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Efficient data structures for model-free data-driven computational mechanics

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2021年 382卷 113855-113855页

作者： Eggersmann, Robert Stainier, Laurent Ortiz, Michael Reese, Stefanie Rhein Westfal TH Aachen Inst Appl Mech Mies van der Rohe Str 1 D-52074 Aachen Germany Ecole Cent Nantes Inst Civil & Mech Engn 1 Rue Noe F-44321 Nantes France CALTECH Div Engn & Appl Sci Pasadena CA 91125 USA Rhein Friedrich Wilhelm Univ Bonn Hausdorff Ctr Math Endenicher Allee 62 D-53115 Bonn Germany

The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material points onto their closest states in the material data set. In this study, we compare and develop several possible data structures for solving the nearest-neighbor problem. We show that approximate nearest-neighbor (ANN) algorithms can accelerate material data searches by several orders of magnitude relative to exact searching algorithms. The approximations are suggested by-and adapted to-the structure of the data-driven iterative solver and result in no significant loss of solution accuracy. We assess the performance of the ANN algorithm with respect to material data set size with the aid of a 3D elasticity test case. We show that computations on a single processor with up to one billion material data points are feasible within a few seconds execution time with a speed up of more than 106 with respect to exact k-d trees. (C) 2021 Published by ElsevierB.V.

关键词： data-driven computing Solid mechanics Nearest neighbor problem Approximate nearest-neighbor search data structures data science

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Model-free data-driven computational mechanics enhanced by tensor voting

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2021年 373卷 113499-113499页

The data-driven computing paradigm initially introduced by Kirchdoerfer and Ortiz (2016) is extended by incorporating locally linear tangent spaces into the data set. These tangent spaces are constructed by means of the tensor voting method introduced by Mordohai and Medioni (2010) which improves the learning of the underlying structure of a data set. Tensor voting is an instance-based machine learning technique which accumulates votes from the nearest neighbors to build up second-order tensors encoding tangents and normals to the underlying data structure. The here proposed second-order data-driven paradigm is a plug-in method for distance-minimizing as well as entropy-maximizing data-driven schemes. Like its predecessor (Kirchdoerfer and Ortiz, 2016), the resulting method aims to minimize a suitably defined free energy over phase space subject to compatibility and equilibrium constraints. The method's implementation is straightforward and numerically efficient since the data structure analysis is performed in an offline step. Selected numerical examples are presented that establish the higher-order convergence properties of the data-driven solvers enhanced by tensor voting for ideal and noisy data sets. (C) 2020 Elsevier B.V. All rights reserved.

关键词： data-driven computing Tensor voting Second-order method data science

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Finite element solver for data-driven finite strain elasticity

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2021年 379卷 113756-113756页

作者： Platzer, Auriane Leygue, Adrien Stainier, Laurent Ortiz, Michael Univ Nantes Ecole Cent Nantes CNRS Inst Rech Genie Civil & Mecan GeMUMR 6183 1 Rue Noe F-44321 Nantes France CALTECH Grad Aerosp Labs 1200 E Calif Blvd Pasadena CA 91125 USA

A nominal finite element solver is proposed for data-driven finite strain elasticity. It bypasses the need for a constitutive model by considering a database of deformation gradient/first Piola-Kirchhoff stress tensors pairs. The boundary value problem is reformulated as the constrained minimization problem of the distance between (i) the mechanical states, i.e. strain-stress, in the body and (ii) the material states coming from the database. The corresponding constraints are of two types: kinematical, i.e. displacement-strain relation, and mechanical, i.e. conservation linear and angular momenta. The solver uses alternated minimization: the material states are determined from a local search in the database using an efficient tree-based nearest neighbor search algorithm, and the mechanical states result from a standard constrained minimization addressed with an augmented Lagrangian approach. The performance of the solver is demonstrated by means of 2D sanity check examples: the data-driven solution converges to the classical finite element solution when the material database increasingly approximates the constitutive model. In addition, we demonstrate that the balance of angular momentum, which was classically not taken into account in previous data-driven studies, must be enforced as a constraint to ensure the convergence of the method. (C) 2021 Elsevier B.V. All rights reserved.

关键词： data-driven computing Finite strain Model-free Optimization methods data science

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data-driven Approach to Inversion Analysis of Three-Dimensional Inner Soil Structure via Wave Propagation Analysis 20th

Data-Driven Approach to Inversion Analysis of Three-Dimensio...

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20th Annual International Conference on Computational Science (ICCS)

作者： Yamaguchi, Takuma Ichimura, Tsuyoshi Fujita, Kohei Hori, Muneo Wijerathne, Lalith Ueda, Naonori Univ Tokyo Earthquake Res Inst Bunkyo Ku Tokyo Japan Univ Tokyo Dept Civil Engn Bunkyo Ku Tokyo Japan Japan Agcy Marine Earth Sci & Technol Res Inst Value Added Informat Generat Yokohama Kanagawa Japan RIKEN Ctr Adv Intelligence Project Tokyo Japan

ISBN: (纸本)9783030504205;9783030504199

Various approaches based on both computational science and data science/machine learning have been proposed with the development of observation systems and network technologies. Computation cost associated with computational science can be reduced by introducing the methods based on data science/machine learning. In the present paper, we focus on a method to estimate inner soil structure via wave propagation analysis. It is regarded as one of the parameter optimization approaches using observation data on the surface. This application is in great demand to ensure better reliability in numerical simulations. Typical optimization requires many forward analyses;thus, massive computation cost is required. We propose an approach to substitute evaluation using neural networks for most cases of forward analyses and to reduce the number of forward analyses. Forward analyses in the proposed method are used for producing the training data for a neural network;thereby they can be computed independently, and the actual elapsed time can be reduced by using a large-scale supercomputer. We demonstrated that the inner soil structure was estimated with the sufficient accuracy for practical damage evaluation. We also confirmed that the proposed method achieved estimating parameters within a shorter time-frame compared to a typical approach based on simulated annealing.

关键词： data-driven computing Finite element analysis Conjugate gradient method GPU computing

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Model-Free data-driven inelasticity

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2019年第Jun.15期350卷 81-99页

作者： Eggersmann, R. Kirchdoerfer, T. Reese, S. Stainier, L. Ortiz, M. Rhein Westfal TH Aachen Inst Appl Mech Mies van der Rohe Str 1 D-52074 Aachen Germany CALTECH Div Engn & Appl Sci 1200 E Calif Blvd Pasadena CA 91125 USA Ecole Cent Nantes UMR 6183 CNRS ECN UN Inst Civil & Mech Engn 1 Rue Noe F-44321 Nantes France

We extend the data-driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from data-driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for the evolving material data sets: (i) materials with memory, i. e., conditioning the material data set to the past history of deformation;(ii) differential materials, i. e., conditioning the material data set to short histories of stress and strain;and (iii) history variables, i. e., conditioning the material data set to ad hoc variables encoding partial information about the history of stress and strain. We also consider combinations of the three paradigms thereof and investigate their ability to represent the evolving data sets of different classes of inelastic materials, including viscoelasticity, viscoplasticity and plasticity. We present selected numerical examples that demonstrate the range and scope of data-driven inelasticity and the numerical performance of implementations thereof. (C) 2019 Elsevier B.V. All rights reserved.

关键词： data-driven computing Inelasticity Viscoelasticity Plasticity

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Mixed-integer programming formulation of a data-driven solver in computational elasticity

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OPTIMIZATION LETTERS 2019年第7期13卷 1505-1514页

作者： Kanno, Yoshihiro Univ Tokyo Math & Informat Ctr Hongo 7-3-1 Tokyo 1138656 Japan

This paper presents a mixed-integer quadratic programming formulation of an existing data-driven approach to computational elasticity. This formulation is suitable for application of a standard mixed-integer programming solver, which finds a global optimal solution. Therefore, the results obtained by the presented method can be used as benchmark instances for any other algorithm. Preliminary numerical experiments are performed to compare quality of solutions obtained by the proposed method and a heuristic conventionally used in the data-driven computational mechanics.

关键词： Global optimization Mixed-integer programming Exact solution method data-driven computing Model-free computational mechanics

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Simple heuristic for data-driven computational elasticity with material data involving noise and outliers: a local robust regression approach

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2018年第3期35卷 1085-1101页

作者： Kanno, Yoshihiro Univ Tokyo Math & Informat Ctr Hongo 7-3-1 Tokyo 1138656 Japan

data-driven computing in applied mechanics utilizes the material data set directly, and hence is free from errors and uncertainties stemming from the conventional material modeling. For data-driven computing in elasticity, this paper presents a simple heuristic that is robust against noise and outliers in a data set. For each structural element, we extract the material property from some nearest data points. Using the nearest neighbors reduces the influence of noise, compared with the existing method that uses a single data point. Also, the robust regression is adopted to reduce the influence of outliers. Numerical experiments on the static equilibrium analysis of trusses are performed to illustrate that the proposed method is robust against the presence of noise and outliers.

关键词： data-driven computing Model-free computational mechanics Outlier Local regression Robust statistics

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3D waveform oscilloscope implemented on coupled FPGA-GPU embedded system 5

3D waveform oscilloscope implemented on coupled FPGA-GPU emb...

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5th International Conference on Information Science and Control Engineering (ICISCE)

作者： Hu, Nan Zhou, Xuehai Li, Xi Wang, Chao Univ Sci & Technol China Dept Comp Sci Hefei Anhui Peoples R China

ISBN: (纸本)9781538655009

FPGA is widely adopted in computing acceleration. In recent years, the embedded GPU on mobile SoC supports OpenCL development which allows GPU to be used in the general-purpose computing. However, the study of cooperation of FPGA and SoC-based mobile GPU in an embedded system is still lacking. We propose methods of cooperation of the FPGA and GPU, which supports software and hardware task partition and unified development by OpenCL. We build an embedded system the storage oscilloscope which supports 3D waveform display. The performance of algorithms such as string matching, matrix operations, histogram, grayscale stretching, are analyzed on the ARM processor, GPU and FPGA. The results show that the coupled FPGA-GPU embedded system achieves approached performance to the pure FPGA with no more than 15% DSP slice resource.

关键词： reconfigurable computing data-driven computing GPU and FPGA cooperation embedded system ARM GPU FPGA benchmark 3D waveforms

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A constraint-driven approach to food supply chain management

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INDUSTRIAL MANAGEMENT & data SYSTEMS 2017年第9期117卷 2115-2138页

作者： Sitek, Pawel Wikarek, Jaroslaw Nielsen, Peter Kielce Univ Technol Dept Informat Syst Kielce Poland Aalborg Univ Dept Mech & Mfg Engn Aalborg Denmark

Purpose - The purpose of this paper is the need to build a novel approach that would allow flexible modeling and solving of food supply chain management (FSCM) problems. The models developed would use the data (data-driven modeling) as early as possible at the modeling phase, which would lead to a better and more realistic representation of the problems being modeled. Design/methodology/approach - An essential feature of the presented approach is its declarativeness. The use of a declarative approach that additionally includes constraint satisfaction problems and provides an opportunity of fast and easy modeling of constrains different in type and character. Implementation of the proposed approach was performed with the use of an original hybrid method in which constraint logic programming (CLP) and mathematical programming (MP) are integrated and transformation of a model is used as a presolving technique. Findings - The proposed constraint-driven approach has proved to be extremely flexible and efficient. The findings obtained during part of experiments dedicated to efficiency were very interesting. The use of the constraint-driven approach has enabled finding a solution depending on the instance data up to 1,000 times faster than using the MP. Research limitations/implications - Due to the limited use of exact methods for NP-hard problems, the future study should be to integrate the CLP with environments other than the MP. It is also possible, e.g., with metaheuristics like genetic algorithms, ant colony optimization, etc. Practical implications - There is a possibility of using the approach as a basis to build a decision support system for FSCM, simple integration with databases, enterprise resource planning systems, management information systems, etc. Originality/value - The new constraint-driven approach to FSCM has been proposed. The proposed approach is an extension of the hybrid approach. Also, a new decision-making model of distribution and logistics for

关键词： Mathematical programming Decision support Food supply chain management Constraint logic programming Constraint satisfaction problem data-driven computing

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A historical survey of algorithms and hardware architectures for neural-inspired and neuromorphic computing applications

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BIOLOGICALLY INSPIRED COGNITIVE ARCHITECTURES 2017年 19卷 49-64页

作者： James, Conrad D. Aimone, James B. Miner, Nadine E. Vineyard, Craig M. Rothganger, Fredrick H. Carlson, Kristofor D. Mulder, Samuel A. Draelos, Timothy J. Faust, Aleksandra Marinella, Matthew J. Naegle, John H. Plimpton, Steven J. Sandia Natl Labs POB 5800 Albuquerque NM 87185 USA Google X Mountain View CA USA

Biological neural networks continue to inspire new developments in algorithms and microelectronic hardware to solve challenging data processing and classification problems. Here, we survey the history of neural-inspired and neuromorphic computing in order to examine the complex and intertwined trajectories of the mathematical theory and hardware developed in this field. Early research focused on adapting existing hardware to emulate the pattern recognition capabilities of living organisms. Contributions from psychologists, mathematicians, engineers, neuroscientists, and other professions were crucial to maturing the field from narrowly-tailored demonstrations to more generalizable systems capable of addressing difficult problem classes such as object detection and speech recognition. Algorithms that leverage fundamental principles found in neuroscience such as hierarchical structure, temporal integration, and robustness to error have been developed, and some of these approaches are achieving world-leading performance on particular data classification tasks. In addition, novel microelectronic hardware is being developed to perform logic and to serve as memory in neuromorphic computing systems with optimized system integration and improved energy efficiency. Key to such advancements was the incorporation of new discoveries in neuroscience research, the transition away from strict structural replication and towards the functional replication of neural systems, and the use of mathematical theory frameworks to guide algorithm and hardware developments. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Neuromorphic computing Algorithms Artificial neural networks data-driven computing Machine learning Pattern recognition

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