I
A
E
S
I
n
t
e
r
n
at
io
n
al
Jou
r
n
al
of
A
r
t
if
ic
ia
l
I
n
t
e
ll
ig
e
n
c
e
(
I
J
-
AI
)
V
ol
.
14
, N
o.
2
,
A
pr
il
2025
, pp.
1
067
~
1
076
I
S
S
N
:
2252
-
8938
,
D
O
I
:
10.11591/
ij
a
i.
v
14
.i
2
.pp
1
067
-
1
076
1067
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
ai
.
ia
e
s
c
or
e
.c
om
S
c
h
e
d
u
l
e
-
f
r
e
e
op
t
i
m
i
z
at
i
on
of
t
h
e
t
r
a
n
sf
or
m
e
r
s
-
b
ase
d
t
i
m
e
se
r
i
e
s f
o
r
e
c
as
t
i
n
g m
od
e
l
K
yr
yl
o Y
e
m
e
t
s
1
,
M
ic
h
al
G
r
e
gu
s
2
1
D
e
pa
r
t
m
e
nt
of
A
r
t
i
f
i
c
i
a
l
I
nt
e
l
l
i
ge
nc
e
, L
vi
v P
ol
yt
e
c
hni
c
N
a
t
i
ona
l
U
ni
ve
r
s
i
t
y, L
vi
v, U
kr
a
i
ne
2
F
a
c
ul
t
y of
M
a
na
ge
m
e
nt
, C
om
e
ni
us
U
ni
ve
r
s
i
t
y B
r
a
t
i
s
l
a
va
,
B
r
a
t
i
s
l
a
va
, S
l
ova
k R
e
publ
i
c
A
r
t
ic
le
I
n
f
o
A
B
S
T
R
A
C
T
A
r
ti
c
le
h
is
to
r
y
:
R
e
c
e
iv
e
d
J
ul
27
,
2024
R
e
vi
s
e
d
O
c
t
26
,
2024
A
c
c
e
pt
e
d
N
ov
14
,
2024
The task of time series forecasting
is important for
many scientific, tec
hnical,
and
applied
fields,
such
as
finance,
economics,
meteorology,
me
dicine,
transporta
tion,
and
telecommunic
ations.
Existing
methods,
su
ch
as
autoregress
ive
models
and
moving
avera
ge
models,
have
their
limit
ations,
especiall
y when wo
rking wi
th non
-
stationary and se
asonal data. I
n this work,
the
basic
architecture
of
transformers
was
modified
to
solve
time
series
forecasting
problems.
Addition
ally,
state
-
of
-
the
-
art
optimizers
were
in
vestigated
and
experimentally
compared,
including
AdamW,
sto
chastic
gradient
descent
(
SGD
)
,
and
new
methods
such
as
schedule
-
free
SG
D
and
schedule
-
free
AdamW, to improve fo
recasting accuracy and the efficiency of
the
training
procedure
for
the
transformer
architecture.
Modelin
g
was
conducted
on
meteorol
ogical
data
that
included
seasonal
tim
e
serie
s.
The
accuracy
evaluatio
n
of
the
optimi
zation
methods
stu
died
in
this
wo
rk
was
performed
using
a
range
of
different
performan
ce
indicators.
The
results
showed
tha
t
the
new
optimization
methods
significantly
improve
forecasting
accuracy compar
ed to t
he use of
traditi
onal opt
imizers
.
K
e
y
w
o
r
d
s
:
A
da
G
r
a
d
F
or
e
c
a
s
ti
ng
R
M
S
pr
op
S
c
he
dul
e
-
F
r
e
e
A
da
m
W
S
c
he
dul
e
-
F
r
e
e
S
G
D
T
im
e
s
e
r
ie
s
T
r
a
ns
f
or
m
e
r
s
This is an
open
acce
ss artic
le unde
r the
CC BY
-
SA
license.
C
or
r
e
s
pon
di
n
g A
u
th
or
:
K
yr
yl
o Y
e
m
e
ts
D
e
pa
r
tm
e
nt
of
A
r
ti
f
ic
ia
l
I
nt
e
ll
ig
e
nc
e
, L
vi
v P
ol
y
te
c
hni
c
N
a
ti
ona
l
U
ni
ve
r
s
it
y
K
ni
a
z
ia
R
om
a
na
s
tr
., 5, L
vi
v 79905, Ukr
a
in
e
E
m
a
il
:
kyr
yl
o.v.ye
m
e
ts
@
lp
nu.ua
1.
I
N
T
R
O
D
U
C
T
I
O
N
T
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
is
a
r
e
le
va
nt
a
nd
e
xt
r
e
m
e
ly
im
por
ta
nt
t
a
s
k
in
va
r
io
us
s
c
ie
nt
if
ic
,
te
c
hni
c
a
l,
a
nd
a
ppl
ie
d
f
ie
ld
s
[
1]
.
T
hi
s
ta
s
k
a
r
is
e
s
in
th
e
c
ont
e
xt
of
di
s
c
ip
li
n
e
s
s
uc
h
a
s
f
in
a
nc
e
,
e
c
onomi
c
s
,
m
e
te
or
ol
ogy,
m
e
di
c
in
e
,
tr
a
ns
por
ta
ti
on,
te
le
c
om
m
uni
c
a
ti
ons
,
a
nd
m
a
ny
ot
he
r
s
,
w
he
r
e
pr
e
di
c
ti
ng
f
ut
ur
e
va
lu
e
s
of
s
pe
c
if
ic
va
r
ia
bl
e
s
ba
s
e
d
on
th
e
ir
hi
s
to
r
ic
a
l
da
ta
is
ne
c
e
s
s
a
r
y
[
2]
,
[
3]
.
T
he
a
c
c
ur
a
c
y
of
s
ol
vi
ng
th
e
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
pr
obl
e
m
pl
a
ys
a
n
im
por
ta
nt
r
ol
e
a
nd
h
a
s
a
di
r
e
c
t
im
pa
c
t
on
th
e
e
f
f
ic
ie
nc
y
a
nd
e
c
onomi
c
be
ne
f
it
of
de
c
i
s
io
ns
m
a
de
.
P
a
r
ti
c
ul
a
r
ly
in
th
e
f
ie
ld
of
m
e
te
or
ol
ogy,
th
e
a
c
c
ur
a
c
y
of
w
e
a
th
e
r
f
or
e
c
a
s
ts
is
c
r
it
ic
a
ll
y
im
por
ta
nt
f
or
pr
e
di
c
ti
ng
na
tu
r
a
l
di
s
a
s
te
r
s
a
nd
pl
a
nni
ng
a
c
ti
vi
ti
e
s
in
va
r
io
us
s
e
c
to
r
s
of
th
e
e
c
onomy
[
4]
.
T
hi
s
ta
s
k
is
a
n
in
te
gr
a
l
pa
r
t
of
e
f
f
e
c
ti
ve
r
e
s
our
c
e
m
a
na
ge
m
e
nt
a
nd s
tr
a
te
gi
c
pl
a
nni
ng.
T
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng i
s
a
c
om
pl
e
x t
a
s
k due
t
o t
he
l
a
r
ge
numb
e
r
of
f
a
c
to
r
s
a
f
f
e
c
ti
ng da
ta
va
r
ia
bi
li
ty
a
nd
th
e
ir
in
te
r
r
e
la
ti
ons
hi
ps
[
5]
.
I
n
pa
r
ti
c
ul
a
r
,
s
e
a
s
ona
l
f
lu
c
tu
a
ti
ons
,
tr
e
nds
,
r
a
ndom
de
vi
a
ti
ons
,
a
nd
ot
he
r
c
om
pone
nt
s
c
a
n
s
ig
ni
f
ic
a
nt
ly
c
om
pl
ic
a
te
th
e
f
or
e
c
a
s
ti
ng
pr
oc
e
s
s
[
6]
–
[
8]
.
O
ne
of
th
e
im
por
ta
nt
ta
s
k
s
is
to
a
de
qua
te
ly
a
c
c
ount
f
or
a
ll
th
e
s
e
f
a
c
to
r
s
w
he
n
bui
ld
in
g
a
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
m
ode
l
[
9]
,
[
10]
.
I
m
pe
r
f
e
c
ti
on
of
da
ta
,
th
e
pr
e
s
e
nc
e
of
noi
s
e
,
a
nd
ga
ps
in
th
e
da
ta
c
a
n
a
ls
o
r
e
duc
e
th
e
a
c
c
ur
a
c
y
of
f
or
e
c
a
s
ts
[
11]
,
[
12]
.
I
n
a
ddi
ti
on,
th
e
s
pe
e
d
of
c
ha
nge
s
in
th
e
e
nvi
r
onm
e
nt
or
m
a
r
ke
t
m
a
y
r
e
qui
r
e
c
ons
ta
nt
upda
ti
ng
of
m
ode
ls
a
nd
th
e
ir
a
da
pt
a
ti
on t
o ne
w
c
ondi
ti
ons
[
13]
, [
14]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
.
14
, N
o.
2
,
A
pr
il
20
25
:
1
067
-
1
076
1068
A
s
of
to
da
y,
th
e
r
e
a
r
e
m
a
ny
m
e
th
od
s
f
or
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
[
15]
.
A
m
ong
th
e
m
,
tr
a
di
ti
ona
l
s
ta
ti
s
ti
c
a
l
m
e
th
od
s
s
houl
d
b
e
hi
ghl
ig
ht
e
d,
s
u
c
h
a
s
a
ut
or
e
gr
e
s
s
i
ve
m
ode
ls
[
16]
,
m
ovi
ng
a
ve
r
a
ge
m
ode
ls
[
17]
,
a
nd
th
e
ir
c
om
bi
na
ti
ons
,
in
pa
r
ti
c
ul
a
r
a
ut
or
e
gr
e
s
s
iv
e
in
te
gr
a
te
d
m
ovi
ng
a
ve
r
a
ge
(
A
R
I
M
A
)
[
18]
,
a
nd
ot
he
r
a
r
ti
f
ic
ia
l
ne
ur
a
l
ne
twor
ks
(
A
N
N
s
)
[
19]
–
[
22]
.
S
pe
c
if
ic
a
ll
y,
th
e
la
tt
e
r
m
e
th
od
a
s
s
um
e
s
a
li
ne
a
r
r
e
la
ti
ons
hi
p
be
twe
e
n
pa
s
t
a
nd
f
ut
ur
e
v
a
lu
e
s
.
H
o
w
e
ve
r
,
w
e
a
th
e
r
pa
tt
e
r
ns
of
te
n
e
xhi
bi
t
non
-
li
ne
a
r
be
ha
vi
or
s
due
to
th
e
c
om
pl
e
x
in
te
r
a
c
ti
ons
be
twe
e
n
va
r
io
us
a
tm
os
phe
r
ic
va
r
ia
bl
e
s
,
w
h
ic
h
A
R
I
M
A
m
ode
ls
c
a
nnot
c
a
pt
ur
e
e
f
f
e
c
ti
ve
ly
[
23]
.
I
n
a
ddi
ti
on,
A
R
I
M
A
m
ode
ls
c
a
n
be
c
om
e
ove
r
ly
c
om
pl
e
x
a
nd
c
om
put
a
ti
ona
ll
y
in
te
ns
iv
e
w
he
n
de
a
li
ng
w
it
h
m
ul
ti
pl
e
s
e
a
s
ona
l
pa
tt
e
r
ns
,
w
hi
c
h
a
r
e
c
om
m
on
in
w
e
a
th
e
r
da
ta
.
I
n
ge
ne
r
a
l,
th
e
s
e
m
e
th
ods
w
or
k
w
e
ll
f
or
f
or
e
c
a
s
ti
ng
s
ta
ti
ona
r
y
pr
oc
e
s
s
e
s
,
but
w
e
a
th
e
r
da
ta
o
f
te
n
e
xhi
b
it
s
e
a
s
ona
li
ty
a
nd
tr
e
nds
,
r
e
qui
r
in
g
e
xt
e
n
s
iv
e
pr
e
-
pr
oc
e
s
s
in
g
to
a
c
hi
e
ve
s
ta
ti
on
a
r
it
y,
w
hi
c
h
c
a
n
be
c
ha
ll
e
ngi
n
g
a
nd
s
om
e
ti
m
e
s
in
a
de
qua
t
e
[
24]
.
T
ha
t'
s
w
hy
th
e
s
e
m
e
th
ods
i
m
pos
e
a
numbe
r
of
l
im
it
a
ti
ons
w
he
n f
or
e
c
a
s
ti
ng
c
om
pl
e
x, non
-
s
ta
ti
ona
r
y t
im
e
s
e
r
ie
s
.
T
he
r
a
pi
d
de
ve
lo
pm
e
nt
of
m
a
c
hi
ne
le
a
r
ni
ng
te
c
hnol
ogi
e
s
ha
s
le
d
to
th
e
e
m
e
r
ge
nc
e
of
ne
w
,
m
or
e
pow
e
r
f
ul
t
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng me
th
ods
, s
uc
h a
s
ne
ur
a
l
ne
two
r
ks
[
13]
, gr
a
di
e
nt
boos
ti
ng
[
25]
, a
nd e
ns
e
m
bl
e
m
e
th
ods
[
26]
,
[
27
]
. I
n
pa
r
ti
c
ul
a
r
,
r
e
c
ur
r
e
nt
ne
ur
a
l
ne
twor
ks
(
R
N
N
)
a
nd
lo
ng
s
hor
t
-
te
r
m
m
e
m
or
y (
L
S
T
M
)
ha
ve
be
c
om
e
popula
r
f
or
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
du
e
to
th
e
ir
a
bi
li
ty
to
a
c
c
ount
f
or
de
pe
nde
n
c
ie
s
ove
r
la
r
ge
ti
m
e
in
te
r
va
ls
.
H
ow
e
ve
r
,
th
e
y
ha
ve
a
num
be
r
of
dr
a
w
ba
c
ks
.
