The current study aims to present a novel design of a sixth-order (SO) nonlinear Emden–Fowler nonlinear system (SONSEFM) along
with its
ive types. The
novel design of SO-NSEFM is
achieved using
the typical
second-order
Emden–Fowler

system. The
detail of
the
singularity and shape
factors is
presented
for
each type of
the SO-NSEFM.
Three
diferent
examples

of
each type of
the designed SO-NSEFM will
be
solved using
the
supervised
neural
network (SNN)
Levenberg–Marquardt

backpropagation
approach
(LMBA), i.e.,
SNN–LMBA. A
reference
dataset using
the
spectral collocation
scheme
with
the

proposed
SNN–LMBA will be
established
for
the designed SO-NSEFM. The
achieved
approximate outcomes of
the
designed

SO-NSEFM
are accessible using
the
procedures of
testing,
veriication, and
training of
the
proposed
neural
networks
to
reduce

the MSE.
For
the
eiciency,
correctness, and
efectiveness of
the
proposed
SNN-LMBA,
the
investigations
are
presented

through
the
proportional
performances of
regression, MSE
results,
correlation and
error
histograms (EHs), and
regression