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Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2021

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

Résumé

The data-driven computing paradigm initially introduced by Kirchdoerfer & 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 & 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, 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.

Dates et versions

hal-03413212 , version 1 (03-11-2021)

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Robert Eggersmann, Laurent Stainier, Michael Ortiz, Stefanie Reese. Model-free data-driven computational mechanics enhanced by tensor voting. Computer Methods in Applied Mechanics and Engineering, 2021, 373, pp.113499. ⟨10.1016/j.cma.2020.113499⟩. ⟨hal-03413212⟩
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