S
pe
c
if
i
c
a
ll
y,
R
N
N
s
of
te
n
f
a
c
e
pr
obl
e
m
s
of
va
ni
s
hi
ng
or
e
xpl
odi
ng
gr
a
di
e
nt
s
dur
in
g
t
r
a
in
in
g,
w
hi
c
h
c
om
pl
ic
a
te
s
th
e
tr
a
in
in
g
of
m
ode
ls
on
lo
ng
ti
m
e
s
e
r
ie
s
[
28]
.
T
hi
s
le
a
ds
to
th
e
m
ode
l
pot
e
nt
ia
ll
y
lo
s
in
g
in
f
or
m
a
ti
on
a
bout
pr
e
vi
ous
s
ta
te
s
or
be
c
om
in
g
uns
ta
bl
e
.
T
he
e
f
f
e
c
ti
ve
ne
s
s
of
L
S
T
M
s
tr
ongl
y
de
pe
nds
on
th
e
c
hoi
c
e
of
hype
r
pa
r
a
m
e
te
r
s
(
e
.g.,
num
be
r
of
la
ye
r
s
,
m
e
m
or
y
c
e
ll
s
iz
e
,
a
nd
le
a
r
ni
ng
r
a
te
s
)
.
I
nc
or
r
e
c
t
c
hoi
c
e
of
hype
r
pa
r
a
m
e
te
r
s
c
a
n
le
a
d
to
poor
m
ode
l
pe
r
f
o
r
m
a
nc
e
[
29]
.
T
ha
t'
s
w
hy,
r
e
c
e
nt
ly
,
tr
a
ns
f
or
m
e
r
s
ha
ve
be
c
om
e
w
id
e
ly
u
s
e
d
-
m
ode
ls
th
a
t
w
e
r
e
in
it
ia
ll
y
de
ve
lo
pe
d
f
or
na
tu
r
a
l
la
ngua
g
e
pr
oc
e
s
s
in
g
[
30]
.
T
he
y
a
ll
ow
a
c
c
ount
in
g
f
or
r
e
la
ti
ons
hi
ps
be
twe
e
n
da
ta
a
t
di
f
f
e
r
e
nt
ti
m
e
s
c
a
le
s
a
nd
pr
ovi
de
hi
gh
f
or
e
c
a
s
t
a
c
c
ur
a
c
y.
T
he
e
m
e
r
ge
n
c
e
of
A
N
N
f
or
de
e
p
le
a
r
ni
ng
b
a
s
e
d
on
th
e
tr
a
ns
f
or
m
e
r
a
r
c
hi
te
c
tu
r
e
ope
ns
up
m
a
ny
ne
w
pos
s
ib
il
it
ie
s
f
or
s
ol
vi
ng
va
r
io
us
a
ppl
ie
d
pr
obl
e
m
s
.
A
lt
hough
th
e
ba
s
ic
a
r
c
hi
te
c
tu
r
e
of
s
uc
h
A
N
N
s
is
de
s
ig
ne
d
f
or
na
tu
r
a
l
la
ngua
ge
pr
oc
e
s
s
in
g
[
31]
,
th
e
r
e
a
r
e
m
a
ny
ot
he
r
t
a
s
ks
w
he
r
e
th
is
a
r
c
hi
te
c
tu
r
e
c
a
n
de
m
on
s
tr
a
te
s
ig
ni
f
ic
a
nt
a
dva
nt
a
ge
s
w
h
e
n
a
ppl
ie
d,
one
of
w
hi
c
h
is
ti
m
e
s
e
r
ie
s
pr
e
di
c
ti
on. T
hi
s
gi
ve
s
r
is
e
to
th
e
f
ir
s
t
ta
s
k
of
th
is
s
tu
dy
-
m
odi
f
yi
ng
th
e
ba
s
ic
a
r
c
hi
te
c
tu
r
e
of
tr
a
n
s
f
or
m
e
r
s
[
31]
to
be
a
b
le
to
s
ol
ve
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
pr
obl
e
m
s
.
T
hi
s
i
s
e
s
pe
c
ia
ll
y
u
s
e
f
ul
w
he
n
w
e
ha
ve
a
huge
a
m
ount
of
c
yc
li
c
a
l
da
ta
,
s
uc
h
a
s
in
m
e
te
or
ol
ogy.
T
a
ki
ng
in
to
a
c
c
ount
th
e
vol
um
e
of
tr
a
ns
f
or
m
e
r
-
ba
s
e
d
f
or
e
c
a
s
ti
ng
m
ode
ls
,
it
is
im
por
ta
nt
not
onl
y
to
ha
ve
th
e
c
or
r
e
c
t
m
ode
l
a
r
c
hi
te
c
tu
r
e
but
a
ls
o
to
us
e
th
e
be
s
t
opt
im
iz
e
r
d
ur
in
g
th
e
tr
a
in
in
g
of
s
uc
h
a
m
ode
l
[
32]
,
[
33]
.
T
he
m
ode
l
a
r
c
hi
te
c
tu
r
e
pl
a
ys
a
s
ig
ni
f
ic
a
nt
r
ol
e
a
s
i
t
d
e
te
r
m
in
e
s
how
i
nf
or
m
a
ti
on i
s
pr
oc
e
s
s
e
d
a
nd r
e
pr
e
s
e
nt
e
d.
H
ow
e
ve
r
,
e
ve
n
th
e
be
s
t
a
r
c
hi
te
c
tu
r
e
m
a
y
not
a
c
hi
e
ve
th
e
e
xpe
c
te
d
r
e
s
ul
ts
w
it
hout
pr
ope
r
tu
ni
ng
a
nd
opt
im
iz
a
ti
on. An optim
iz
e
r
i
s
a
n
a
lg
or
it
hm
us
e
d t
o
a
dj
us
t
th
e
w
e
ig
ht
s
of
a
n
e
ur
a
l
ne
twor
k t
o m
in
im
iz
e
t
he
l
os
s
f
unc
ti
on
[
32]
.
T
he
c
hoi
c
e
of
opt
im
iz
e
r
c
a
n
h
a
ve
a
bi
g
im
pa
c
t
on
c
onve
r
ge
nc
e
s
pe
e
d,
tr
a
in
in
g
s
ta
bi
li
ty
,
a
nd
f
in
a
l
m
ode
l
a
c
c
ur
a
c
y.
T
he
r
e
a
r
e
m
a
ny
di
f
f
e
r
e
nt
opt
im
iz
e
r
s
,
e
a
c
h
w
it
h
it
s
ow
n
a
dva
nt
a
ge
s
a
nd
di
s
a
dv
a
nt
a
ge
s
.
F
or
e
xa
m
pl
e
,
s
to
c
ha
s
ti
c
gr
a
di
e
nt
de
s
c
e
nt
(
S
G
D
)
is
one
of
th
e
s
im
pl
e
s
t
a
nd
m
os
t
f
r
e
que
nt
ly
us
e
d
opt
im
iz
e
r
s
[
34]
.
I
t
is
e
f
f
e
c
ti
ve
f
or
la
r
ge
da
ta
s
e
ts
but
c
a
n
s
uf
f
e
r
f
r
om
s
lo
w
c
onve
r
ge
nc
e
a
nd
ge
t
s
tu
c
k
in
lo
c
a
l
m
in
im
a
.
A
da
pt
iv
e
m
e
th
ods
,
s
uc
h
a
s
A
da
m
,
r
oot
m
e
a
n
s
qua
r
e
pr
opa
ga
ti
on
(
R
M
S
pr
op)
,
a
nd
a
da
pt
iv
e
gr
a
di
e
nt
a
lg
or
it
hm
(
A
da
G
r
a
d
)
,
us
e
di
f
f
e
r
e
nt
a
ppr
oa
c
he
s
to
a
dj
us
t
th
e
le
a
r
ni
ng
r
a
te
of
e
a
c
h
pa
r
a
m
e
te
r
,
w
hi
c
h
c
a
n
le
a
d
to
f
a
s
te
r
a
nd
m
or
e
s
ta
bl
e
c
onve
r
ge
nc
e
.
I
n
pa
r
ti
c
ul
a
r
,
R
M
S
pr
op
m
a
in
ta
in
s
a
n
a
da
pt
iv
e
le
a
r
ni
ng
r
a
te
th
a
t
c
ha
nge
s
f
or
e
a
c
h
p
a
r
a
m
e
te
r
ba
s
e
d
on
th
e
a
ve
r
a
ge
s
qua
r
e
of
pr
e
vi
ous
gr
a
di
e
nt
s
[
35
]
.
T
hi
s
he
lp
s
a
voi
d
th
e
pr
obl
e
m
o
f
la
r
ge
or
s
m
a
ll
le
a
r
ni
ng
r
a
te
s
,
w
hi
c
h c
a
n be
us
e
f
ul
f
or
m
ode
ls
w
it
h hi
gh va
r
ia
bi
li
ty
i
n pa
r
a
m
e
t
e
r
s
c
a
le
. R
M
S
pr
op ha
s
s
e
ve
r
a
l
dr
a
w
ba
c
ks
t
ha
t
c
a
n a
f
f
e
c
t
opt
im
iz
a
ti
on e
f
f
ic
ie
nc
y. O
n
e
of
t
he
m
a
in
pr
obl
e
m
s
i
s
th
e
bi
a
s
i
n m
om
e
nt
e
s
ti
m
a
te
s
due
t
o t
he
us
e
of
e
xpone
nt
ia
l
s
m
oot
hi
ng
to
c
a
lc
ul
a
te
th
e
a
ve
r
a
ge
s
qua
r
e
of
gr
a
di
e
nt
s
.
T
hi
s
bi
a
s
is
pa
r
ti
c
ul
a
r
ly
not
ic
e
a
bl
e
in
th
e
e
a
r
ly
s
ta
ge
s
of
t
r
a
in
in
g a
nd c
a
n
ne
ga
ti
ve
ly
a
f
f
e
c
t
th
e
i
ni
ti
a
l
pha
s
e
of
opt
im
iz
a
ti
on. Additi
ona
ll
y, R
M
S
pr
op c
a
n
be
s
e
ns
it
iv
e
to
in
it
ia
l
c
ondi
ti
ons
,
m
e
a
ni
ng
in
c
or
r
e
c
t
w
e
ig
ht
in
it
ia
li
z
a
ti
on
c
a
n
le
a
d
to
c
onve
r
ge
nc
e
pr
obl
e
m
s
a
nd
ge
tt
in
g
s
tu
c
k
in
lo
c
a
l
m
in
im
a
.
A
not
he
r
im
por
ta
nt
is
s
ue
is
th
e
de
pe
nde
nc
e
on
ba
t
c
h
s
iz
e
.
A
n
in
a
ppr
opr
ia
te
ba
tc
h
s
iz
e
c
a
n
a
f
f
e
c
t
th
e
c
a
lc
ul
a
ti
on
of
t
he
a
ve
r
a
ge
s
qua
r
e
of
gr
a
di
e
nt
s
a
nd
ove
r
a
ll
opt
im
iz
a
ti
on
e
f
f
ic
ie
nc
y.
A
da
G
r
a
d
m
odi
f
ie
s
th
e
le
a
r
ni
ng
r
a
te
ba
s
e
d
on
th
e
f
r
e
que
nc
y
o
f
pa
r
a
m
e
te
r
upda
te
s
,
a
ll
ow
in
g
r
a
r
e
ly
upda
te
d
pa
r
a
m
e
te
r
s
to
ha
ve
a
hi
ghe
r
le
a
r
ni
ng
r
a
te
[
36]
.
H
ow
e
ve
r
,
ove
r
ti
m
e
,
th
e
le
a
r
ni
ng
r
a
te
c
a
n
de
c
r
e
a
s
e
to
ve
r
y
s
m
a
ll
va
lu
e
s
,
w
hi
c
h
c
a
n
s
lo
w
dow
n
le
a
r
ni
ng.
A
da
pt
iv
e
m
om
e
nt
e
s
ti
m
a
ti
on
(
A
da
m
)
is
one
of
th
e
m
os
t
popula
r
opt
im
iz
e
r
s
t
ha
t
c
om
bi
ne
s
t
he
a
dva
nt
a
ge
s
of
bot
h A
da
G
r
a
d a
nd R
M
S
pr
op. I
t
us
e
s
bot
h t
he
f
ir
s
t
m
om
e
nt
(
m
e
a
n
of
gr
a
di
e
nt
s
)
a
nd t
he
s
e
c
ond mom
e
nt
(
m
e
a
n of
s
qua
r
e
d gr
a
di
e
nt
s
)
t
o dyna
m
ic
a
ll
y a
dj
us
t
th
e
l
e
a
r
ni
ng r
a
te
[
37]
.
T
hi
s
a
ll
ow
s
f
a
s
te
r
r
e
a
c
hi
ng of
t
he
l
os
s
f
unc
ti
on mi
ni
m
um
, e
s
pe
c
ia
ll
y i
n t
he
e
a
r
ly
s
ta
g
e
s
of
t
r
a
in
in
g. T
h
e
A
da
m
opt
im
iz
e
r
a
ls
o
ha
s
it
s
dr
a
w
b
a
c
ks
th
a
t
s
houl
d
b
e
c
on
s
id
e
r
e
d.
S
im
il
a
r
to
R
M
S
pr
op,
A
da
m
us
e
s
e
xpon
e
nt
ia
l
s
m
oot
hi
ng
to
c
a
lc
ul
a
t
e
th
e
f
ir
s
t
a
nd
s
e
c
o
nd
m
om
e
nt
s
of
gr
a
di
e
nt
s
,
w
hi
c
h
c
a
n
le
a
d
to
bi
a
s
e
d
e
s
ti
m
a
te
s
in
th
e
e
a
r
ly
s
ta
ge
s
of
tr
a
in
in
g
a
nd
a
f
f
e
c
t
opt
im
iz
a
ti
on
s
ta
bi
li
ty
.
