Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manifold embedding data-driven mechanics   This article introduces a new data-driven approach that leverages a manifold
embedding generated by the invertible neural network to improve the robustness,
efficiency, and accuracy of the constitutive-law-free simulations with limited
data. We achieve this by training a deep neural network to globally map data
from the constitutive manifold onto a lower-dimensional Euclidean vector space.
As such, we establish the relation between the norm of the mapped Euclidean
vector space and the metric of the manifold and lead to a more physically
consistent notion of distance for the material data. This treatment in return
allows us to bypass the expensive combinatorial optimization, which may
significantly speed up the model-free simulations when data are abundant and of
high dimensions. Meanwhile, the learning of embedding also improves the
robustness of the algorithm when the data is sparse or distributed unevenly in
the parametric space. Numerical experiments are provided to demonstrate and
measure the performance of the manifold embedding technique under different
circumstances. Results obtained from the proposed method and those obtained via
the classical energy norms are compared.

4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con