Efficient Data Structures for Model-free Data-Driven Computational Mechanics

TL;DR

This paper introduces and compares efficient data structures, especially approximate nearest-neighbor algorithms, to significantly speed up data-driven computational mechanics without sacrificing accuracy.

Contribution

It develops and evaluates approximate nearest-neighbor algorithms tailored for data-driven mechanics, enabling rapid searches in billion-scale data sets.

Findings

ANN algorithms accelerate searches by several orders of magnitude.

No significant loss of accuracy with approximate methods.

Single-processor computations with billion data points are feasible within seconds.

Abstract

The data-driven computing paradigm initially introduced by Kirchdoerfer and 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 speedup of more than 106 with respect to exact k-d trees.