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# Computational Mathematics: Accelerating the Discovery of Science Juan Meza Lawrence Berkeley National Laboratory

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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  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

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

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

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 1965 1968 1973 1976 1980 1986 1996 Algorithms Computers 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+2 1.E+3 CPU time (sec.) Sparse GE Gauss-Seidel SOR PCG Multigrid Jacobi Gaussian Elimination/CDC 3600 CDC 6600 CDC 7600 Cray 1 Cray YMP 1 GFlop 1 Teraflop

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