A
lt
hough
A
da
m
w
or
ks
w
e
ll
on
m
a
ny
ta
s
ks
,
it
m
a
y
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a
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im
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s
pe
c
i
a
ll
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pr
obl
e
m
a
ti
c
f
or
c
om
pl
e
x
or
ve
r
y
n
oi
s
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ta
s
k
s
.
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ddi
ti
ona
ll
y,
A
da
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r
e
qui
r
e
s
m
or
e
c
om
put
a
ti
ona
l
r
e
s
our
c
e
s
c
om
pa
r
e
d t
o s
im
pl
e
r
m
e
th
ods
l
ik
e
S
G
D
, w
hi
c
h c
a
n be
a
pr
obl
e
m
f
o
r
l
a
r
ge
m
ode
ls
or
la
r
ge
da
ta
s
e
ts
.
I
n ge
ne
r
a
l,
t
he
c
hoi
c
e
of
opt
im
iz
e
r
de
pe
nds
on t
he
s
pe
c
if
ic
t
a
s
k,
m
ode
l
a
r
c
hi
te
c
tu
r
e
, a
nd da
ta
s
e
t
[
30]
,
[
38]
.
A
n
in
c
or
r
e
c
t
c
hoi
c
e
c
a
n
le
a
d
to
pr
ol
onge
d
tr
a
in
in
g,
in
s
t
a
bi
li
ty
,
or
uns
a
ti
s
f
a
c
to
r
y
r
e
s
ul
ts
.
A
s
a
r
e
s
ul
t,
s
uc
c
e
s
s
in
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
de
p
e
nds
not
onl
y
on
th
e
m
od
e
l
a
r
c
hi
te
c
tu
r
e
but
a
ls
o
on
th
e
e
f
f
e
c
ti
ve
c
hoi
c
e
of
opt
im
iz
e
r
,
w
hi
c
h
unde
r
s
c
or
e
s
th
e
im
por
ta
nc
e
of
it
s
us
e
w
h
e
n
c
r
e
a
ti
ng
hi
ghl
y
e
f
f
e
c
ti
ve
f
or
e
c
a
s
ti
ng
m
ode
ls
ba
s
e
d
on
a
r
ti
f
ic
ia
l
ne
ur
a
l
ne
twor
ks
.
T
he
r
e
f
or
e
,
th
e
s
e
c
ond
ta
s
k of
th
is
s
tu
dy a
r
is
e
s
,
w
hi
c
h
in
vol
ve
s
th
e
c
or
r
e
c
t
s
e
le
c
ti
on
of
a
n
opt
im
iz
e
r
f
or
th
e
m
odi
f
ie
d
tr
a
ns
f
or
m
e
r
m
ode
l
t
ha
t
w
oul
d
p
r
ovi
de
th
e
be
s
t
m
ode
l
pe
r
f
or
m
a
nc
e
c
ha
r
a
c
te
r
is
ti
c
s
a
c
c
or
di
ng t
o us
e
r
-
s
e
le
c
te
d c
r
it
e
r
ia
.
T
ha
t
is
w
hy
th
i
s
w
or
k
a
im
s
to
m
odi
f
y
th
e
ba
s
i
c
a
r
c
hi
te
c
tu
r
e
of
tr
a
ns
f
or
m
e
r
s
to
s
ol
ve
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
pr
obl
e
m
s
a
nd
to
s
e
le
c
t,
s
tu
dy,
a
nd
e
xpe
r
im
e
nt
a
ll
y
a
na
ly
z
e
th
e
la
te
s
t
opt
im
iz
a
ti
on
m
e
th
ods
to
im
pr
ove
th
e
e
f
f
ic
ie
nc
y
of
th
e
m
odi
f
ie
d
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
m
ode
l
in
m
e
te
or
ol
ogy.
T
he
m
a
in
c
ont
r
ib
ut
io
ns
of
t
hi
s
pa
pe
r
a
r
e
t
he
f
ol
lo
w
in
g:
−
W
e
m
odi
f
ie
d t
he
a
r
c
hi
te
c
tu
r
e
of
t
he
t
r
a
n
s
f
or
m
e
r
m
ode
l
by r
e
m
o
vi
ng t
he
t
oke
ni
z
e
r
a
nd
e
m
be
ddi
ng l
a
ye
r
, a
s
w
e
ll
a
s
r
e
pl
a
c
in
g
pos
it
io
na
l
e
nc
odi
ng
w
it
h
s
in
us
oi
da
l
po
s
it
io
na
l
e
nc
odi
ng
a
nd
ba
tc
h
nor
m
a
li
z
a
ti
on
w
it
h
la
ye
r
nor
m
a
li
z
a
ti
on,
w
hi
c
h
e
na
bl
e
d
e
f
f
e
c
ti
ve
s
ol
vi
ng
of
ti
m
e
s
e
r
i
e
s
f
or
e
c
a
s
ti
ng
ta
s
ks
in
th
e
c
a
s
e
of
a
na
ly
z
in
g
a
l
a
r
ge
a
m
ount
of
da
ta
w
it
h pr
onounc
e
d s
e
a
s
ona
li
ty
.
−
W
e
s
e
le
c
te
d,
s
tu
di
e
d,
a
nd
c
onduc
te
d
a
n
e
xpe
r
im
e
nt
a
l
c
om
p
a
r
is
o
n
of
a
num
be
r
of
s
ta
te
-
of
-
th
e
-
a
r
t
opt
im
iz
e
r
s
,
e
s
pe
c
ia
ll
y
th
e
ir
s
c
he
dul
e
-
f
r
e
e
ve
r
s
io
n
s
,
to
im
pr
ove
f
or
e
c
a
s
ti
ng
a
c
c
ur
a
c
y
a
nd
r
e
du
c
e
th
e
s
iz
e
of
th
e
m
odi
f
ie
d
tr
a
ns
f
or
m
e
r
m
ode
l
a
nd,
a
c
c
or
di
ngl
y,
it
s
tr
a
in
in
g
ti
m
e
w
he
n
s
ol
vi
ng
s
e
a
s
on
a
l
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
pr
obl
e
m
s
i
n t
he
f
ie
ld
of
m
e
te
or
ol
ogy.
T
he
pa
pe
r
is
s
tr
uc
tu
r
e
d
a
s
f
ol
lo
w
s
:
s
e
c
ti
on
2
pr
e
s
e
nt
s
th
e
m
odi
f
ic
a
ti
on
of
th
e
tr
a
ns
f
or
m
e
r
m
ode
l
f
o
r
s
ol
vi
ng
th
e
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
pr
obl
e
m
,
it
s
a
r
c
hi
te
c
tu
r
e
is
p
r
e
s
e
nt
e
d,
a
ll
c
ha
nge
s
m
a
de
a
nd
th
e
ir
a
dva
nt
a
ge
s
a
r
e
e
xpl
a
in
e
d.
T
hi
s
s
e
c
ti
on
a
ls
o
de
s
c
r
ib
e
s
th
e
pr
in
c
ip
le
s
of
ope
r
a
ti
on,
a
dva
nt
a
ge
s
,
a
nd
di
s
a
dva
nt
a
g
e
s
of
a
num
be
r
of
s
ta
te
-
of
-
th
e
-
a
r
t
opt
im
iz
e
r
s
th
a
t
w
e
r
e
us
e
d
in
pr
a
c
ti
c
a
l
r
e
s
e
a
r
c
h
to
im
pr
ove
th
e
e
f
f
ic
ie
nc
y
of
us
in
g
th
e
m
odi
f
ie
d
tr
a
ns
f
or
m
e
r
m
ode
l.
S
e
c
ti
on
3
pr
ovi
de
s
a
de
s
c
r
ip
ti
on
of
th
e
da
ta
s
e
t
u
s
e
d
f
or
m
ode
li
ng,
in
di
c
a
to
r
s
of
th
e
e
f
f
e
c
ti
ve
ne
s
s
of
us
in
g
th
e
tr
a
ns
f
or
m
e
r
m
ode
l.
A
l
s
o,
he
r
e
,
m
ode
li
ng
of
th
e
w
or
k
of
a
num
b
e
r
of
s
tu
di
e
d
opt
im
iz
e
r
s
i
s
c
a
r
r
ie
d out a
nd t
he
r
e
s
ul
ts
of
t
he
ir
w
or
k a
r
e
s
um
m
a
r
iz
e
d ba
s
e
d on s
e
v
e
r
a
l
c
r
it
e
r
ia
. A
c
om
pa
r
is
on
of
th
e
ir
w
or
k
is
p
e
r
f
or
m
e
d
a
nd
th
e
c
hoi
c
e
of
th
e
b
e
s
t
of
th
e
m
f
or
pr
a
c
ti
c
a
l
im
pl
e
m
e
nt
a
ti
on
a
nd
u
s
e
of
th
e
m
odi
f
ie
d
tr
a
ns
f
or
m
e
r
m
ode
l
f
or
f
or
e
c
a
s
ti
ng
s
e
a
s
on
a
l
ti
m
e
s
e
r
ie
s
in
th
e
f
ie
ld
of
m
e
te
or
ol
ogy
is
ju
s
ti
f
ie
d.
S
e
c
ti
on 4 pr
e
s
e
nt
s
c
onc
lu
s
io
ns
on t
he
obt
a
in
e
d r
e
s
ul
ts
a
nd d
e
s
c
r
ib
e
s
pr
os
pe
c
ts
f
or
f
ur
th
e
r
r
e
s
e
a
r
c
h.
2.
M
E
T
H
O
D
S
T
hi
s
s
e
c
ti
on
pr
e
s
e
nt
s
a
m
odi
f
ic
a
ti
on
of
th
e
tr
a
ns
f
or
m
e
r
m
ode
l
f
or
s
ol
vi
ng
th
e
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
pr
obl
e
m
,
a
s
w
e
ll
a
s
th
e
pr
in
c
ip
le
s
of
ope
r
a
ti
on,
a
dva
nt
a
g
e
s
, a
nd
di
s
a
dva
nt
a
ge
s
of
a
num
be
r
of
s
ta
te
-
of
-
th
e
-
a
r
t
opt
im
iz
e
r
s
f
or
t
hi
s
m
ode
l.
2.1. M
od
if
ie
d
ar
c
h
it
e
c
t
u
r
e
of
t
h
e
t
r
an
s
f
or
m
e
r
s
f
o
r
s
ol
vi
n
g t
im
e
s
e
r
ie
s
f
or
e
c
as
t
in
g t
as
k
s
T
he
tr
a
n
s
f
or
m
e
r
a
r
c
hi
te
c
tu
r
e
ha
s
be
c
om
e
one
of
th
e
m
o
s
t
po
pul
a
r
m
e
th
ods
in
m
a
c
hi
ne
l
e
a
r
ni
ng,
e
s
pe
c
ia
ll
y
in
na
tu
r
a
l
la
ngu
a
ge
pr
oc
e
s
s
in
g
[
31]
.
T
r
a
ns
f
or
m
e
r
s
a
r
e
us
e
d
in
ta
s
k
s
s
u
c
h
a
s
t
e
xt
tr
a
ns
la
ti
on,
que
s
ti
on
a
ns
w
e
r
in
g,
a
nd
s
e
nt
im
e
nt
a
na
ly
s
i
s
,
due
to
th
e
ir
a
bi
li
ty
to
e
f
f
ic
ie
nt
ly
pr
oc
e
s
s
lo
ng
s
e
que
nc
e
s
of
da
ta
a
nd
c
a
pt
ur
e
de
pe
nde
nc
ie
s
be
twe
e
n
di
s
ta
nt
e
le
m
e
nt
s
.
T
he
m
a
in
c
om
pone
nt
s
of
a
tr
a
ns
f
or
m
e
r
a
r
e
th
e
e
nc
ode
r
a
nd
de
c
ode
r
,
w
hi
c
h a
ll
ow
t
he
m
ode
l
to
unde
r
s
ta
nd t
he
c
ont
e
xt
a
nd s
tr
uc
tu
r
e
of
i
nput
da
ta
[
31]
.
T
r
a
ns
f
or
m
e
r
s
c
a
n
a
ls
o
be
e
f
f
e
c
ti
ve
ly
a
ppl
ie
d
to
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng.
T
hi
s
is
e
s
pe
c
ia
ll
y
us
e
f
ul
w
he
n
a
na
ly
z
in
g
m
a
ny
ti
m
e
s
e
r
ie
s
r
e
la
te
d
to
a
s
in
gl
e
to
pi
c
,
s
uc
h
a
s
w
e
a
th
e
r
c
ondi
ti
ons
.
I
n
th
e
c
a
s
e
of
w
e
a
th
e
r
f
or
e
c
a
s
ti
ng, we
ha
ve
v
a
r
io
us
va
r
ia
bl
e
s
s
uc
h
a
s
t
e
m
pe
r
a
tu
r
e
, hu
m
id
it
y, a
tm
os
phe
r
ic
pr
e
s
s
ur
e
, a
nd
pr
e
c
ip
it
a
ti
on,
w
hi
c
h i
nt
e
r
a
c
t
w
it
h
e
a
c
h
ot
he
r
a
nd h
a
ve
c
om
pl
e
x t
im
e
d
e
pe
nde
nc
ie
s
.
T
r
a
ns
f
or
m
e
r
s
a
ll
ow
t
he
m
ode
l
t
o c
a
pt
ur
e
th
e
s
e
de
pe
nd
e
nc
ie
s
a
nd us
e
t
he
m
f
or
a
c
c
ur
a
te
pr
e
di
c
ti
on of
f
ut
ur
e
va
lu
e
s
.
T
he
s
tr
uc
tu
r
e
a
nd
m
a
in
c
om
pon
e
nt
s
of
th
e
m
odi
f
ie
d
tr
a
ns
f
or
m
e
r
a
r
c
hi
te
c
tu
r
e
f
or
th
e
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
ta
s
k,
in
c
lu
di
ng
th
e
e
nc
ode
r
a
nd
de
c
ode
r
,
a
r
e
pr
e
s
e
n
te
d
in
F
ig
ur
e
1.
