Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Framework for Data-Driven Computational Mechanics Based on Nonlinear
  Optimization   Data-Driven Computational Mechanics is a novel computing paradigm that
enables the transition from standard data-starved approaches to modern
data-rich approaches. At this early stage of development, one can distinguish
two mainstream directions. The first one relies on a discrete-continuous
optimization problem and seeks to assign to each material point a point in the
phase space that satisfies compatibility and equilibrium, while being closest
to the data set provided. The second one is a data driven inverse approach that
seeks to reconstruct a constitutive manifold from data sets by manifold
learning techniques, relying on a well-defined functional structure of the
underlying constitutive law. In this work, we propose a third route that
combines the strengths of the two existing directions and mitigates some of
their weaknesses. This is achieved by the formulation of an approximate
nonlinear optimization problem, which can be robustly solved, is
computationally efficient, and does not rely on any special functional
structure of the reconstructed constitutive manifold. Additional benefits
include the natural incorporation of kinematic constraints and the possibility
to operate with implicitly defined stress-strain relations. We discuss
important mathematical aspects of our approach for a data-driven truss element
and investigate its key numerical behavior for a data-driven beam element that
makes use of all components of our methodology.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci