International Journal for Numerical Methods in Engineering,
Journal Year:
2024,
Volume and Issue:
unknown
Published: Sept. 12, 2024
Abstract
In
recent
years,
the
rapid
advancement
of
deep
learning
has
significantly
impacted
various
fields,
particularly
in
solving
partial
differential
equations
(PDEs)
realm
solid
mechanics,
benefiting
greatly
from
remarkable
approximation
capabilities
neural
networks.
PDEs,
physics‐informed
networks
(PINNs)
and
energy
method
(DEM)
have
garnered
substantial
attention.
The
principle
minimum
potential
complementary
are
two
important
variational
principles
mechanics.
However,
well‐known
DEM
is
based
on
energy,
but
it
lacks
form
energy.
To
bridge
this
gap,
we
propose
(DCEM)
output
function
DCEM
stress
function,
which
inherently
satisfies
equilibrium
equation.
We
present
numerical
results
classical
linear
elasticity
using
Prandtl
Airy
functions,
compare
with
existing
PINNs
algorithms
when
modeling
representative
mechanical
problems.
demonstrate
that
outperforms
terms
accuracy
efficiency
an
advantage
dealing
complex
displacement
boundary
conditions,
supported
by
theoretical
analyses
simulations.
extend
to
DCEM‐Plus
(DCEM‐P),
adding
satisfy
PDEs.
Furthermore,
a
operator
(DCEM‐O)
combining
physical
equations.
Initially,
train
DCEM‐O
high‐fidelity
then
incorporate
DCEM‐P
further
enhance
DCEM.
Journal of Computing and Information Science in Engineering,
Journal Year:
2024,
Volume and Issue:
24(4)
Published: Jan. 8, 2024
Abstract
Advancements
in
computing
power
have
recently
made
it
possible
to
utilize
machine
learning
and
deep
push
scientific
forward
a
range
of
disciplines,
such
as
fluid
mechanics,
solid
materials
science,
etc.
The
incorporation
neural
networks
is
particularly
crucial
this
hybridization
process.
Due
their
intrinsic
architecture,
conventional
cannot
be
successfully
trained
scoped
when
data
are
sparse,
which
the
case
many
engineering
domains.
Nonetheless,
provide
foundation
respect
physics-driven
or
knowledge-based
constraints
during
training.
Generally
speaking,
there
three
distinct
network
frameworks
enforce
underlying
physics:
(i)
physics-guided
(PgNNs),
(ii)
physics-informed
(PiNNs),
(iii)
physics-encoded
(PeNNs).
These
methods
advantages
for
accelerating
numerical
modeling
complex
multiscale
multiphysics
phenomena.
In
addition,
recent
developments
operators
(NOs)
add
another
dimension
these
new
simulation
paradigms,
especially
real-time
prediction
systems
required.
All
models
also
come
with
own
unique
drawbacks
limitations
that
call
further
fundamental
research.
This
study
aims
present
review
four
(i.e.,
PgNNs,
PiNNs,
PeNNs,
NOs)
used
state-of-the-art
architectures
applications
reviewed,
discussed,
future
research
opportunities
presented
terms
improving
algorithms,
considering
causalities,
expanding
applications,
coupling
solvers.
Computers & Structures,
Journal Year:
2024,
Volume and Issue:
297, P. 107342 - 107342
Published: April 4, 2024
This
paper
presents
a
literature
review
on
methods
for
enabling
real-time
analysis
in
digital
twins,
which
are
virtual
models
of
physical
systems.
The
advantages
twins
numerous,
including
cost
reduction,
risk
mitigation,
efficiency
enhancement,
and
decision-making
support.
However,
their
implementation
faces
challenges
such
as
the
need
data
analysis,
resource
limitations,
uncertainty.
focuses
reducing
computational
demands,
have
not
been
systematically
discussed
literature.
reviews
categorizes
tools
accelerating
modeling
phenomena
needs
twins.
