<s>
Empirical	B-Application
dynamic	I-Application
modeling	I-Application
(	O
EDM	O
)	O
is	O
a	O
framework	O
for	O
analysis	O
and	O
prediction	O
of	O
nonlinear	O
dynamical	O
systems	O
.	O
</s>
<s>
It	O
can	O
be	O
considered	O
a	O
methodology	O
for	O
data	B-Application
modeling	I-Application
,	O
predictive	B-General_Concept
analytics	I-General_Concept
,	O
dynamical	O
system	O
analysis	O
,	O
machine	O
learning	O
and	O
time	O
series	O
analysis	O
.	O
</s>
<s>
EDM	O
is	O
thus	O
a	O
state-space	O
,	O
nearest-neighbors	B-Algorithm
paradigm	O
where	O
system	O
dynamics	O
are	O
inferred	O
from	O
states	O
derived	O
from	O
observational	O
time	O
series	O
.	O
</s>
<s>
As	O
of	O
2022	O
,	O
the	O
main	O
algorithms	O
are	O
Simplex	O
projection	O
,	O
Sequential	O
locally	O
weighted	O
global	O
linear	B-Architecture
maps	I-Architecture
(	O
S-Map	O
)	O
projection	O
,	O
Multivariate	O
embedding	O
in	O
Simplex	O
or	O
S-Map	O
,	O
</s>
<s>
Convergent	B-General_Concept
cross	I-General_Concept
mapping	I-General_Concept
(	O
CCM	O
)	O
,	O
</s>
<s>
S-Map	O
extends	O
the	O
state-space	O
prediction	O
in	O
Simplex	O
from	O
an	O
average	O
of	O
the	O
nearest	O
neighbors	O
to	O
a	O
linear	B-General_Concept
regression	I-General_Concept
fit	O
to	O
all	O
neighbors	O
,	O
but	O
localised	O
with	O
an	O
exponential	O
decay	O
kernel	O
.	O
</s>
<s>
Another	O
feature	O
of	O
S-Map	O
is	O
that	O
for	O
a	O
properly	O
fit	O
model	O
,	O
the	O
regression	B-General_Concept
coefficients	I-General_Concept
between	O
variables	O
have	O
been	O
shown	O
to	O
approximate	O
the	O
gradient	O
(	O
directional	O
derivative	O
)	O
of	O
variables	O
along	O
the	O
manifold	O
.	O
</s>
<s>
Convergent	B-General_Concept
cross	I-General_Concept
mapping	I-General_Concept
(	O
CCM	O
)	O
leverages	O
a	O
corollary	O
to	O
the	O
Generalized	O
Takens	O
Theorem	O
that	O
it	O
should	O
be	O
possible	O
to	O
cross	O
predict	O
or	O
cross	O
map	O
between	O
variables	O
observed	O
from	O
the	O
same	O
system	O
.	O
</s>
<s>
Multiview	O
Embedding	O
is	O
a	O
Dimensionality	B-Algorithm
reduction	I-Algorithm
technique	O
where	O
a	O
large	O
number	O
of	O
state-space	O
time	O
series	O
vectors	O
are	O
combitorially	O
assessed	O
towards	O
maximal	O
model	O
predictability	O
.	O
</s>
