Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Machine learning materials physics: Integrable deep neural networks
  enable scale bridging by learning free energy functions   The free energy of a system is central to many material models. Although free
energy data is not generally found directly, its derivatives can be observed or
calculated. In this work, we present an Integrable Deep Neural Network (IDNN)
that can be trained to derivative data, then analytically integrated to recover
an accurate representation of the free energy. The IDNN is demonstrated by
training to the chemical potential values of a binary alloy with B2 ordering.
The resulting DNN representation of the free energy is used in a phase field
simulation and found to predict the appropriate formation of antiphase
boundaries in the material. In contrast, a B-spline representation of the same
data failed to represent the physics of the system with sufficient fidelity to
resolve the antiphase boundaries.

33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con