  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.
