Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Dual-Dimer Method for Training Physics-Constrained Neural Networks
  with Minimax Architecture   Data sparsity is a common issue to train machine learning tools such as
neural networks for engineering and scientific applications, where experiments
and simulations are expensive. Recently physics-constrained neural networks
(PCNNs) were developed to reduce the required amount of training data. However,
the weights of different losses from data and physical constraints are adjusted
empirically in PCNNs. In this paper, a new physics-constrained neural network
with the minimax architecture (PCNN-MM) is proposed so that the weights of
different losses can be adjusted systematically. The training of the PCNN-MM is
searching the high-order saddle points of the objective function. A novel
saddle point search algorithm called Dual-Dimer method is developed. It is
demonstrated that the Dual-Dimer method is computationally more efficient than
the gradient descent ascent method for nonconvex-nonconcave functions and
provides additional eigenvalue information to verify search results. A heat
transfer example also shows that the convergence of PCNN-MMs is faster than
that of traditional PCNNs.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th