Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deep Monte Carlo Quantile Regression for Quantifying Aleatoric
  Uncertainty in Physics-informed Temperature Field Reconstruction   For the temperature field reconstruction (TFR), a complex image-to-image
regression problem, the convolutional neural network (CNN) is a powerful
surrogate model due to the convolutional layer's good image feature extraction
ability. However, a lot of labeled data is needed to train CNN, and the common
CNN can not quantify the aleatoric uncertainty caused by data noise. In actual
engineering, the noiseless and labeled training data is hardly obtained for the
TFR. To solve these two problems, this paper proposes a deep Monte Carlo
quantile regression (Deep MC-QR) method for reconstructing the temperature
field and quantifying aleatoric uncertainty caused by data noise. On the one
hand, the Deep MC-QR method uses physical knowledge to guide the training of
CNN. Thereby, the Deep MC-QR method can reconstruct an accurate TFR surrogate
model without any labeled training data. On the other hand, the Deep MC-QR
method constructs a quantile level image for each input in each training epoch.
Then, the trained CNN model can quantify aleatoric uncertainty by quantile
level image sampling during the prediction stage. Finally, the effectiveness of
the proposed Deep MC-QR method is validated by many experiments, and the
influence of data noise on TFR is analyzed.

11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int