Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: State-of-the-Art Review of Design of Experiments for Physics-Informed
  Deep Learning   This paper presents a comprehensive review of the design of experiments used
in the surrogate models. In particular, this study demonstrates the necessity
of the design of experiment schemes for the Physics-Informed Neural Network
(PINN), which belongs to the supervised learning class. Many complex partial
differential equations (PDEs) do not have any analytical solution; only
numerical methods are used to solve the equations, which is computationally
expensive. In recent decades, PINN has gained popularity as a replacement for
numerical methods to reduce the computational budget. PINN uses physical
information in the form of differential equations to enhance the performance of
the neural networks. Though it works efficiently, the choice of the design of
experiment scheme is important as the accuracy of the predicted responses using
PINN depends on the training data. In this study, five different PDEs are used
for numerical purposes, i.e., viscous Burger's equation, Shr\"{o}dinger
equation, heat equation, Allen-Cahn equation, and Korteweg-de Vries equation. A
comparative study is performed to establish the necessity of the selection of a
DoE scheme. It is seen that the Hammersley sampling-based PINN performs better
than other DoE sample strategies.

9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph