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

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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

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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

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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