Student: Fan Bai Instructor: Dr. Sushil K. Prasad Csc8530 Spring 2012

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Student: Fan
Bai

Instructor: Dr.
Sushil

K. Prasad

Csc8530 Spring 2012

Outline


Introduction of MC method



Sequential Monte Carlo Methods (SMC)



Parallel Monte Carlo Methods (PMC)



PMC vs Cloud Computing



Conclusion

Introduction


Monte

Carlo

methods

are

stochastic

techniques
.




Monte

Carlo

method

is

very

general
.




We

can

find

MC

methods

used

in

everything

from

economics

to

nuclear

physics

to

regulating

the

flow

of

traffic
.


Introduction


Nuclear reactor design


Quantum chromodynamics


Radiation cancer therapy


Traffic flow


Stellar evolution


Econometrics


Dow
-
Jones forecasting


Oil well exploration


VLSI design



Introduction


A Monte Carlo method can be loosely described as a
statistical method used in simulation of data
.




And a simulation is defined to be a method that utilizes
sequences of random numbers as data.

Major Components


Probability distribution function


Random number generator


Sampling rule


Scoring/Tallying

Parallel

Centralizatio
n

Method

Software

Cloud
Computing

Super
Computer

GUI

Web Servers

Methods

Sequential Monte Carlo Methods



Sequential Monte Carlo Methods (SMC) methods are
sample
-
based methods that use Bayesian inference and
stochastic sampling techniques to recursively estimate the
state of dynamic systems from some given observations.

Centralizatio
n

Particle Filter

DEVSFIRESprea
d

Cloud
Computing

Super
Computer

GUI

Web Servers

Parallel

Methods

Monte Carlo Method

Suppose you have an existing serial Monte Carlo simulation:

PROGRAM
monte_carlo


CALL
read_input
(…)


DO realization = 1,
number_of_realizations


CALL
generate_random_realization
(…)


CALL
calculate_properties
(…)


END DO


CALL
calculate_average
(…)

END PROGRAM
monte_carlo

How would you parallelize this?


Parallel Monte Carlo Method

PROGRAM
monte_carlo


[MPI startup]


IF (
my_rank

==
server_rank
) THEN


CALL
read_input
(…)


END IF


CALL
MPI_Bcast
(…)


DO realization = 1,
number_of_realizations


CALL
generate_random_realization
(…)


CALL
calculate_realization_properties
(…)


CALL
calculate_local_running_average
(...)


END DO


IF (
my_rank

==
server_rank
) THEN


[collect properties]


ELSE


[send properties]


END IF


CALL
calculate_global_average_from_local_averages
(…)


CALL
output_overall_average
(...)


[MPI shutdown]

END PROGRAM
monte_carlo


Initialize
N
particles

Node2

Node1

Node3

Node5

500

Node4

100

100

100

100

100

S

O

F

T

W

A

R

E

Node2

Node1

Node3

Node5

Node4

100

100

100

100

100

Senor
Data

W
-
Node2

W
-
Node1

W
-
Node3

W
-
Node5

W
-
Node4

Normalized


Weights

+

Resampling

Parallel

Centralizatio
n

MC method

Software

Cloud
Computing

Super
Computer

GUI

Web Servers

Our environment:

Cheetah
: 1
headnode

VS 9 computing nodes

5 nodes in Cheetah and 4 GUPs

64*1024*1024

Hdfs
-
site.xml

Conclusions


Monte Carlo Algorithms are very easy to convert to
parallel algorithms
.



Care Must be taken in choosing random number
algorithms
.



While
vectorization

is easy, improvements in load
balancing can be had by considering different ways to
partition the problem.

References


[1] Parallel computing and Monte Carlo algorithms. Jeffrey S. Rosenthal, Far East Journal of Theoretical Statistics 4
(2000), 207

236.


[2] Don’t Trust Parallel Monte Carlo! P
Hallekalek
. Proceedings of the 1998 Workshop on Parallel and Distributed
Simulation. Volume 1, Page(s): 82
-
89


[3] The Monte Carlo Method. Nicholas Metropolis,
S.Ulam
. Journal of the American Statistical Association,
Vol.44, No.247,(1949 ) PP 335
-
341.


[4] Parallel Monte Carlo Simulations.
K.Esselink
,
L.D.J.C.Loyens
, and
B.Smit.Physical

Review E, volume 51,
number 2.


[5] Monte Carlo and quasi
-
Monte Carlo methods.
Russel

E.
Caflisch
.
Ada

Numerica

(1998), pp. 1
-
49


[6] Monte Carlo Methods and Importance Sampling, Eric C. Anderson Lecture Notes for Stat Statistical
Genetics 20 October 1999


[7]. The Basics of Monte Carlo Simulations University of Nebraska
-
Lincoln Physical Chemistry Lab (
Chem

484) Written by lab TA Joy
Woller
, Spring 1996


[8]. JAZWINSKI, A.H. 1970. Stochastic processes and filtering theory. Mathematics in Science and
Engineering. Academic Press, New York, USA.


[9]. CRISAN, D. 2001. Particle filters

A theoretical perspective. Sequential Monte Carlo Methods in Practice
(
eds

A.
Doucet
, J. F. G. de
Freitas

and N. J. Gordon). New York: Springer
-
Verlag
.


[10]. GORDON, N.J., SALMOND, D.J., AND SMITH, A.F.M. 1993. Novel approach to nonlinear/non
-
Gaussian
Bayesian state estimation. In IEE Proceedings on Radar and Signal Processing 140, 107
-
113.


[11]. H.
Xue
, F.
Gu
, X.
Hu
, Data Assimilation Using Sequential Monte Carlo Methods in Wildfire Spread
Simulation, The ACM Transactions on Modeling and Computer Simulation (TOMACS), 2012


[12]. F.
Bai
, S.
Guo
, X.
Hu
, Towards parameter estimation in wildfire spread simulation based on Sequential
Monte Carlo Methods, Proc. 44th Annual Simulation Symposium (ANSS), 2011 Spring Simulation
Multiconference

(SpringSim'11), pp. 159
-
166, 2011