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

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Presentation on theme: "Computational Mathematics: Accelerating the Discovery of Science Juan Meza Lawrence Berkeley National Laboratory"— Presentation transcript:

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

2 Outline  Quick tour of computational science problems  Computational Science research challenges  Thoughts on CSME programs  CSME Education issues  Diversity Issues

3 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

4 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

5 Target Temp=1027 C Optimized power distribution enhances wafer temperature uniformity

6 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

7 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

8 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

9 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

10 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

11 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?

12 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

13 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

14 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

15 The End

16 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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