Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: PAGP: A physics-assisted Gaussian process framework with active learning
  for forward and inverse problems of partial differential equations   In this work, a Gaussian process regression(GPR) model incorporated with
given physical information in partial differential equations(PDEs) is
developed: physics-assisted Gaussian processes(PAGP). The targets of this model
can be divided into two types of problem: finding solutions or discovering
unknown coefficients of given PDEs with initial and boundary conditions. We
introduce three different models: continuous time, discrete time and hybrid
models. The given physical information is integrated into Gaussian process
model through our designed GP loss functions. Three types of loss function are
provided in this paper based on two different approaches to train the standard
GP model. The first part of the paper introduces the continuous time model
which treats temporal domain the same as spatial domain. The unknown
coefficients in given PDEs can be jointly learned with GP hyper-parameters by
minimizing the designed loss function. In the discrete time models, we first
choose a time discretization scheme to discretize the temporal domain. Then the
PAGP model is applied at each time step together with the scheme to approximate
PDE solutions at given test points of final time. To discover unknown
coefficients in this setting, observations at two specific time are needed and
a mixed mean square error function is constructed to obtain the optimal
coefficients. In the last part, a novel hybrid model combining the continuous
and discrete time models is presented. It merges the flexibility of continuous
time model and the accuracy of the discrete time model. The performance of
choosing different models with different GP loss functions is also discussed.
The effectiveness of the proposed PAGP methods is illustrated in our numerical
section.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph