Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deep learning of parameterized equations with applications to
  uncertainty quantification   We propose a numerical method for discovering unknown parameterized dynamical
systems by using observational data of the state variables. Our method is built
upon and extends the recent work of discovering unknown dynamical systems, in
particular those using deep neural network (DNN). We propose a DNN structure,
largely based upon the residual network (ResNet), to not only learn the unknown
form of the governing equation but also take into account the random effect
embedded in the system, which is generated by the random parameters. Once the
DNN model is successfully constructed, it is able to produce system prediction
over longer term and for arbitrary parameter values. For uncertainty
quantification, it allows us to conduct uncertainty analysis by evaluating
solution statistics over the parameter space.

12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th