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Published January 1, 2021 | public
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Model-free data-driven computational mechanics enhanced by tensor voting


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.

Additional Information

© 2020 Elsevier. Received 6 April 2020, Revised 7 October 2020, Accepted 8 October 2020, Available online 15 October 2020. MO gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft (DFG), Germany through the Sonderforschungsbereich 1060 "The mathematics of emergent effects". SR and RE gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG) through the project RE 1057/40-2 "Model order reduction in space and parameter dimension — towards damage-based modeling of polymorphic uncertainty in the context of robustness and reliability" within the priority program SPP 1886 "Polymorphic uncertainty modelling for the numerical design of structures". Further, SR and RE rewardingly acknowledge the funding by the Excellence Initiative of the German federal and state governments through the project "Predictive Hierarchical Simulation". Finally, all authors acknowledge the financial support of the DFG and French Agence Nationale de la Recherche (ANR) through the project "Direct Data-Driven Computational Mechanics for Anelastic Material Behaviours" (project numbers: ANR-19-CE46-0012-01, RE 1057/47-1) within the French–German Collaboration for Joint Projects in Natural, Life and Engineering (NLE) Sciences. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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August 22, 2023
August 22, 2023