Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: ADCME: Learning Spatially-varying Physical Fields using Deep Neural
  Networks   ADCME is a novel computational framework to solve inverse problems involving
physical simulations and deep neural networks (DNNs). This paper benchmarks its
capability to learn spatially-varying physical fields using DNNs. We
demonstrate that our approach has superior accuracy compared to the
discretization approach on a variety of problems, linear or nonlinear, static
or dynamic. Technically, we formulate our inverse problem as a PDE-constrained
optimization problem. We express both the numerical simulations and DNNs using
computational graphs and therefore, we can calculate the gradients using
reverse-mode automatic differentiation. We apply a physics constrained learning
algorithm (PCL) to efficiently back-propagate gradients through iterative
solvers for nonlinear equations. The open-source software which accompanies the
present paper can be found at https://github.com/kailaix/ADCME.jl.

21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
3
The categories of this paper are: physics