Applied Computational Intelligence and Soft Computing,
Journal Year:
2024,
Volume and Issue:
2024(1)
Published: Jan. 1, 2024
The
nonlinear
sine‐Gordon
equation
is
a
prevalent
feature
in
numerous
scientific
and
engineering
problems.
In
this
paper,
we
propose
machine
learning‐based
approach,
physics‐informed
neural
networks
(PINNs),
to
investigate
explore
the
solution
of
generalized
non‐linear
equation,
encompassing
Dirichlet
Neumann
boundary
conditions.
To
incorporate
physical
information
for
multiobjective
loss
function
has
been
defined
consisting
residual
governing
partial
differential
(PDE),
initial
conditions,
various
Using
multiple
densely
connected
independent
artificial
(ANNs),
called
feedforward
deep
designed
handle
equations,
PINNs
have
trained
through
automatic
differentiation
minimize
that
incorporates
given
PDE
governs
laws
phenomena.
illustrate
effectiveness,
validity,
practical
implications
our
proposed
two
computational
examples
from
are
presented.
We
developed
PINN
algorithm
implemented
it
using
Python
software.
Various
experiments
were
conducted
determine
an
optimal
architecture.
network
training
was
employed
by
current
state‐of‐the‐art
optimization
methods
learning
known
as
Adam
L‐BFGS‐B
minimization
techniques.
Additionally,
solutions
method
compared
with
established
analytical
found
literature.
findings
show
approach
accurate
efficient
solving
equations
variety
conditions
well
any
complex
problems
across
disciplines.
