Computational Mathematics:
Accelerating the Discovery of Science
Juan Meza
Lawrence Berkeley National Laboratory
http://www.nersc.gov/~meza
Outline
 Quick tour of computational science problems
 Computational Science research challenges
 Thoughts on CSME programs
 CSME Education issues
 Diversity Issues
First problem I ever worked on at SNL
 Solution of a linear system of equations derived
from a thermal analysis problem
 Everybody “knew” that iterative methods would
not work
 Size of systems they wanted to study was
stressing the memory limits of the computer
 Iterative methods in fact turned out to work, but
for a very interesting reason
I’m not saying I’m especially proud of this
achievement, but it should be at least indicative
of the need for computational mathematicians
The design of a small-batch fast-ramp LPCVD
furnace can be posed as an optimization problem
•Temperature uniformity across
the wafer stack is critical
Heater zones
Silicon wafers
(200 mm dia.)
Thermocouple
Quartz pedestal
•Independently controlled heater
zones regulate temperature
•Wafers are radiatively heated
•Design parameters:
• Number of heater zones
• Size / position of heater
zones
• Pedestal configuration
• Wafer pitch
• Insulation thickness
• Baseplate cooling
Optimized power distribution enhances wafer
temperature uniformity
Target Temp=1027 C
1050
Temperature ( oC)
1025
1000
975
950
925
900
Uniform Power
Partial Optimization
Optimized Power
0
5
10
15
20
25
30
Vertical Position from Bottom Wafer (in)
Computational chemistry is used to design
and study new molecules and drugs
 Drugs are typically small
Docking model for environmental
carcinogen bound in Pseudomonas Putida
cytochrome P450
molecules which bind to
and inhibit a target
receptor
 Pharmaceutical design
involves screening
thousands of potential
drugs
 A single new drug may
cost over $500 million to
develop
 The design process is
time consuming (typically
about 13 years)
Drug design: an optimization problem in
computational chemistry
 The drug design problem
can be formulated as an
energy minimization
problem
 Typically there are
thousands of parameters
with thousands for
constraints
 There are many
(thousands) of local
minimum
HIV-1 Protease Complexed with
Vertex drug VX-478
Extreme UltraViolet Lithography (EUVL)
 Find model parameters,
satisfying some bounds, for
which the simulation
matches the observed
temperature profiles
 Computing objective
function requires running
thermal analysis code
N
min
x
s. t.
* 2
(
T
(
x
)

T
 i
i )
i 1
0 xu
Data Fitting Example From EUVL
120
100
Temperature (C)
 Objective function
TC1
TC2
TC3
TC4
TC5
TC6
TC1mod
TC2mod
TC3mod
TC4mod
TC5mod
TC6mod
80
60
40
20
0
5
10
Time (min)
15
20
consists of computing
the max temperature
difference over 5 curves
 Each simulation
requires approximately
7 hours on 1 processor
 Uncertainty in both the
measurements and the
model parameters
Observations
 Always worked on a (multidisciplinary) team
 Learning each other’s jargon was usually the
first and biggest hurdle
 Projects averaged 2-3 years
 Connections between many of the problems
Specifics of a particular discipline are not as
important as the general concepts for
understanding and communication
Thoughts on CSME programs
 Need to teach the importance of working on
teams
 Rarely have a single PI
 We need to recognize team efforts
 Need more opportunities for students to solve
“real” problems in a research environment
 We need opportunities for everybody to learn
new fields
 Integration between agencies as well as
integration across disciplines?
Thoughts on CSME research challenges
 Biotechnology
 Biophysical simulations
 Data management
 Stochastic dynamical systems
 Nanoscience
 Multiple scales (time and length)
 Scalable algorithms for molecular systems
 Optimization and predictability
Communication, Communication, Communication
 “A CSE graduate is trained to communicate with
and collaborate with an engineer or physicist
and/or a computer scientist or mathematician to
solve difficult practical problems.”, SIAM Review, Vol
43, No. 1, pp 163-177.
 Most graduates are completely unaware of
(unprepared for?) the importance of giving good
talks
 All graduates need more experience in writing
Diversity in CSME
 Practical experiences are the best instruments
for attracting and retaining students from
underrepresented groups
 Students need to see what their impact will be on
the society and their community
 Universities, labs, and agencies need to
establish strong, active, continuous
communication with under-represented groups
The End
New algorithms have yielded greater reductions in
solution time than hardware improvements
Gaussian Elimination/CDC 3600
CDC 6600
1.E+3
CDC 7600
Cray 1
1.E+2
CPU time (sec.)
Cray YMP
1.E+1
1.E+0
1 GFlop
1.E-1 Sparse GE
Jacobi
1.E-2
Gauss-Seidel
1.E-3
1.E-4
1965
SOR
1968
1973
1976
1980
1 Teraflop
PCG
1986
Multigrid
1996
Computers
Algorithms