Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Data-driven method to learn the most probable transition pathway and
  stochastic differential equations   Transition phenomena between metastable states play an important role in
complex systems due to noisy fluctuations. In this paper, the physics informed
neural networks (PINNs) are presented to compute the most probable transition
pathway. It is shown that the expected loss is bounded by the empirical loss.
And the convergence result for the empirical loss is obtained. Then, a sampling
method of rare events is presented to simulate the transition path by the
Markovian bridge process. And we investigate the inverse problem to extract the
stochastic differential equation from the most probable transition pathway data
and the Markovian bridge process data, respectively. Finally, several numerical
experiments are presented to verify the effectiveness of our methods.

34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th