I
t'
s
w
or
th
not
in
g
a
num
be
r
of
di
f
f
e
r
e
nc
e
s
f
r
om
t
he
c
la
s
s
ic
t
r
a
ns
f
or
m
e
r
a
r
c
hi
te
c
tu
r
e
[
31]
:
−
R
e
m
ova
l
of
th
e
to
ke
ni
z
e
r
.
I
n
th
e
c
la
s
s
ic
tr
a
ns
f
or
m
e
r
a
r
c
hi
te
c
tu
r
e
,
th
e
to
ke
ni
z
e
r
is
us
e
d
to
c
onve
r
t
in
put
da
ta
in
to
t
oke
ns
. I
n t
he
a
da
pt
e
d
a
r
c
hi
te
c
tu
r
e
, t
hi
s
c
om
pon
e
nt
w
a
s
r
e
m
ove
d, s
im
pl
if
yi
ng t
he
m
ode
l
a
nd r
e
duc
in
g
it
s
c
om
put
a
ti
ona
l
c
om
pl
e
xi
ty
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
.
14
, N
o.
2
,
A
pr
il
20
25
:
1
067
-
1
076
1070
−
R
e
m
ova
l
of
t
he
e
m
be
ddi
ng l
a
ye
r
. I
n t
he
c
la
s
s
ic
a
r
c
hi
te
c
tu
r
e
, t
he
e
m
be
ddi
ng l
a
ye
r
i
s
u
s
e
d t
o
c
onve
r
t
to
ke
ns
in
to
f
ix
e
d
-
di
m
e
ns
io
n
ve
c
to
r
s
.
I
n
th
e
a
da
pt
e
d
a
r
c
hi
te
c
tu
r
e
,
th
i
s
l
a
ye
r
w
a
s
a
ls
o
r
e
m
ove
d,
f
ur
th
e
r
s
im
pl
if
yi
ng
th
e
m
ode
l.
−
S
in
us
oi
da
l
pos
it
io
na
l
e
nc
odi
ng.
I
ns
te
a
d
of
tr
a
di
ti
ona
l
pos
it
io
na
l
e
nc
odi
ng,
s
in
us
oi
da
l
pos
it
io
na
l
e
nc
odi
ng
w
a
s
us
e
d.
T
hi
s
e
nc
odi
ng
h
a
s
no
le
a
r
na
bl
e
pa
r
a
m
e
te
r
s
a
nd
is
s
pe
c
if
ic
a
ll
y
de
s
ig
n
e
d
to
be
tt
e
r
r
e
f
le
c
t
th
e
c
ha
r
a
c
te
r
is
ti
c
s
of
ti
m
e
s
e
que
nc
e
s
.
I
t
na
tu
r
a
ll
y
gi
ve
s
m
or
e
w
e
ig
ht
to
r
e
c
e
nt
e
le
m
e
nt
s
a
nd
a
ll
ow
s
th
e
m
ode
l
to
pr
e
s
e
r
ve
th
e
or
de
r
of
da
ta
in
th
e
ti
m
e
s
e
que
nc
e
,
w
hi
c
h
is
c
r
it
ic
a
ll
y
im
por
ta
nt
w
he
n
a
na
ly
z
in
g
ti
m
e
s
e
r
ie
s
.
−
L
a
ye
r
nor
m
a
li
z
a
ti
on.
I
n
th
e
c
la
s
s
ic
a
r
c
hi
te
c
tu
r
e
,
ba
tc
h
nor
m
a
li
z
a
ti
on
is
of
te
n
u
s
e
d,
w
hi
c
h
nor
m
a
li
z
e
s
th
e
out
put
s
of
pr
e
vi
ous
l
a
y
e
r
s
us
in
g
s
ta
ti
s
ti
c
s
f
r
om
t
he
e
nt
ir
e
ba
tc
h
of
da
ta
. H
ow
e
ve
r
, f
or
m
ode
l
s
w
or
ki
ng w
it
h
ti
m
e
s
e
r
ie
s
,
th
is
a
ppr
oa
c
h
m
a
y
not
be
th
e
be
s
t
c
hoi
c
e
.
U
s
in
g
la
y
e
r
nor
m
a
li
z
a
ti
on
in
th
e
a
da
pt
e
d
a
r
c
hi
te
c
tu
r
e
e
ns
ur
e
s
tr
a
in
in
g
s
ta
bi
li
ty
,
a
s
th
e
nor
m
a
li
z
a
ti
on
o
f
out
put
s
is
c
a
r
r
i
e
d
out
e
xc
lu
s
iv
e
ly
ba
s
e
d
on
th
e
di
s
tr
ib
ut
io
n
m
om
e
nt
s
of
a
s
in
gl
e
la
y
e
r
a
nd
do
e
s
not
de
pe
nd
on
th
e
ba
tc
h s
iz
e
.
T
hi
s
m
it
ig
a
te
s
pr
obl
e
m
s
a
s
s
o
c
ia
te
d
w
it
h
a
c
c
ount
in
g f
or
pos
s
ib
le
s
e
a
s
ona
l
or
c
yc
li
c
a
l
c
om
pone
nt
s
of
t
im
e
s
e
r
ie
s
.
F
ig
ur
e
1. T
he
m
odi
f
ie
d a
r
c
hi
te
c
tu
r
e
of
t
he
t
r
a
ns
f
or
m
e
r
m
ode
l
f
o
r
t
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
R
e
m
ovi
ng
th
e
to
ke
ni
z
e
r
a
nd
e
m
be
ddi
ng
la
ye
r
,
w
hi
c
h
a
r
e
t
ypi
c
a
ll
y
us
e
d
f
or
na
tu
r
a
l
la
ngua
ge
pr
oc
e
s
s
in
g,
a
ll
ow
s
s
im
pl
if
yi
ng
th
e
m
ode
l
a
nd
r
e
duc
in
g
it
s
c
om
put
a
ti
ona
l
c
om
pl
e
xi
ty
.
U
s
in
g
s
in
u
s
oi
da
l
pos
it
io
na
l
e
nc
odi
ng i
n t
he
a
da
pt
e
d
a
r
c
hi
te
c
tu
r
e
f
or
t
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng pr
ovi
de
s
b
e
tt
e
r
r
e
pr
e
s
e
nt
a
ti
on of
t
he
da
ta
s
e
que
nc
e
a
nd pr
e
s
e
r
va
ti
on of
t
he
ir
o
r
de
r
.
L
a
ye
r
nor
m
a
li
z
a
t
io
n, i
n t
ur
n,
pr
ovi
de
s
gr
e
a
te
r
t
r
a
in
in
g s
ta
bi
li
ty
,
r
e
ga
r
dl
e
s
s
of
th
e
ba
t
c
h
s
iz
e
,
w
hi
c
h
is
e
s
p
e
c
ia
ll
y
im
por
ta
nt
w
he
n
w
or
ki
ng
w
it
h
ti
m
e
s
e
r
ie
s
.
A
l
l
th
e
s
e
c
ha
nge
s
m
a
ke
t
he
a
da
pt
e
d t
r
a
n
s
f
or
m
e
r
a
r
c
hi
te
c
tu
r
e
m
or
e
a
da
pt
iv
e
a
nd r
obus
t
f
or
a
na
ly
z
in
g va
r
io
us
dyna
m
ic
pr
ope
r
ti
e
s
of
da
ta
,
im
pr
ovi
ng
ove
r
a
ll
a
c
c
ur
a
c
y
a
nd
c
om
put
a
ti
ona
l
e
f
f
ic
ie
nc
y.
T
hi
s
a
ll
ow
s
obt
a
in
in
g
m
or
e
a
c
c
ur
a
te
f
or
e
c
a
s
ts
a
nd
r
e
duc
in
g
c
om
put
a
ti
ona
l
c
os
t
s
,
w
hi
c
h
is
im
por
ta
nt
w
he
n
s
ol
vi
ng
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
pr
obl
e
m
s
.
2.2. Clas
s
ic
al
an
d
s
t
at
e
-
of
-
t
h
e
-
ar
t
s
op
t
im
iz
e
r
s
f
or
ar
t
i
f
ic
ia
l
n
e
u
r
al
n
e
t
w
or
k
s
A
n i
m
por
ta
nt
c
om
pone
nt
of
a
hi
ghl
y e
f
f
e
c
ti
ve
t
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng mode
l
ba
s
e
d on tr
a
ns
f
or
m
e
r
s
i
s
th
e
opt
im
iz
e
r
i
t
us
e
s
. I
n t
hi
s
pa
pe
r
,
t
he
e
f
f
e
c
ti
ve
ne
s
s
of
s
e
v
e
r
a
l
c
la
s
s
ic
a
l
a
nd
c
om
pl
e
te
ly
ne
w
[
31]
opt
im
iz
a
ti
on
m
e
th
ods
de
ve
lo
pe
d
in
2024
w
a
s
in
ve
s
ti
ga
te
d
.
O
ne
of
th
e
c
la
s
s
ic
a
l
opt
im
iz
e
r
s
us
e
d
dur
in
g
th
e
tr
a
in
in
g
of
a
r
ti
f
ic
ia
l
ne
ur
a
l
ne
twor
ks
is
th
e
S
G
D
m
e
th
od.
T
hi
s
m
e
th
od
in
v
ol
ve
s
upda
ti
ng
th
e
m
ode
l
pa
r
a
m
e
te
r
s
ba
s
e
d
on
th
e
gr
a
di
e
nt
s
of
th
e
lo
s
s
f
unc
ti
on
c
onc
e
r
ni
ng
th
e
m
ode
l
pa
r
a
m
e
te
r
s
[
34]
.
I
n
th
e
S
G
D
m
e
th
od,
pa
r
a
m
e
te
r
upda
te
s
a
r
e
c
a
r
r
ie
d
out
f
or
e
a
c
h
in
di
vi
dua
l
s
a
m
pl
e
(
or
s
m
a
ll
ba
tc
h
of
s
a
m
pl
e
s
)
f
r
om
th
e
tr
a
in
in
g
da
ta
s
e
t.
T
he
upda
t
e
f
or
m
ul
a
i
n t
hi
s
c
a
s
e
l
ooks
l
ik
e
t
hi
s
[
34]
:
+
1
=
−
×
(
(
)
)
(
1)
T
he
S
G
D
m
e
th
od ha
s
s
e
ve
r
a
l
im
por
ta
nt
a
dva
nt
a
ge
s
[
34]
.
F
ir
s
tl
y, i
t
is
c
ha
r
a
c
te
r
iz
e
d by high s
pe
e
d, a
s
pa
r
a
m
e
te
r
upda
te
s
a
r
e
c
a
r
r
ie
d
out
a
f
te
r
e
a
c
h
s
a
m
pl
e
or
s
m
a
ll
ba
tc
h
of
s
a
m
pl
e
s
.
T
hi
s
m
a
ke
s
it
s
ig
ni
f
ic
a
nt
ly
f
a
s
te
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
Sc
he
dul
e
-
fr
e
e
opt
imi
z
at
io
n of
t
he
tr
an
s
fo
r
m
e
r
s
-
ba
s
e
d t
ime
s
e
r
i
e
s
f
or
e
c
a
s
ti
ng m
ode
l
(
K
y
r
y
lo
Y
e
m
e
ts
)
1071
th
a
n
c
la
s
s
ic
a
l
gr
a
di
e
nt
de
s
c
e
nt
,
e
s
pe
c
ia
ll
y
f
or
la
r
ge
da
ta
s
e
ts
.
S
e
c
ondl
y,
th
e
m
e
th
od
is
m
e
m
or
y
e
f
f
ic
ie
nt
,
a
s
it
r
e
qui
r
e
s
le
s
s
m
e
m
or
y,
pr
oc
e
s
s
in
g
s
m
a
ll
por
ti
ons
of
da
ta
a
t
a
ti
m
e
.
H
ow
e
ve
r
,
th
e
m
e
th
od
a
ls
o
ha
s
c
e
r
ta
in
di
s
a
dva
nt
a
ge
s
[
34]
.
F
or
e
xa
m
pl
e
,
pa
r
a
m
e
t
e
r
upda
te
s
c
a
n
b
e
ve
r
y
noi
s
y,
w
hi
c
h
c
a
n
le
a
d
to
s
ig
ni
f
ic
a
nt
f
lu
c
tu
a
ti
ons
in
th
e
lo
s
s
f
unc
ti
on.
A
ddi
ti
ona
ll
y,
c
hoos
in
g
th
e
c
o
r
r
e
c
t
le
a
r
ni
ng
r
a
te
is
c
r
it
ic
a
ll
y
im
por
ta
nt
.
T
oo
hi
gh or
t
oo l
ow
l
e
a
r
ni
ng r
a
te
c
a
n l
e
a
d t
o c
onve
r
ge
nc
e
pr
obl
e
m
s
,
c
om
pl
ic
a
ti
ng t
he
m
o
de
l
tr
a
in
in
g pr
oc
e
s
s
.
A
ne
w
v
e
r
s
io
n
of
th
is
m
e
th
od
c
a
ll
e
d
s
c
he
dul
e
-
f
r
e
e
S
G
D
[
39]
,
w
hi
c
h
w
a
s
de
ve
lo
pe
d
in
2024,
a
im
s
to
r
e
m
ove
th
e
s
e
dr
a
w
ba
c
ks
.
O
ne
of
th
e
m
a
in
a
dva
nt
a
ge
s
of
s
c
he
dul
e
-
f
r
e
e
S
G
D
is
th
a
t
it
e
li
m
in
a
te
s
th
e
ne
e
d
t
o
a
dj
us
t
th
e
le
a
r
ni
ng
r
a
te
.
I
n
c
la
s
s
ic
a
l
S
G
D
,
th
is
pa
r
a
m
e
te
r
r
e
qui
r
e
s
c
a
r
e
f
ul
tu
ni
ng
a
nd
m
a
y
r
e
qui
r
e
th
e
us
e
of
a
ddi
ti
ona
l
m
e
th
ods
,
s
uc
h
a
s
le
a
r
ni
ng
r
a
te
s
c
he
dul
e
r
s
,
to
dyn
a
m
ic
a
ll
y
c
ha
nge
th
e
le
a
r
ni
ng
r
a
te
dur
in
g
th
e
op
ti
m
iz
a
ti
on
pr
oc
e
s
s
.
I
n
s
c
he
dul
e
-
f
r
e
e
S
G
D
,
th
is
ne
c
e
s
s
it
y
di
s
a
ppe
a
r
s
,
s
im
pl
if
yi
ng
th
e
m
ode
l
tu
ni
ng
p
r
oc
e
s
s
a
nd r
e
duc
in
g pr
e
pa
r
a
ti
on t
im
e
. I
n pa
r
ti
c
ul
a
r
, i
ts
i
m
pl
e
m
e
nt
a
ti
on c
a
n be
de
s
c
r
ib
e
d a
s
f
ol
lo
w
s
[
39]
:
=
(
1
−
)
+
(
2)
+
1
=
−
×
(
(
,
)
)
(
3)
+
1
=
(
1
−
+
1
)
+
+
1
+
1
(
4)
O
ne
of
th
e
w
id
e
ly
us
e
d
opt
im
iz
a
ti
on
m
e
th
ods
is
a
da
pt
iv
e
m
om
e
nt
e
s
ti
m
a
ti
on
w
it
h
w
e
ig
ht
de
c
a
y
(
A
da
m
W
)
, w
hi
c
h i
s
a
n i
m
pr
ove
d ve
r
s
io
n of
t
he
popula
r
A
da
m
opt
im
iz
e
r
, de
ve
lo
pe
d t
o s
ol
ve
pr
obl
e
m
s
r
e
la
te
d
to
w
e
ig
ht
r
e
gul
a
r
iz
a
ti
on
in
ne
ur
a
l
ne
twor
ks
[
38]
.
T
he
m
a
in
id
e
a
of
A
da
m
W
is
to
s
e
pa
r
a
te
th
e
pr
oc
e
s
s
of
w
e
ig
ht
upda
ti
ng
a
nd
r
e
gul
a
r
iz
a
ti
on,
w
hi
c
h
a
ll
ow
s
a
voi
di
ng
s
om
e
of
t
he
dr
a
w
ba
c
ks
of
th
e
or
ig
in
a
l
A
da
m
a
lg
or
it
h
m
[
40]
.
L
ik
e
A
da
m
,
A
da
m
W
c
om
bi
ne
s
id
e
a
s
f
r
om
A
da
G
r
a
d
a
nd
R
M
S
pr
op
m
e
th
ods
f
or
a
da
pt
iv
e
le
a
r
ni
ng
r
a
te
a
dj
us
tm
e
nt
f
or
e
a
c
h
pa
r
a
m
e
te
r
.
H
ow
e
ve
r
,
unl
ik
e
A
da
m
,
A
d
a
m
W
a
ppl
ie
s
w
e
ig
ht
r
e
gul
a
r
iz
a
ti
on
s
e
pa
r
a
te
ly
f
r
om
gr
a
di
e
nt
upda
te
s
, pr
ovi
di
ng be
tt
e
r
c
onve
r
ge
nc
e
a
nd
e
f
f
ic
i
e
nc
y.
A
t
e
a
c
h
it
e
r
a
ti
on,
th
e
A
da
m
W
opt
im
iz
e
r
c
a
lc
ul
a
te
s
th
e
gr
a
di
e
nt
to
m
in
im
iz
e
th
e
f
unc
ti
on.
T
he
ps
e
udoc
ode
f
or
A
da
m
W
i
s
s
how
n
in
F
ig
ur
e
2.
T
he
n
w
e
up
da
te
th
e
w
e
ig
ht
s
ta
ki
ng
in
to
a
c
c
ount
w
e
ig
ht
r
e
gul
a
r
iz
a
ti
on [
39]
:
←
−
1
−
−
1
(
5)
A
f
te
r
t
ha
t
upda
ti
ng mom
e
nt
um
of
f
i
r
s
t
a
nd s
e
c
ond or
de
r
[
39]
:
←
1
−
1
+
(
1
−
1
)
(
6)
←
2
−
1
+
(
1
−
2
)
2
(
7)
A
f
te
r
t
hi
s
, bi
a
s
-
c
or
r
e
c
te
d m
om
e
nt
um
s
:
←
/
(
1
−
1
)
(
8)
̂
←
/
(
1
−
2
)
(
9)
A
nd w
e
upda
te
t
he
w
e
ig
ht
s
a
ga
in
c
on
s
id
e
r
in
g t
he
m
om
e
nt
um
s
:
←
−
̂
/
(
√
̂
+
)
(
10)
A
da
m
W
ha
s
s
e
ve
r
a
l
im
por
ta
nt
a
dva
nt
a
ge
s
.
F
ir
s
tl
y,
th
a
nks
to
t
he
s
e
pa
r
a
ti
on
of
w
e
ig
ht
upda
te
s
a
nd
r
e
gul
a
r
iz
a
ti
on,
m
or
e
s
ta
bl
e
a
nd
f
a
s
t
le
a
r
ni
ng
i
s
e
n
s
ur
e
d,
c
ont
r
ib
ut
in
g
to
be
tt
e
r
c
onve
r
ge
nc
e
.
S
e
c
ondl
y,
e
f
f
e
c
ti
ve
w
e
ig
ht
r
e
gul
a
r
iz
a
ti
on
oc
c
ur
s
s
e
p
a
r
a
te
ly
,
w
hi
c
h
a
ll
o
w
s
a
voi
di
n
g
pr
obl
e
m
s
a
s
s
oc
ia
te
d
w
it
h
e
xc
e
s
s
iv
e
w
e
ig
ht
r
e
gul
a
r
iz
a
ti
on.
T
hi
r
dl
y,
li
ke
A
da
m
,
A
d
a
m
W
a
ut
om
a
ti
c
a
ll
y
a
dj
us
ts
th
e
le
a
r
ni
ng
r
a
te
f
or
e
a
c
h
pa
r
a
m
e
te
r
,
m
a
ki
ng
it
e
f
f
e
c
ti
ve
f
or
di
f
f
e
r
e
nt
t
ype
s
of
t
a
s
ks
. H
ow
e
ve
r
, A
da
m
W
a
ls
o
ha
s
di
s
a
dva
nt
a
ge
s
. F
or
e
xa
m
pl
e
, pr
ope
r
t
uni
ng
of
hype
r
pa
r
a
m
e
te
r
s
c
a
n
b
e
di
f
f
ic
ul
t,
a
s
w
it
h
ot
he
r
a
da
pt
iv
e
opt
im
iz
e
r
s
.
A
ddi
ti
ona
ll
y,
A
da
m
W
r
e
qui
r
e
s
m
or
e
c
om
put
a
ti
ona
l
r
e
s
our
c
e
s
c
om
p
a
r
e
d t
o s
im
pl
e
r
m
e
th
ods
s
uc
h
a
s
S
G
D
.
T
hi
s
pr
obl
e
m
of
A
da
m
W
,
s
uc
h
a
s
hype
r
pa
r
a
m
e
te
r
tu
ni
ng,
is
s
ol
ve
d
by
it
s
s
c
he
dul
e
-
f
r
e
e
m
odi
f
ic
a
ti
on,
a
nd
th
is
is
ho
w
th
e
m
odi
f
ie
d
s
c
he
dul
e
-
f
r
e
e
ve
r
s
io
n
of
A
da
m
W
lo
oks
.
I
n
th
is
v
e
r
s
io
n
of
th
e
opt
im
iz
e
r
,
th
e
c
a
lc
ul
a
ti
on
of
th
e
s
e
c
ond
-
or
de
r
m
om
e
nt
is
r
e
pl
a
c
e
d
b
y
a
c
om
bi
n
a
ti
on
of
in
te
r
pol
a
ti
ons
a
nd
a
ve
r
a
ge
s
.
T
he
a
dde
d
ve
r
s
io
n l
ooks
l
ik
e
t
hi
s
[
39]
:
=
×
(
1
,
/
)
(
11)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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N
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8938
I
nt
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A
r
ti
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I
nt
e
ll
, V
ol
.
14
, N
o.
2
,
A
pr
il
20
25
:
1
067
-
1
076
1072
+
1
=
−
/
(
√
̂
+
)
−
(
12)
+
1
=
2
∑
=
1
2
(
13)
+
1
=
(
1
−
+
1
)
+
+
1
+
1
(
14)
T
he
s
e
opt
im
iz
e
r
s
de
s
c
r
ib
e
d
a
bov
e
w
e
r
e
u
s
e
d
in
th
i
s
w
or
k
to
c
on
duc
t
e
xpe
r
im
e
nt
a
l
s
tu
di
e
s
to
de
te
r
m
in
e
th
e
be
s
t
of
t
he
m
w
he
n s
ol
vi
ng t
he
t
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng pr
obl
e
m
ba
s
e
d
on t
he
m
odi
f
ie
d t
r
a
ns
f
or
m
e
r
m
ode
l.
3.
R
E
S
U
L
T
S
A
N
D
D
I
S
C
U
S
S
I
O
N
T
he
t
r
a
ns
f
or
m
e
r
m
ode
l
f
or
t
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng w
it
h di
f
f
e
r
e
n
t
opt
im
iz
e
r
s
w
a
s
t
r
a
in
e
d on a
w
e
a
th
e
r
da
ta
s
e
t
[
41]
. T
hi
s
da
ta
s
e
t
c
ont
a
in
s
3010 da
il
y t
im
e
s
e
r
ie
s
r
e
pr
e
s
e
nt
in
g c
ha
nge
s
i
n f
our
w
e
a
th
e
r
va
r
ia
bl
e
s
:
r
a
in
,
m
in
im
um
te
m
pe
r
a
tu
r
e
,
m
a
xi
m
um
te
m
pe
r
a
tu
r
e
,
a
nd
s
ol
a
r
r
a
di
a
ti
on,
m
e
a
s
ur
e
d
a
t
m
e
te
or
ol
ogi
c
a
l
s
ta
ti
ons
in
A
us
tr
a
li
a
.
T
hi
s
da
ta
s
e
t,
pr
ovi
de
d
by
th
e
A
us
tr
a
li
a
n
B
ur
e
a
u
of
M
e
te
or
ol
ogy
(
B
oM
)
,
in
c
lu
d
e
s
c
ur
r
e
nt
w
e
a
th
e
r
da
ta
f
or
s
pe
c
if
ic
s
ta
ti
ons
,
da
il
y
f
or
e
c
a
s
ts
f
or
a
ll
A
us
tr
a
li
a
n
f
or
e
c
a
s
t
lo
c
a
ti
ons
,
a
gr
ic
ul
tu
r
a
l
bul
le
ti
ns
w
it
h
s
um
m
a
r
iz
e
d
w
e
a
th
e
r
obs
e
r
va
ti
on
s
f
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c
h
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te
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r
it
or
y,
a
nd
s
a
te
ll
it
e
im
a
ge
s
in
G
e
oT
I
F
F
f
or
m
a
t.
T
he
da
ta
s
e
t
is
a
va
il
a
bl
e
in
X
M
L
a
nd
J
S
O
N
f
or
m
a
ts
a
nd
c
a
n
b
e
a
c
c
e
s
s
e
d
th
r
ough
a
n
a
nonymou
s
F
T
P
s
e
r
ve
r
.
T
he
da
ta
s
e
t
is
w
e
ll
-
s
tr
uc
tu
r
e
d
a
nd
of
f
e
r
s
f
e
a
tu
r
e
s
f
or
a
ut
om
a
ti
c
r
e
tr
ie
va
l
a
nd
pa
r
s
in
g
of
da
ta
in
to
or
de
r
e
d
da
ta
f
r
a
m
e
s
.
T
he
da
ta
ha
s
a
ppl
ic
a
ti
ons
in
a
gr
ic
ul
tu
r
e
, m
a
ppi
ng r
e
ne
w
a
bl
e
e
ne
r
gy pote
nt
ia
l,
a
nd pla
nni
ng f
o
r
m
uni
c
ip
a
li
ti
e
s
r
e
ga
r
di
ng e
xt
r
e
m
e
w
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th
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ve
nt
s
a
nd i
nf
r
a
s
tr
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tu
r
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ne
e
d
s
.
E
xpe
r
im
e
nt
a
l
s
tu
di
e
s
on
t
he
e
f
f
e
c
ti
v
e
ne
s
s
of
di
f
f
e
r
e
nt
opt
im
i
z
e
r
s
w
e
r
e
pe
r
f
or
m
e
d
by
r
unni
ng
th
e
m
ode
l
a
nd
th
e
c
or
r
e
s
pon
di
ng
opt
im
iz
e
r
w
it
h
di
f
f
e
r
e
nt
c
o
nt
e
x
t
le
ngt
hs
. I
t
w
a
s
a
m
ul
ti
pl
e
of
th
e
s
e
a
s
o
na
li
t
y
of
th
e
d
a
ta
in
th
e
da
t
a
s
e
t,
w
hi
c
h
e
s
s
e
nt
i
a
ll
y
r
e
pr
e
s
e
nt
s
o
ne
m
ont
h.
T
h
us
,
th
e
tr
a
n
s
f
or
m
e
r
m
ode
l
w
a
s
tr
a
in
e
d
on
l
e
ngt
hs
of
30,
6
0,
a
nd
90
d
a
y
s
.
T
he
e
v
a
lu
a
ti
on
of
th
e
m
od
e
l'
s
p
e
r
f
or
m
a
n
c
e
w
a
s
b
a
s
e
d
on
th
e
f
ol
l
ow
in
g
in
di
c
a
to
r
s
[
27]
,
[
34]
:
‒
M
e
a
n
a
b
s
ol
ut
e
e
r
r
or
(
M
A
E
):
=
1
∑
=
1
|
−
|
(
15)
‒
M
e
a
n s
qu
a
r
e
e
r
r
or
(
M
S
E
):
=
1
∑
=
1
(
−
)
2
(
16)
‒
R
oot
m
e
a
n s
qua
r
e
e
r
r
or
(
R
M
S
E
):
=
√
1
∑
=
1
(
−
)
2
(
17)
‒
S
ym
m
e
tr
ic
m
e
a
n a
bs
ol
ut
e
pe
r
c
e
nt
a
ge
e
r
r
or
(
S
М
А
P
Е
)
:
=
1
∑
=
1
|
−
|
(
|
|
+
|
|
)
/
2
(
18)
‒
M
e
a
n a
b
s
ol
ut
e
s
c
a
le
d e
r
r
or
(
М
А
S
Е
)
:
=
1
∑
=
1
|
−
|
|
−
|
(
19)
W
e
a
ls
o
us
e
d
th
e
num
be
r
of
tr
a
in
a
bl
e
m
ode
l
pa
r
a
m
e
te
r
s
,
e
xpr
e
s
s
e
d
in
th
ous
a
nds
,
w
hi
c
h
c
a
n
s
how
how
m
a
ny
r
e
s
our
c
e
s
w
e
w
il
l
ne
e
d
f
or
it
s
tr
a
in
in
g
a
nd
w
ha
t
th
e
d
e
la
y
w
il
l
be
w
he
n
e
xe
c
ut
e
d
in
a
pr
oduc
ti
on
e
nvi
r
onm
e
nt
.
T
he
r
e
s
ul
t
s
of
th
e
e
xpe
r
im
e
nt
s
b
a
s
e
d
on
a
ll
th
e
a
bove
pe
r
f
or
m
a
nc
e
in
di
c
a
to
r
s
a
r
e
pr
e
s
e
nt
e
d
in
T
a
bl
e
1. T
he
obt
a
in
e
d r
e
s
ul
ts
s
ho
w
t
ha
t
th
e
S
G
D
opt
im
iz
e
r
gi
v
e
s
t
he
w
or
s
t
r
e
s
ul
ts
. F
or
e
xa
m
pl
e
, f
or
a
c
ont
e
xt
le
ngt
h
of
60
da
ys
,
th
e
M
A
S
E
va
lu
e
is
4.34,
w
hi
c
h
is
s
ig
ni
f
ic
a
nt
ly
w
or
s
e
c
om
pa
r
e
d
to
ot
he
r
opt
im
iz
e
r
s
.
U
s
in
g
th
e
s
c
he
dul
e
-
f
r
e
e
S
G
D
opt
im
iz
e
r
im
pr
ove
s
th
e
s
e
in
di
c
a
to
r
s
,
r
e
duc
in
g
M
A
S
E
to
1.116
f
or
th
e
s
a
m
e
c
ont
e
xt
le
ngt
h,
w
hi
c
h
is
a
n
im
pr
ove
m
e
nt
of
a
ppr
oxi
m
a
te
ly
74%
.
T
he
A
d
a
m
W
opt
im
iz
e
r
s
how
s
b
e
tt
e
r
r
e
s
ul
ts
c
om
pa
r
e
d
to
s
c
he
dul
e
-
f
r
e
e
S
G
D
,
w
it
h
a
M
A
S
E
va
lu
e
of
0.954
f
o
r
a
60
-
d
a
y
c
ont
e
xt
le
ngt
h,
w
hi
c
h
is
a
n
im
pr
ove
m
e
nt
of
14%
.
H
ow
e
ve
r
,
th
e
b
e
s
t
r
e
s
ul
ts
a
r
e
de
m
ons
tr
a
te
d
by
th
e
s
c
he
du
le
-
f
r
e
e
A
da
m
W
opt
im
iz
e
r
,
w
he
r
e
f
or
a
60
-
da
y
c
ont
e
xt
le
ngt
h,
M
A
S
E
is
0.987,
w
hi
c
h
is
s
li
ght
ly
w
or
s
e
th
a
n
A
da
m
W
,
but
ove
r
a
ll
s
ho
w
s
s
ta
bl
e
r
e
s
ul
ts
f
or
a
ll
c
ont
e
xt
le
ngt
hs
.
T
hu
s
,
f
r
om
th
e
poi
nt
of
vi
e
w
of
s
ta
bi
li
ty
a
nd
o
ve
r
a
ll
e
f
f
ic
ie
nc
y,
s
c
he
dul
e
-
f
r
e
e
A
da
m
W
is
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
Sc
he
dul
e
-
fr
e
e
opt
imi
z
at
io
n of
t
he
tr
an
s
fo
r
m
e
r
s
-
ba
s
e
d t
ime
s
e
r
i
e
s
f
or
e
c
a
s
ti
ng m
ode
l
(
K
y
r
y
lo
Y
e
m
e
ts
)
1073
be
s
t
c
hoi
c
e
a
m
ong
a
ll
te
s
te
d
opt
im
iz
e
r
s
.
H
o
w
e
ve
r
,
if
w
e
c
ons
id
e
r
th
e
r
e
s
ul
ts
in
te
r
m
s
of
S
M
A
P
E
,
th
e
s
c
he
dul
e
-
f
r
e
e
S
G
D
opt
im
iz
e
r
de
m
ons
tr
a
te
s
th
e
be
s
t
pe
r
f
or
m
a
nc
e
.
F
or
e
x
a
m
pl
e
,
f
or
a
30
-
da
y
c
ont
e
xt
le
ngt
h,
S
M
A
P
E
is
0.651,
w
hi
c
h
is
be
tt
e
r
th
a
n
a
ll
ot
he
r
opt
im
iz
e
r
s
.
F
or
60
-
da
y a
nd
90
-
da
y
c
ont
e
xt
l
e
ngt
hs
,
S
M
A
P
E
a
ls
o
r
e
m
a
in
s
lo
w
e
r
t
ha
n ot
he
r
opt
im
iz
e
r
s
, m
a
ki
ng
s
c
he
dul
e
-
f
r
e
e
S
G
D
t
he
be
s
t
c
hoi
c
e
f
or
t
he
S
M
A
P
E
m
e
tr
ic
.
T
a
bl
e
1. E
f
f
ic
ie
nc
y e
s
ti
m
a
te
s
of
t
he
t
r
a
ns
f
or
m
e
r
m
ode
l
in
s
ol
vi
ng t
he
t
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng pr
obl
e
m
us
in
g
di
f
f
e
r
e
nt
opt
im
iz
e
r
s
s
tu
di
e
d i
n t
he
w
or
k
C
ont
e
xt
l
e
ngt
h
M
A
S
E
S
M
A
P
E
M
A
E
M
S
E
R
M
S
E
M
ode
l
s
i
z
e
S
c
he
dul
e
-
f
r
e
e
A
da
m
W
opt
i
m
i
z
e
r
30
0.94
0.691
2.041
17.606
2.832
80359
60
0.987
0.691
2.154
18.781
2.963
82279
90
0.931
0.686
2.046
17.83
2.836
84199
A
da
m
W
opt
i
m
i
z
e
r
30
1.206
0.666
2.295
19.248
3.056
80359
60
0.954
0.703
2.071
17.955
2.87
82279
90
1.063
0.7
2.307
20.074
3.148
84199
S
c
he
dul
e
-
f
r
e
e
S
G
D
opt
i
m
i
z
e
r
30
1.122
0.651
2.556
20.486
3.203
80359
60
1.116
0.658
2.574
20.222
3.238
82279
90
1.184
0.652
2.621
20.669
3.296
84199
S
G
D
opt
i
m
i
z
e
r
30
1.236
0.724
2.655
21.834
3.489
80359
60
4.34
1.378
7.704
107.351
8.632
82279
90
1.573
0.703
2.792
23.33
3.593
84199
F
ig
ur
e
2
s
how
s
a
c
om
pa
r
a
ti
ve
gr
a
ph
of
opt
im
iz
e
r
s
w
it
h
di
f
f
e
r
e
nt
c
ont
e
xt
s
iz
e
s
,
r
e
la
ti
ve
to
two
ke
y
m
e
tr
ic
s
:
M
A
S
E
a
nd
S
M
A
P
E
.
T
he
s
iz
e
of
e
a
c
h
poi
nt
c
or
r
e
s
ponds
to
th
e
num
be
r
of
m
ode
l
pa
r
a
m
e
te
r
s
.
T
he
c
lo
s
e
r
th
e
poi
nt
is
to
th
e
or
ig
in
of
th
e
c
oor
di
na
te
s
ys
te
m
,
th
e
be
tt
e
r
it
is
s
ui
te
d
f
or
m
ode
l
tr
a
in
in
g.
A
s
c
a
n
be
s
e
e
n
f
r
om
th
e
gr
a
ph,
th
e
s
c
he
dul
e
-
f
r
e
e
ve
r
s
io
ns
of
S
G
D
a
nd
A
d
a
m
W
pe
r
f
or
m
e
d
th
e
be
s
t.
D
e
pe
ndi
ng
on
w
hi
c
h
m
e
tr
ic
is
pr
io
r
it
iz
e
d,
th
e
r
e
w
il
l
be
di
f
f
e
r
e
nt
r
e
s
ul
ts
.
F
or
M
A
S
E
,
i
t'
s
s
c
he
dul
e
-
f
r
e
e
A
da
m
W
,
a
nd
f
or
S
M
A
P
E
,
it
'
s
s
c
he
dul
e
-
f
r
e
e
S
G
D
.
I
n
th
e
f
ut
ur
e
,
w
e
c
a
n
in
ve
s
ti
ga
te
how
s
c
he
dul
e
-
f
r
e
e
opt
im
iz
e
r
s
a
f
f
e
c
t
th
e
c
onf
id
e
nc
e
in
te
r
va
l
of
t
im
e
s
e
r
ie
s
m
ode
l
pr
e
di
c
ti
ons
.
F
ig
ur
e
2. G
r
a
ph w
it
h c
om
pa
r
is
on of
opt
im
iz
e
r
s
by S
M
A
P
E
a
nd M
A
S
E
m
e
tr
ic
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
.
14
, N
o.
2
,
A
pr
il
20
25
:
1
067
-
1
076
1074
F
ut
ur
e
r
e
s
e
a
r
c
h
w
il
l
a
ddr
e
s
s
s
e
ve
r
a
l
ke
y
a
r
e
a
s
to
e
nha
nc
e
th
e
a
c
c
ur
a
c
y
a
nd
a
ppl
ic
a
bi
li
ty
of
f
or
e
c
a
s
ti
ng
m
ode
ls
.
F
ir
s
tl
y,
w
hi
le
c
ur
r
e
nt
s
tu
di
e
s
ha
ve
ut
il
iz
e
d
a
s
in
gl
e
da
t
a
s
e
t,
f
ut
ur
e
w
or
k
w
il
l
e
xpa
nd
th
is
r
e
s
e
a
r
c
h
to
in
c
lu
de
m
ul
ti
pl
e
da
ta
s
e
ts
,
a
ll
ow
in
g
f
or
m
or
e
r
obus
t
a
nd
ge
ne
r
a
li
z
a
bl
e
f
in
di
ngs
.
A
ddi
ti
ona
ll
y,
th
e
im
pa
c
t
o
f
c
onf
id
e
nc
e
in
te
r
va
l
m
a
gni
tu
de
on
f
or
e
c
a
s
ti
ng
a
c
c
ur
a
c
y
h
a
s
n
ot
ye
t
be
e
n
e
xpl
or
e
d
a
s
a
di
s
ti
nc
t
p
a
r
a
m
e
te
r
;
in
ve
s
ti
ga
ti
ng
th
is
a
s
pe
c
t
c
oul
d
pr
ovi
de
va
lu
a
bl
e
in
s
ig
ht
s
.
R
e
s
e
a
r
c
h
w
il
l
a
ls
o
f
oc
us
on
id
e
nt
if
yi
ng
th
e
m
os
t
e
f
f
e
c
ti
ve
opt
im
iz
e
r
s
f
or
im
pr
ovi
ng
f
or
e
c
a
s
t
pe
r
f
or
m
a
nc
e
.
A
not
he
r
pr
om
is
in
g
a
ve
nue
f
or
f
ut
ur
e
r
e
s
e
a
r
c
h
is
th
e
de
ve
lo
pm
e
nt
of
tr
a
ns
f
or
m
e
r
-
ba
s
e
d
e
ns
e
m
bl
e
m
ode
ls
,
w
hi
c
h
c
oul
d
s
ig
ni
f
ic
a
nt
ly
e
nha
nc
e
f
or
e
c
a
s
t
a
c
c
ur
a
c
y
a
c
r
os
s
va
r
io
us
a
ppl
i
c
a
ti
on a
r
e
a
s
[
42]
.
4.
C
O
N
C
L
U
S
I
O
N
T
im
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
is
e
xt
r
e
m
e
ly
im
por
ta
nt
in
va
r
io
us
s
c
ie
nt
if
ic
,
te
c
hni
c
a
l,
a
nd
a
ppl
ie
d
f
ie
ld
s
s
uc
h
a
s
f
in
a
nc
e
,
e
c
onomi
c
s
,
m
e
te
or
ol
ogy,
m
e
di
c
in
e
,
tr
a
ns
por
ta
ti
on,
a
nd
te
le
c
om
m
uni
c
a
ti
ons
.
T
hi
s
ta
s
k
h
e
lp
s
pr
e
di
c
t
f
ut
ur
e
va
lu
e
s
of
va
r
ia
bl
e
s
ba
s
e
d
on
th
e
ir
hi
s
to
r
ic
a
l
da
ta
,
w
hi
c
h
ha
s
a
di
r
e
c
t
im
pa
c
t
on
th
e
e
f
f
ic
ie
nc
y
a
nd
e
c
onomi
c
be
ne
f
it
of
de
c
is
io
ns
m
a
de
.
I
n
m
e
t
e
or
ol
ogy,
th
e
a
c
c
ur
a
c
y
of
w
e
a
th
e
r
f
or
e
c
a
s
ts
is
c
r
it
ic
a
ll
y
im
por
ta
nt
f
or
pr
e
di
c
ti
ng
na
tu
r
a
l
di
s
a
s
te
r
s
a
nd
pl
a
nni
ng
a
c
ti
vi
ti
e
s
in
va
r
io
us
s
e
c
to
r
s
of
t
he
e
c
onomy.
I
n
th
is
pa
pe
r
,
th
e
ba
s
ic
a
r
c
hi
te
c
tu
r
e
of
tr
a
ns
f
or
m
e
r
s
w
a
s
m
odi
f
ie
d
to
s
ol
ve
ti
m
e
s
e
r
ie
s
f
or
e
c
a
s
ti
ng
pr
obl
e
m
s
.
T
he
r
e
m
ova
l
of
th
e
to
ke
ni
z
e
r
a
nd
e
m
be
ddi
ng
la
ye
r
,
a
s
w
e
ll
a
s
th
e
r
e
pl
a
c
e
m
e
nt
of
pos
it
io
na
l
e
nc
odi
ng
w
it
h
s
in
us
oi
da
l
pos
it
io
na
l
e
nc
odi
n
g
a
nd
ba
tc
h
nor
m
a
li
z
a
ti
on
w
it
h
la
ye
r
nor
m
a
li
z
a
ti
on,
pr
ovi
de
d
th
e
a
bi
li
ty
to
w
or
k
w
it
h
da
ta
w
it
h
pr
onounc
e
d
s
e
a
s
ona
li
ty
.
S
ta
te
-
of
-
th
e
-
a
r
t
opt
im
iz
e
r
s
,
e
s
pe
c
ia
ll
y
th
e
ir
s
c
he
dul
e
-
f
r
e
e
ve
r
s
io
ns
,
w
e
r
e
s
tu
di
e
d
a
nd
e
xpe
r
im
e
nt
a
ll
y
c
om
pa
r
e
d
to
im
pr
ove
f
or
e
c
a
s
ti
ng
a
c
c
ur
a
c
y
a
nd
r
e
duc
e
th
e
s
iz
e
of
th
e
tr
a
ns
f
or
m
e
r
m
ode
l
a
nd
it
s
tr
a
in
in
g
ti
m
e
.
M
ode
li
ng w
a
s
c
onduc
te
d
by
u
s
in
g
th
e
m
odi
f
ie
d
t
r
a
ns
f
or
m
e
r
a
r
c
hi
te
c
tu
r
e
ba
s
e
d
on
a
l
a
r
ge
s
e
t
of
m
e
te
or
ol
ogi
c
a
l
da
ta
,
w
hi
c
h
in
c
lu
de
s
va
r
io
us
va
r
ia
bl
e
s
s
uc
h
a
s
te
m
pe
r
a
tu
r
e
,
hum
id
it
y,
a
t
m
os
phe
r
ic
pr
e
s
s
ur
e
,
a
nd
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e
c
ip
it
a
ti
on.
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he
d
a
ta
w
a
s
pr
e
-
pr
oc
e
s
s
e
d
to
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e
m
ove
noi
s
e
a
nd
ga
ps
. T
he
m
ode
l
w
a
s
tr
a
in
e
d
on
hi
s
to
r
ic
a
l
da
ta
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it
h
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f
f
e
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e
nt
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ont
e
xt
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iz
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s
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e
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c
h
opt
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iz
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r
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te
r
w
hi
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h
te
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ti
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lu
a
te
t
he
a
c
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ur
a
c
y of
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or
e
c
a
s
ts
. T
h
e
r
e
s
ul
ts
of
di
f
f
e
r
e
nt
opt
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iz
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r
s
w
e
r
e
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om
pa
r
e
d ba
s
e
d on c
r
it
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ia
s
uc
h
a
s
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M
A
P
E
,
M
A
S
E
,
M
A
E
,
M
S
E
,
a
nd
R
M
S
E
.
T
h
e
r
e
s
ul
ts
s
how
e
d
th
a
t
th
e
m
odi
f
ie
d
s
c
he
dul
e
-
f
r
e
e
opt
im
iz
e
r
s
s
ig
ni
f
ic
a
nt
ly
im
pr
ove
d
th
e
a
c
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ur
a
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y
of
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e
a
s
ona
l
t
im
e
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e
r
ie
s
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or
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a
s
ti
ng
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om
pa
r
e
d
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la
s
s
ic
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l
m
e
th
ods
. T
he
m
os
t
r
e
le
va
nt
a
r
e
bot
h
s
c
he
dul
e
-
f
r
e
e
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G
D
a
nd
s
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he
dul
e
-
f
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e
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da
m
W
. A
s
a
r
e
s
ul
t
of
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om
pa
r
in
g
opt
im
iz
e
r
s
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c
he
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e
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f
r
e
e
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da
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pr
ove
d t
o be
t
he
be
s
t.
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s
c
a
n
be
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e
e
n f
r
om
t
he
r
e
s
ul
t
s
i
n t
he
t
a
bl
e
, w
it
h t
hi
s
opt
im
iz
e
r
,
th
e
m
ode
l
s
how
s
th
e
be
s
t
m
e
tr
ic
s
w
it
h
th
e
s
m
a
ll
e
s
t
c
o
nt
e
xt
,
w
hi
c
h
a
l
s
o
m
a
ke
s
th
e
m
ode
l
s
m
a
ll
e
r
a
nd
th
us
f
a
s
te
r
bot
h dur
in
g t
r
a
in
in
g a
nd i
nf
e
r
e
nc
e
.
A
C
K
N
O
WL
E
D
G
E
M
E
N
T
S
T
he
a
ut
hor
s
th
a
nk
D
r
.
I
va
n
I
z
oni
n
f
or
hi
s
in
va
lu
a
bl
e
gui
da
nc
e
a
nd
r
e
c
om
m
e
nda
ti
ons
,
w
hi
c
h
s
ig
ni
f
ic
a
nt
ly
e
nha
nc
e
d
th
e
pr
e
s
e
nt
a
ti
on
of
th
is
r
e
s
e
a
r
c
h
.
P
r
of
.
M
ic
ha
l
G
r
e
gus
w
a
s
s
uppor
te
d
by
th
e
S
lo
va
k
R
e
s
e
a
r
c
h
a
nd
D
e
ve
lo
pm
e
nt
A
ge
nc
y
unde
r
th
e
c
ont
r
a
c
t
N
o.
A
P
V
V
19
-
0581
.
T
hi
s
w
or
k
is
f
unde
d
by
th
e
E
ur
ope
a
n
U
ni
on’
s
H
or
iz
on
E
ur
ope
r
e
s
e
a
r
c
h
a
nd
in
nova
ti
on
pr
ogr
a
m
unde
r
gr
a
nt
a
gr
e
e
m
e
nt
N
o
101138678,
pr
oj
e
c
t
Z
E
B
A
I
(
I
nnova
ti
ve
m
e
th
odol
ogi
e
s
f
or
th
e
de
s
ig
n
of
Z
e
r
o
-
E
m
is
s
io
n
a
nd
c
os
t
-
e
f
f
e
c
ti
ve
B
ui
ld
in
gs
e
nha
nc
e
d by Ar
ti
f
ic
i
a
l
I
nt
e
ll
ig
e
nc
e
)
.
R
E
F
E
R
E
N
C
E
S
[
1]
M
.
G
e
ur
t
s
,
G
.
E
.
P
.
B
ox,
a
nd
G
.
M
.
J
e
nki
ns
,
“
T
i
m
e
s
e
r
i
e
s
a
na
l
y
s
i
s
:
f
or
e
c
a
s
t
i
ng
a
nd
c
ont
r
ol
,”
J
our
nal
of
M
ar
k
e
t
i
ng
R
e
s
e
ar
c
h
,
vol
. 14, no. 2, M
a
y 1977, doi
:
10.2307/
3150485.
[
2]
R
.
T
ka
c
he
nko,
“
A
n
i
nt
e
gr
a
l
s
of
t
w
a
r
e
s
ol
ut
i
on
of
t
he
s
gt
m
ne
ur
a
l
-
l
i
ke
s
t
r
uc
t
ur
e
s
i
m
pl
e
m
e
nt
a
t
i
on
f
or
s
ol
vi
ng
di
f
f
e
r
e
nt
da
t
a
m
i
ni
ng
t
a
s
ks
,”
i
n
L
e
c
t
u
r
e
N
ot
e
s
i
n C
om
put
at
i
onal
I
nt
e
l
l
i
ge
nc
e
and D
e
c
i
s
i
on M
ak
i
ng
, v
ol
. 77, 2022, pp. 696
–
713
, doi
:
10.1007/
978
-
3
-
030
-
82014
-
5_48.
[
3]
M
.
H
a
vr
yl
i
uk,
R
.
K
a
m
i
ns
kyy,
K
.
Y
e
m
e
t
s
,
a
nd
T
.
L
i
s
ovyc
h,
“
I
nt
e
r
a
c
t
i
ve
i
nf
or
m
a
t
i
on
s
ys
t
e
m
f
or
a
ut
om
a
t
e
d
i
de
nt
i
f
i
c
a
t
i
on
of
ope
r
a
t
o
r
pe
r
s
onne
l
by
s
c
hul
t
e
t
a
bl
e
s
b
a
s
e
d
on
i
ndi
vi
dua
l
t
i
m
e
s
e
r
i
e
s
,
”
i
n
A
dv
anc
e
s
i
n
A
r
t
i
f
i
c
i
al
Sy
s
t
e
m
s
f
o
r
L
ogi
s
t
i
c
s
E
ngi
ne
e
r
i
ng
I
I
I
,
vol
. 180, 2023, pp. 372
–
381
, doi
:
10.1007/
978
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3
-
031
-
36115
-
9_34.
[
4]
S
. R
a
ks
ha
, J
. S
. G
r
a
c
e
l
i
ne
, J
. A
nba
r
a
s
i
, M
. P
r
a
s
a
nna
, a
nd S
. K
a
m
a
l
e
s
hkum
a
r
, “
W
e
a
t
he
r
f
or
e
c
a
s
t
i
ng f
r
a
m
e
w
or
k f
or
t
i
m
e
s
e
r
i
e
s
da
t
a
us
i
ng
i
nt
e
l
l
i
ge
nt
l
e
a
r
ni
ng
m
ode
l
s
,
”
i
n
2021
5t
h
I
nt
e
r
nat
i
onal
C
onf
e
r
e
nc
e
on
E
l
e
c
t
r
i
c
al
,
E
l
e
c
t
r
oni
c
s
,
C
om
m
uni
c
at
i
on,
C
om
put
e
r
T
e
c
hnol
ogi
e
s
and
O
pt
i
m
i
z
at
i
on
T
e
c
hni
que
s
(
I
C
E
E
C
C
O
T
)
,
I
E
E
E
,
D
e
c
.
2021,
pp.
783
–
787
,
doi
:
10.1109/
I
C
E
E
C
C
O
T
52851.2021.9707971.
[
5]
W
.
S
ul
a
nda
r
i
,
S
.
S
uba
na
r
,
S
.
S
uha
r
t
ono,
H
.
U
t
a
m
i
,
M
.
H
.
L
e
e
,
a
nd
P
.
C
.
R
od
r
i
gue
s
,
“
S
S
A
-
ba
s
e
d
hybr
i
d
f
or
e
c
a
s
t
i
ng
m
od
e
l
s
a
n
d
a
ppl
i
c
a
t
i
ons
,”
B
ul
l
e
t
i
n
of
E
l
e
c
t
r
i
c
al
E
ngi
ne
e
r
i
ng
and
I
nf
or
m
at
i
c
s
,
vol
.
9,
no.
5,
pp.
2178
–
2188,
O
c
t
.
2020,
doi
:
10.11591/
e
e
i
.v9i
5.1950.
[
6]
D
. K
. S
i
ngh a
nd
N
. R
a
w
a
t
, “
M
a
c
hi
ne
l
e
a
r
ni
ng f
or
w
e
a
t
he
r
f
or
e
c
a
s
t
i
ng:
xgboo
s
t
vs
s
vm
vs
r
a
ndom
f
or
e
s
t
i
n pr
e
di
c
t
i
ng t
e
m
pe
r
a
t
ur
e
f
or
vi
s
a
kha
pa
t
na
m
,”
I
nt
e
r
nat
i
onal
J
our
nal
of
I
nt
e
l
l
i
ge
nt
Sy
s
t
e
m
s
and
A
ppl
i
c
at
i
ons
,
vol
.
15,
no.
5,
pp.
57
–
69,
O
c
t
.
2023,
doi
:
10.5815/
i
j
i
s
a
.2023.05.05.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
Sc
he
dul
e
-
fr
e
e
opt
imi
z
at
io
n of
t
he
tr
an
s
fo
r
m
e
r
s
-
ba
s
e
d t
ime
s
e
r
i
e
s
f
or
e
c
a
s
ti
ng m
ode
l
(
K
y
r
y
lo
Y
e
m
e
ts
)
1075
[
7]
D
.
U
hr
yn
e
t
al
.
,
“
M
ode
l
l
i
ng
of
a
n
i
nt
e
l
l
i
ge
nt
ge
og
r
a
phi
c
i
nf
or
m
a
t
i
on
s
ys
t
e
m
f
or
popul
a
t
i
on
m
i
gr
a
t
i
on
f
or
e
c
a
s
t
i
ng,”
I
nt
e
r
nat
i
onal
J
our
nal
of
M
ode
r
n E
duc
at
i
on and C
om
put
e
r
Sc
i
e
nc
e
, vol
. 15, no. 4, pp. 69
–
79,
A
ug. 2023, doi
:
10.5815/
i
j
m
e
c
s
.2023.04.06.
