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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 - PowerPoint PPT Presentation
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Computational Mathematics: Accelerating the Discovery of Science
Juan Meza
Lawrence Berkeley National Laboratoryhttp://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
Heater zones
Silicon wafers (200 mm dia.)
Quartz pedestal
Thermocouple
•Temperature uniformity across the wafer stack is critical
•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
The design of a small-batch fast-ramp LPCVD furnace can be posed as an optimization problem
900
925
950
975
1000
1025
1050
0 5 10 15 20 25 30
Uniform PowerPartial Optimization Optimized Power
Tem
pera
ture
(oC
)
Vertical Position from Bottom Wafer (in)
Target Temp=1027 C
Optimized power distribution enhances wafer temperature uniformity
Computational chemistry is used to design and study new molecules and drugs
Drugs are typically small 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)
Docking model for environmental carcinogen bound in Pseudomonas Putida cytochrome P450
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
ux
TxTN
iii
x
0 t.s.
) )(( min1
2*
Data Fitting Example From EUVL
Objective function 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
20
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0 5 10 15 20
TC1TC2TC3TC4TC5TC6TC1modTC2modTC3modTC4modTC5modTC6mod
Tem
pera
ture (
C)
Time (min)
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
19651968
19731976
19801986
1996
AlgorithmsComputers
1.E-4
1.E-3
1.E-2
1.E-1
1.E+0
1.E+1
1.E+2
1.E+3
CP
U t
ime
(sec
.)
Sparse GE
Gauss-Seidel
SORPCG
Multigrid
Jacobi
Gaussian Elimination/CDC 3600
CDC 6600CDC 7600
Cray 1Cray YMP
1 GFlop
1 Teraflop
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