  We develop a new computing paradigm, which we refer to as data-driven
computing, according to which calculations are carried out directly from
experimental material data and pertinent constraints and conservation laws,
such as compatibility and equilibrium, thus bypassing the empirical material
modeling step of conventional computing altogether. Data-driven solvers seek to
assign to each material point the state from a prespecified data set that is
closest to satisfying the conservation laws. Equivalently, data-driven solvers
aim to find the state satisfying the conservation laws that is closest to the
data set. The resulting data-driven problem thus consists of the minimization
of a distance function to the data set in phase space subject to constraints
introduced by the conservation laws. We motivate the data-driven paradigm and
investigate the performance of data-driven solvers by means of two examples of
application, namely, the static equilibrium of nonlinear three-dimensional
trusses and linear elasticity. In these tests, the data-driven solvers exhibit
good convergence properties both with respect to the number of data points and
with regard to local data assignment. The variational structure of the
data-driven problem also renders it amenable to analysis. We show that, as the
data set approximates increasingly closely a classical material law in phase
space, the data-driven solutions converge to the classical solution. We also
illustrate the robustness of data-driven solvers with respect to spatial
discretization. In particular, we show that the data-driven solutions of
finite-element discretizations of linear elasticity converge jointly with
respect to mesh size and approximation by the data set.