[
8]
О
.
K
or
ys
t
i
n,
S
.
N
a
t
a
l
i
i
a
,
a
nd
O
.
M
i
t
i
na
,
“
R
i
s
k
f
or
e
c
a
s
t
i
ng
of
da
t
a
c
onf
i
de
n
t
i
a
l
i
t
y
br
e
a
c
h
us
i
ng
l
i
ne
a
r
r
e
gr
e
s
s
i
on
a
l
gor
i
t
hm
,”
I
nt
e
r
nat
i
onal
J
our
nal
of
C
om
put
e
r
N
e
t
w
or
k
and
I
nf
or
m
at
i
on
Se
c
ur
i
t
y
,
vol
.
14,
no.
4,
pp.
1
–
13,
A
ug.
2022,
doi
:
10.5815/
i
j
c
ni
s
.2022.04.01.
[
9]
H
.
D
a
l
ka
ni
,
M
.
M
oj
a
r
a
d,
a
nd
H
.
A
r
f
a
e
i
ni
a
,
“
M
ode
l
l
i
ng
e
l
e
c
t
r
i
c
i
t
y
c
ons
um
pt
i
on
f
or
e
c
a
s
t
i
ng
us
i
ng
t
he
m
a
r
kov
pr
oc
e
s
s
a
nd
hybr
i
d
f
e
a
t
ur
e
s
s
e
l
e
c
t
i
on,”
I
nt
e
r
nat
i
onal
J
our
nal
of
I
nt
e
l
l
i
ge
nt
Sy
s
t
e
m
s
and
A
ppl
i
c
at
i
ons
,
vol
.
13,
no.
5,
pp.
14
–
23,
O
c
t
.
2021,
doi
:
10.5815/
i
j
i
s
a
.2021.05.02.
[
10]
P
.
B
.
A
ngon,
I
.
S
a
l
e
hi
n,
M
.
M
.
R
.
K
ha
n,
a
nd
S
.
M
onda
l
,
“
C
r
opl
a
nd
m
a
ppi
ng
e
xpa
ns
i
on
f
or
pr
oduc
t
i
on
f
or
e
c
a
s
t
:
r
a
i
nf
a
l
l
,
r
e
l
a
t
i
v
e
hum
i
di
t
y
a
nd
t
e
m
pe
r
a
t
ur
e
e
s
t
i
m
a
t
i
on,”
I
nt
e
r
nat
i
onal
J
our
nal
of
E
ngi
ne
e
r
i
ng
a
nd
M
anuf
ac
t
ur
i
ng
,
vol
.
11,
no.
5,
pp.
25
–
40,
O
c
t
.
2021, doi
:
10.5815/
i
j
e
m
.2021.05.03.
[
11]
O
.
M
ul
e
s
a
,
F
.
G
e
c
he
,
A
.
B
a
t
yuk,
a
nd
V
.
B
uc
hok,
“
D
e
ve
l
opm
e
nt
of
c
om
bi
ne
d
i
nf
or
m
a
t
i
on
t
e
c
hnol
ogy
f
or
t
i
m
e
s
e
r
i
e
s
pr
e
di
c
t
i
on,”
i
n
A
dv
anc
e
s
i
n I
nt
e
l
l
i
ge
nt
Sy
s
t
e
m
s
and
C
om
put
i
ng
, 2018, pp. 361
–
373
, doi
:
10.1007/
978
-
3
-
319
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m
e
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va
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t
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a
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r
a
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M
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t
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r
a
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t
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he
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or
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ha
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ve
r
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pe
r
c
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ut
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m
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r
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w
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t
h
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a
c
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ur
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t
w
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T
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C
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c
t
i
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o
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s
t
i
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a
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l
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ne
a
r
a
ut
or
e
gr
e
s
s
i
ve
m
ode
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s
a
nd
r
e
c
ur
r
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nt
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ur
a
l
ne
t
w
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t
i
de
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ve
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l
oa
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a
s
t
i
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t
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t
e
r
m
m
e
m
or
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e
c
ur
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nt
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of
s
ys
t
e
m
f
or
ge
ne
r
a
t
i
ng
que
s
t
i
ons
,
a
ns
w
e
r
s
,
di
s
t
r
a
c
t
or
s
us
i
ng
t
r
a
ns
f
or
m
e
r
s
,”
I
nt
e
r
nat
i
onal
J
our
nal
of
E
l
e
c
t
r
i
c
al
and
C
om
put
e
r
E
ngi
ne
e
r
i
ng
(
I
J
E
C
E
)
,
vol
.
14,
no.
2,
pp.
1851
–
1863,
A
pr
.
2024,
doi
:
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i
j
e
c
e
.v14i
2.pp1851
-
1863.
[
31]
A
. V
a
s
w
a
ni
e
t
al
.
, “
A
t
t
e
nt
i
on i
s
a
l
l
you ne
e
d,”
A
dv
anc
e
s
i
n N
e
u
r
al
I
nf
or
m
at
i
on P
r
oc
e
s
s
i
ng Sy
s
t
e
m
s
, vol
. 1, 2017.
[
32]
C
.
G
a
ngul
i
,
S
.
K
.
S
ha
ndi
l
ya
,
M
.
N
e
hr
e
y,
a
nd
M
.
H
a
vr
yl
i
uk,
“
A
da
pt
i
ve
a
r
t
i
f
i
c
i
a
l
be
e
c
ol
ony
a
l
gor
i
t
hm
f
or
na
t
ur
e
-
i
ns
pi
r
e
d
c
ybe
r
de
f
e
ns
e
,”
Sy
s
t
e
m
s
, vol
. 11, no. 1, J
a
n. 2023, doi
:
10.3390/
s
ys
t
e
m
s
11010027.
[
33]
M
.
H
a
vr
yl
i
uk,
N
.
H
ovdys
h,
Y
.
T
ol
s
t
ya
k,
V
.
C
hopya
kb,
a
nd
N
.
K
us
t
r
a
,
“
I
nve
s
t
i
ga
t
i
on
of
pnn
opt
i
m
i
z
a
t
i
on
m
e
t
hod
s
t
o
i
m
pr
ove
c
l
a
s
s
i
f
i
c
a
t
i
on pe
r
f
or
m
a
nc
e
i
n t
r
a
ns
pl
a
nt
a
t
i
on m
e
di
c
i
ne
,”
i
n
C
E
U
R
W
or
k
s
hop P
r
oc
e
e
di
ngs
, 2023, pp. 338
–
345.
[
34]
I
.
I
z
oni
n,
R
.
T
ka
c
he
nko,
R
.
H
ol
ove
n,
K
.
Y
e
m
e
t
s
,
M
.
H
a
vr
yl
i
uk,
a
nd
S
.
K
.
S
ha
ndi
l
ya
,
“
S
G
D
-
ba
s
e
d
c
a
s
c
a
de
s
c
he
m
e
f
or
hi
ghe
r
de
gr
e
e
s
w
i
e
ne
r
pol
ynom
i
a
l
a
ppr
oxi
m
a
t
i
on
of
l
a
r
ge
bi
om
e
di
c
a
l
da
t
a
s
e
t
s
,”
M
ac
hi
ne
L
e
ar
ni
ng
and
K
now
l
e
dge
E
x
t
r
ac
t
i
on
,
vol
.
4,
no. 4, pp. 1088
–
1106, N
ov. 2022, doi
:
10.3390/
m
a
ke
4040055.
[
35]
J
.
H
ua
ng,
“
R
M
S
P
r
op,”
C
or
ne
l
l
U
ni
v
e
r
s
i
t
y
.
A
c
c
e
s
s
e
d:
S
e
p.
13,
2024.
[
O
nl
i
ne
]
.
A
va
i
l
a
bl
e
:
ht
t
ps
:
/
/
opt
i
m
i
z
a
t
i
on.c
be
.c
or
ne
l
l
.e
du/
i
nde
x.php?
t
i
t
l
e
=R
M
S
P
r
op
[
36]
J
.
D
uc
hi
,
E
.
H
a
z
a
n,
a
nd
Y
.
S
i
nge
r
,
“
A
da
pt
i
ve
s
ubgr
a
di
e
nt
m
e
t
hods
f
or
onl
i
ne
l
e
a
r
ni
ng
a
nd
s
t
oc
ha
s
t
i
c
opt
i
m
i
z
a
t
i
on,”
J
our
nal
of
M
ac
hi
ne
L
e
ar
ni
ng R
e
s
e
ar
c
h
, vol
. 12, no. 61, pp. 2121
–
2159, 2011.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
, V
ol
.
14
, N
o.
2
,
A
pr
il
20
25
:
1
067
-
1
076
1076
[
37]
D
. P
. K
i
ngm
a
a
nd J
. B
a
, “
A
da
m
:
a
m
e
t
hod f
or
s
t
oc
ha
s
t
i
c
opt
i
m
i
z
a
t
i
on,”
a
r
X
i
v
-
C
om
put
e
r
Sc
i
e
n
c
e
,
pp. 1
-
15,
2014.
[
38]
N
. X
i
a
o, X
. H
u, X
. L
i
u,
a
nd K
.
-
C
. T
oh, “
A
da
m
-
f
a
m
i
l
y m
e
t
hods
f
or
nons
m
oot
h opt
i
m
i
z
a
t
i
on w
i
t
h c
onve
r
ge
nc
e
gua
r
a
nt
e
e
s
,”
ar
X
i
v
-
M
at
he
m
at
i
c
s
,
pp. 1
-
53,
2023.
[
39]
A
.
D
e
f
a
z
i
o,
X
.
A
.
Y
a
ng,
H
. M
e
ht
a
,
K
.
M
i
s
hc
he
nko,
A
.
K
ha
l
e
d,
a
nd
A
.
C
ut
kos
k
y,
“
T
he
r
oa
d
l
e
s
s
s
c
he
dul
e
d,”
i
n
38t
h C
onf
e
r
e
n
c
e
o
n
N
e
ur
al
I
nf
or
m
at
i
on P
r
oc
e
s
s
i
ng Sy
s
t
e
m
s
(
N
e
ur
I
P
S 2024)
, 2024.
[
40]
P
yT
or
c
h,
“
A
da
m
W
:
i
m
pl
e
m
e
nt
s
a
da
m
w
a
l
gor
i
t
hm
,”
P
y
T
or
c
h
C
ont
r
i
but
or
s
.
A
c
c
e
s
s
e
d:
J
ul
.
13,
2024.
[
O
nl
i
ne
]
.
A
va
i
l
a
bl
e
:
ht
t
ps
:
/
/
pyt
or
c
h.or
g/
doc
s
/
s
t
a
bl
e
/
ge
ne
r
a
t
e
d/
t
or
c
h.opt
i
m
.A
da
m
W
.ht
m
l
[
41]
A
.
H
S
pa
r
ks
,
M
.
P
a
dgha
m
,
H
.
P
a
r
s
ona
ge
,
a
nd
K
.
P
e
m
bl
e
t
on,
“
B
om
r
a
ng:
f
e
t
c
h
A
us
t
r
a
l
i
a
n
gove
r
nm
e
nt
bur
e
a
u
of
m
e
t
e
or
ol
ogy
da
t
a
i
n r
,”
T
he
J
our
nal
of
O
pe
n Sour
c
e
Sof
t
w
a
r
e
, vol
. 2, no. 17, S
e
p. 2017, doi
:
10.2
1105/
j
os
s
.00411.
[
42]
I
.
I
z
oni
n,
R
.
M
uz
yka
,
R
.
T
ka
c
he
nko,
I
.
D
r
onyuk,
K
.
Y
e
m
e
t
s
,
a
nd
S
.
-
A
.
M
i
t
oul
i
s
,
“
A
m
e
t
hod
f
or
r
e
duc
i
ng
t
r
a
i
ni
ng
t
i
m
e
of
ML
-
ba
s
e
d
c
a
s
c
a
de
s
c
he
m
e
f
or
l
a
r
ge
-
vol
um
e
da
t
a
a
na
l
ys
i
s
,”
Se
n
s
or
s
, vol
. 24, no. 15, J
ul
. 2
024, doi
:
10.3390/
s
24154762.
B
I
O
G
R
A
P
H
I
E
S
O
F
A
U
T
H
O
R
S
Kyrylo
Yemets
is
a
Ph
.D.
student
at
the
Department
of
Artificial
Intelligence
of
Lviv
Polytechnic
National
University,
Ukraine,
and
a
machine
learnin
g
engineer.
He
receive
d
an
M
.
Sc
.
degree
in
computer
science
from
the
National
Te
chnic
al
University
"
Kharkiv
Polytec
hnic
Institute
"
,
Ukrai
ne
in
2021.
His
resea
rch
intere
sts
incl
ude
time
serie
s,
natura
l
language
processing
,
transforme
rs,
and
ensemble
methods
where
he
is
the
author/co
-
author
of
over 10 researc
h public
ations.
He can be co
ntacted at
email:
kyrylo
.v.yemet
s@
lpnu.ua
.
Prof.
Michal
Greguš
is
a
Professor
of
the
Faculty
of
Management,
Comenius
University
Bratislava,
Bratislava,
Slovak
Republic.
He
finished
his
university
studies
with
summa
cumlaude
and
obtained
his
Ph
.
D
.
degree
in
the
fi
eld
of
math
ematical
analysis
at
the
Faculty
of
Mathem
atics
and
Physics
at
Comenius
Univer
sity
in
Bratisla
va.
He
has
been
working
previously
in
the
field
of
functional
analysis
and
its
applications.
At
present,
his
research
interests
are
in
manageme
nt
information
systems,
in
modelling
of
ec
onomic
processe
s
and
i
n
business analytics. He can be conta
cted at email:
michal.gre
gus
@
fm.uniba.sk
.
Evaluation Warning : The document was created with Spire.PDF for Python.