<s>
The	O
space	B-Algorithm
mapping	I-Algorithm
methodology	O
for	O
modeling	O
and	O
design	O
optimization	O
of	O
engineering	O
systems	O
was	O
first	O
discovered	O
by	O
John	O
Bandler	O
in	O
1993	O
.	O
</s>
<s>
The	O
space	B-Algorithm
mapping	I-Algorithm
methodology	O
employs	O
a	O
"	O
quasi-global	O
"	O
formulation	O
that	O
intelligently	O
links	O
companion	O
"	O
coarse	O
"	O
(	O
ideal	O
or	O
low-fidelity	O
)	O
and	O
"	O
fine	O
"	O
(	O
practical	O
or	O
high-fidelity	O
)	O
models	O
of	O
different	O
complexities	O
.	O
</s>
<s>
In	O
engineering	O
design	O
,	O
space	B-Algorithm
mapping	I-Algorithm
aligns	O
a	O
very	O
fast	O
coarse	O
model	O
with	O
the	O
expensive-to-compute	O
fine	O
model	O
so	O
as	O
to	O
avoid	O
direct	O
expensive	O
optimization	O
of	O
the	O
fine	O
model	O
.	O
</s>
<s>
The	O
alignment	O
can	O
be	O
done	O
either	O
off-line	O
(	O
model	O
enhancement	O
)	O
or	O
on-the-fly	O
with	O
surrogate	O
updates	O
(	O
e.g.	O
,	O
aggressive	O
space	B-Algorithm
mapping	I-Algorithm
)	O
.	O
</s>
<s>
The	O
latter	O
(	O
fast	O
model	O
)	O
is	O
usually	O
referred	O
to	O
as	O
the	O
"	O
coarse	O
"	O
model	O
(	O
coarse	B-Algorithm
space	I-Algorithm
)	O
.	O
</s>
<s>
The	O
optimization	O
space	O
,	O
where	O
conventional	O
optimization	O
is	O
carried	O
out	O
,	O
incorporates	O
the	O
coarse	O
model	O
(	O
or	O
surrogate	B-Algorithm
model	I-Algorithm
)	O
,	O
for	O
example	O
,	O
the	O
low-fidelity	O
physics	O
or	O
"	O
knowledge	O
"	O
model	O
.	O
</s>
<s>
In	O
a	O
space-mapping	B-Algorithm
design	O
optimization	O
phase	O
,	O
there	O
is	O
a	O
prediction	O
or	O
"	O
execution	O
"	O
step	O
,	O
where	O
the	O
results	O
of	O
an	O
optimized	O
"	O
mapped	O
coarse	O
model	O
"	O
(	O
updated	O
surrogate	O
)	O
are	O
assigned	O
to	O
the	O
fine	O
model	O
for	O
validation	O
.	O
</s>
<s>
The	O
mapping	O
formulation	O
itself	O
incorporates	O
"	O
intuition	B-Application
"	O
,	O
part	O
of	O
the	O
engineer	O
's	O
so-called	O
"	O
feel	O
"	O
for	O
a	O
problem	O
.	O
</s>
<s>
In	O
particular	O
,	O
the	O
Aggressive	O
Space	B-Algorithm
Mapping	I-Algorithm
(	O
ASM	O
)	O
process	O
displays	O
key	O
characteristics	O
of	O
cognition	O
(	O
an	O
expert	O
's	O
approach	O
to	O
a	O
problem	O
)	O
,	O
and	O
is	O
often	O
illustrated	O
in	O
simple	O
cognitive	O
terms	O
.	O
</s>
<s>
Following	O
John	O
Bandler	O
's	O
concept	O
in	O
1993	O
,	O
algorithms	O
have	O
utilized	O
Broyden	O
updates	O
(	O
aggressive	O
space	B-Algorithm
mapping	I-Algorithm
)	O
,	O
trust	O
regions	O
,	O
and	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
.	O
</s>
<s>
Developments	O
include	O
implicit	O
space	B-Algorithm
mapping	I-Algorithm
,	O
in	O
which	O
we	O
allow	O
preassigned	O
parameters	O
not	O
used	O
in	O
the	O
optimization	O
process	O
to	O
change	O
in	O
the	O
coarse	O
model	O
,	O
and	O
output	O
space	B-Algorithm
mapping	I-Algorithm
,	O
where	O
a	O
transformation	O
is	O
applied	O
to	O
the	O
response	O
of	O
the	O
model	O
.	O
</s>
<s>
Tuning	O
space	B-Algorithm
mapping	I-Algorithm
utilizes	O
a	O
so-called	O
tuning	O
model	O
—	O
constructed	O
invasively	O
from	O
the	O
fine	O
model	O
—	O
as	O
well	O
as	O
a	O
calibration	O
process	O
that	O
translates	O
the	O
adjustment	O
of	O
the	O
optimized	O
tuning	O
model	O
parameters	O
into	O
relevant	O
updates	O
of	O
the	O
design	O
variables	O
.	O
</s>
<s>
The	O
space	B-Algorithm
mapping	I-Algorithm
concept	O
has	O
been	O
extended	O
to	O
neural-based	O
space	B-Algorithm
mapping	I-Algorithm
for	O
large-signal	O
statistical	O
modeling	O
of	O
nonlinear	O
microwave	O
devices	O
.	O
</s>
<s>
Space	B-Algorithm
