium. For example, the temperature of the furnace could be reset, but it takes some time for the test chamber to reach the new temperature and rest at that temperature for a while until all components in the chamber settle at that new setting. Similarly, a critical gas flow component also required a settling period before data could be collected that would be representative of that input setting value. In all, the experiment involved 5 factors, where 4 of the 5 were time-consuming and costly to adjust, with the duration of time needed to reach new equilibrium being dependent on how far the previous setting was from the new one for the combination of these 4 factors. For example, changing from 150° to 200° would reach equilibrium faster than changing from 100° to 200°.
97 MATHEMATICS AND COMPUTING↗
Preparing an Incompressible-Flow Fluid Dynamics Code for Exascale-Class Wind Energy Simulations: Preprint
The US Department of Energy has identified Exascale-Class wind farm simulation tools as critical to wind energy scientific discovery. A primary objective of the Exawind project is to build high-performance, predictive Computational Fluid Dynamics tools that satisfy these modeling needs. GPU accelerators will serve as the computational thoroughbreds of next generation, Exascale-Class, platforms. Here, we report on our efforts for preparing the Exawind unstructured mesh solver, Nalu-Wind, for Exascale-Class machines. For computing at this scale, a simple port of the incompressible-flow algorithms to GPUs is not sufficient. One needs novel algorithms that are application aware, memory efficient, and optimized for latest generation GPU devices to get high-performance. The result of our efforts are unstructured mesh simulations of wind turbines that use 1/6 the compute resources of Summit supercomputer at Oak Ridge National Lab. In particular, we demonstrate a first-of-its-kind, simulation using Algebraic Multigrid solvers on over 4000 GPUs.
algebraic multigrid↗
Transforming Energy through Computational Excellence. Exascale Computing: Combustion; Deep Learning for Presumed Probability Density Function (PDF) Models
NREL researchers use advanced machine learning techniques to define improved methods using deep learning models to resolve reacting flows in turbulent combustion flows, reducing the computational burden, increasing computational speed, and improving accuracy. These advancements reduce cost and improve fidelity of rapid-turn-around engineering calculations.
combustion↗
Enabling Combustion Science Simulations for Future Exascale Machines
Reacting flow simulations for combustion applications require extensive computing capabilities. Leveraging the AMReX library, the Pele suite of combustion simulation tools targets the largest supercomputers available and future exascale machines. We introduce PeleC, the compressible solver in the Pele suite, and detail its capabilities, including complex geometry representation, chemistry integration, and discretization. We present a comparison of development efforts using both OpenACC and AMReX's C++ performance portability framework for execution on multiple GPU architectures. We discuss relevant details that have allowed PeleC to achieve high performance and scalability. PeleC's performance characteristics are measured through relevant simulations on multiple supercomputers. The success of PeleC's design for exascale is exhibited through demonstration of a 160 billion cell simulation and weak scaling onto 100\% of Summit, an NVIDIA-based GPU supercomputer at Oak Ridge National Laboratory. Our results provide confidence that PeleC will enable future combustion science simulations with unprecedented fidelity.
combustion↗
Improving the Performance of DGEMM with MoA and Cache-Blocking: Preprint
The goal of this paper is to demonstrate performance enhancements of the high performance dense linear algebra matrix-matrix multiply DGEMM kernel, widely implemented by vendors in the basic linear algebra subroutine BLAS library. The mathematics of arrays (MoA) paradigm due to Mullin (1988) results in contiguous memory accesses in combination with Church-Rosser complete language constructs optimized for target processor architectures [3]. Our performance studies demonstrate that the MoA implementation of DGEMM combined with optimal cache-blocking strategies results in at least a 25% performance gain on both Intel Xeon Skylake and IBM Power-9 processors over the vendor supplied Intel MKL and IBM ESSL basic linear algebra libraries. Results are presented for the NREL Eagle and ORNL Summit supercomputers.
cache-blocking↗