Model-Assisted Pattern Search

Computer simulations of complex physical phenomena are used in many contexts, including that of engineering design. Increasingly scientists and engineers have also been trying to optimize problems defined by such simulations (e.g. to determine design parameters for a physical product). However, these problems often have several features that hinder the use of standard optimization techniques. The lack of derivative information and numerical error induced by the simulation can cause problems for derivative-based optimization methods. Likewise, extreme computational expense can make the use of direct search methods problematic. The Model-Assisted Pattern Search (MAPS) algorithm, which is the subject of this research, attempts to address the issue. While maintaining a pattern search framework, MAPS makes use of easily constructed surrogates to the objective function in order to speed the optimization process. Numerical results for MAPS and several other algorithms are presented here for a variety of different objective functions

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part II: application to partial differential equations

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application

Graph Neural Networks and Applied Linear Algebra

Sparse matrix computations are ubiquitous in scientific computing. With the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NN). Unfortunately, multi-layer perceptron (MLP) neural networks are typically not natural for either graph or sparse matrix computations. The issue lies with the fact that MLPs require fixed-sized inputs while scientific applications generally generate sparse matrices with arbitrary dimensions and a wide range of nonzero patterns (or matrix graph vertex interconnections). While convolutional NNs could possibly address matrix graphs where all vertices have the same number of nearest neighbors, a more general approach is needed for arbitrary sparse matrices, e.g. arising from discretized partial differential equations on unstructured meshes. Graph neural networks (GNNs) are one approach suitable to sparse matrices. GNNs define aggregation functions (e.g., summations) that operate on variable size input data to produce data of a fixed output size so that MLPs can be applied. The goal of this paper is to provide an introduction to GNNs for a numerical linear algebra audience. Concrete examples are provided to illustrate how many common linear algebra tasks can be accomplished using GNNs. We focus on iterative methods that employ computational kernels such as matrix-vector products, interpolation, relaxation methods, and strength-of-connection measures. Our GNN examples include cases where parameters are determined a-priori as well as cases where parameters must be learned. The intent with this article is to help computational scientists understand how GNNs can be used to adapt machine learning concepts to computational tasks associated with sparse matrices. It is hoped that this understanding will stimulate data-driven extensions of classical sparse linear algebra tasks

Model-assisted pattern search methods for optimizing expensive computer simulations

The design and analysis of computer experiments (DACE) usually envisions performing a single experiment, then replacing the expensive simulation with an approximation. When the simulation is a nonlinear function to be optimized, DACE may be inefficient, and sequential strategies that synthesize ideas from DACE and numerical optimization may be warranted. We consider several such strategies within a unified framework in which sequential approximations constructed by kriging are used to accelerate a conventional direct search method. Computational experiments reveal that hybrid strategies outperform both DACE and traditional pattern search.

SANDIA REPORT Simulation Information Regarding Sandia National Laboratories' Trinity Capability Improvement Metric Simulation Information Regarding Sandia National Laboratories' Trinity Capability Improvement Metric

Abstract Sandia National Laboratories, Los Alamos National Laboratory, and Lawrence Livermore National Laboratory each selected a representative simulation code to be used as a performance benchmark for the Trinity Capability Improvement Metric. Sandia selected SIERRA Low Mach Module: Nalu, which is a fluid dynamics code that solves many variable-density, acoustically incompressible problems of interest spanning from laminar to turbulent flow regimes, since it is fairly representative of implicit codes that have been developed under ASC. The simulations for this metric were performed on the Cielo Cray XE6 platform during dedicated application time and the chosen case utilized 131,072 Cielo cores to perform a canonical turbulent open jet simulation within an approximately 9-billion-elementunstructured-hexahedral computational mesh. This report will document some of the results from these simulations as well as provide instructions to perform these simulations for comparison

A Global Meta-analysis Of The Relative Extent Of Intraspecific Trait Variation In Plant Communities

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Recent studies have shown that accounting for intraspecific trait variation (ITV) may better address major questions in community ecology. However, a general picture of the relative extent of ITV compared to interspecific trait variation in plant communities is still missing. Here, we conducted a meta-analysis of the relative extent of ITV within and among plant communities worldwide, using a data set encompassing 629 communities (plots) and 36 functional traits. Overall, ITV accounted for 25% of the total trait variation within communities and 32% of the total trait variation among communities on average. The relative extent of ITV tended to be greater for whole-plant (e.g. plant height) vs. organ-level traits and for leaf chemical (e.g. leaf N and P concentration) vs. leaf morphological (e.g. leaf area and thickness) traits. The relative amount of ITV decreased with increasing species richness and spatial extent, but did not vary with plant growth form or climate. These results highlight global patterns in the relative importance of ITV in plant communities, providing practical guidelines for when researchers should include ITV in trait-based community and ecosystem studies.181214061419National Science Foundation Graduate Research Fellowship [DGE-1247399]NSF [DEB-03089]Marie Curie International Outgoing Fellowship within the 7th European Community Framework Program (DiversiTraits project) [221060]European Research Council (ERC) Starting Grant Project 'Ecophysiological and biophysical constraints on domestication in crop plants' [ERC-StG-2014-639706-CONSTRAINTS]European Research Council under the 7th European Community Framework Program FP7 [281422]Chilean Fondo Nacional de Desarrollo Cientifico y Tecnologico (FONDECYT) project [1120171]Czech Science Foundation [P505/12/1296]Discovery Grants from the Natural Science and Engineering Research Council of CanadaSwiss National Science Foundation [PA00P3_136474, PZ00P3_148261]Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)JSPS as a Postdoctoral Fellow for Research AbroadFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)New Zealand Ministry of Business, Innovation and Employment core fundingMinistry for the Environmentproject Postdoc USB [CZ.1.07/2.3.00/30.0006]European Social FundCzech State BudgetPontifical Catholic University of Ecuadorgovernment of EcuadorAndrew W. Mellon FoundationSmithsonian Tropical Research InstituteUniversity of Aarhus of DenmarkCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CAPES [BEX 7913/13-3]CAPES [1454013]CNPq [479083/2008-8, 141451/2011-4, 306573/2009-1, 303534/2012-5, 303714/2010-7

A global Fine-Root Ecology Database to address below-ground challenges in plant ecology

Variation and tradeoffs within and among plant traits are increasingly being harnessed by empiricists and modelers to understand and predict ecosystem processes under changing environmental conditions. While fine roots play an important role in ecosystem functioning, fine-root traits are underrepresented in global trait databases. This has hindered efforts to analyze fine-root trait variation and link it with plant function and environmental conditions at a global scale. This Viewpoint addresses the need for a centralized fine-root trait database, and introduces the Fine-Root Ecology Database (FRED, http://roots.ornl.gov) which so far includes > 70 000 observations encompassing a broad range of root traits and also includes associated environmental data. FRED represents a critical step toward improving our understanding of below-ground plant ecology. For example, FRED facilitates the quantification of variation in fine-root traits across root orders, species, biomes, and environmental gradients while also providing a platform for assessments of covariation among root, leaf, and wood traits, the role of fine roots in ecosystem functioning, and the representation of fine roots in terrestrial biosphere models. Continued input of observations into FRED to fill gaps in trait coverage will improve our understanding of changes in fine-root traits across space and time