mapping	I-Algorithm
is	O
supported	O
by	O
sound	O
convergence	O
theory	O
and	O
is	O
related	O
to	O
the	O
defect-correction	O
approach	O
.	O
</s>
<s>
A	O
2016	O
state-of-the-art	O
review	O
is	O
devoted	O
to	O
aggressive	O
space	B-Algorithm
mapping	I-Algorithm
.	O
</s>
<s>
A	O
comprehensive	O
2021	O
review	O
paper	O
discusses	O
space	B-Algorithm
mapping	I-Algorithm
in	O
the	O
context	O
of	O
radio	O
frequency	O
and	O
microwave	O
design	O
optimization	O
;	O
in	O
the	O
context	O
of	O
engineering	O
surrogate	B-Algorithm
model	I-Algorithm
,	O
feature-based	O
and	O
cognition-driven	O
design	O
;	O
and	O
in	O
the	O
context	O
of	O
machine	O
learning	O
,	O
intuition	B-Application
,	O
and	O
human	O
intelligence	O
.	O
</s>
<s>
The	O
space	B-Algorithm
mapping	I-Algorithm
methodology	O
can	O
also	O
be	O
used	O
to	O
solve	O
inverse	O
problems	O
.	O
</s>
<s>
Proven	O
techniques	O
include	O
the	O
Linear	O
Inverse	O
Space	B-Algorithm
Mapping	I-Algorithm
(	O
LISM	O
)	O
algorithm	O
,	O
as	O
well	O
as	O
the	O
Space	B-Algorithm
Mapping	I-Algorithm
with	O
Inverse	O
Difference	O
(	O
SM-ID	O
)	O
method	O
.	O
</s>
<s>
Space	B-Algorithm
mapping	I-Algorithm
optimization	O
belongs	O
to	O
the	O
class	O
of	O
surrogate-based	O
optimization	O
methods	O
,	O
that	O
is	O
to	O
say	O
,	O
optimization	O
methods	O
that	O
rely	O
on	O
a	O
surrogate	B-Algorithm
model	I-Algorithm
.	O
</s>
<s>
The	O
space	B-Algorithm
mapping	I-Algorithm
technique	O
has	O
been	O
applied	O
in	O
a	O
variety	O
of	O
disciplines	O
including	O
microwave	O
and	O
electromagnetic	O
design	O
,	O
civil	O
and	O
mechanical	O
applications	O
,	O
aerospace	O
engineering	O
,	O
and	O
biomedical	O
research	O
.	O
</s>
<s>
Various	O
simulators	O
can	O
be	O
involved	O
in	O
a	O
space	B-Algorithm
mapping	I-Algorithm
optimization	O
and	O
modeling	O
processes	O
.	O
</s>
<s>
Three	O
international	O
workshops	O
have	O
focused	O
significantly	O
on	O
the	O
art	O
,	O
the	O
science	O
and	O
the	O
technology	O
of	O
space	B-Algorithm
mapping	I-Algorithm
.	O
</s>
<s>
There	O
is	O
a	O
wide	O
spectrum	O
of	O
terminology	O
associated	O
with	O
space	B-Algorithm
mapping	I-Algorithm
:	O
ideal	O
model	O
,	O
coarse	O
model	O
,	O
coarse	B-Algorithm
space	I-Algorithm
,	O
fine	O
model	O
,	O
companion	O
model	O
,	O
cheap	O
model	O
,	O
expensive	O
model	O
,	O
surrogate	B-Algorithm
model	I-Algorithm
,	O
low	O
fidelity	O
(	O
resolution	O
)	O
model	O
,	O
high	O
fidelity	O
(	O
resolution	O
)	O
model	O
,	O
empirical	O
model	O
,	O
simplified	O
physics	O
model	O
,	O
physics-based	O
model	O
,	O
quasi-global	O
model	O
,	O
physically	O
expressive	O
model	O
,	O
device	O
under	O
test	O
,	O
electromagnetics-based	O
model	O
,	O
simulation	O
model	O
,	O
computational	O
model	O
,	O
tuning	O
model	O
,	O
calibration	O
model	O
,	O
surrogate	B-Algorithm
model	I-Algorithm
,	O
surrogate	O
update	O
,	O
mapped	O
coarse	O
model	O
,	O
surrogate	O
optimization	O
,	O
parameter	O
extraction	O
,	O
target	O
response	O
,	O
optimization	O
space	O
,	O
validation	O
space	O
,	O
neuro-space	O
mapping	O
,	O
implicit	O
space	B-Algorithm
mapping	I-Algorithm
,	O
output	O
space	B-Algorithm
mapping	I-Algorithm
,	O
port	O
tuning	O
,	O
predistortion	O
(	O
of	O
design	O
specifications	O
)	O
,	O
manifold	O
mapping	O
,	O
defect	O
correction	O
,	O
model	O
management	O
,	O
multi-fidelity	O
models	O
,	O
variable	O
fidelity/variable	O
complexity	O
,	O
multigrid	O
method	O
,	O
coarse	O
grid	O
,	O
fine	O
grid	O
,	O
surrogate-driven	O
,	O
simulation-driven	O
,	O
model-driven	O
,	O
feature-based	O
modeling	O
.	O
</s>
