  Wave propagation problems are typically formulated as partial differential
equations (PDEs) on unbounded domains to be solved. The classical approach to
solving such problems involves truncating them to problems on bounded domains
by designing the artificial boundary conditions or perfectly matched layers,
which typically require significant effort, and the presence of nonlinearity in
the equation makes such designs even more challenging. Emerging deep
learning-based methods for solving PDEs, with the physics-informed neural
networks (PINNs) method as a representative, still face significant challenges
when directly used to solve PDEs on unbounded domains. Calculations performed
in a bounded domain of interest without imposing boundary constraints can lead
to a lack of unique solutions thus causing the failure of PINNs. In light of
this, this paper proposes a novel and effective operator learning-based method
for solving PDEs on unbounded domains. The key idea behind this method is to
generate high-quality training data. Specifically, we construct a family of
approximate analytical solutions to the target PDE based on its initial
condition and source term. Then, using these constructed data comprising exact
solutions, initial conditions, and source terms, we train an operator learning
model called MIONet, which is capable of handling multiple inputs, to learn the
mapping from the initial condition and source term to the PDE solution on a
bounded domain of interest. Finally, we utilize the generalization ability of
this model to predict the solution of the target PDE. The effectiveness of this
method is exemplified by solving the wave equation and the Schrodinger equation
defined on unbounded domains. More importantly, the proposed method can deal
with nonlinear problems, which has been demonstrated by solving Burger's
equation and Korteweg-de Vries (KdV) equation.
