1 / 16

Computational Mathematics: Accelerating the Discovery of Science

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

kohana
Download Presentation

Computational Mathematics: Accelerating the Discovery of Science

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Computational Mathematics: Accelerating the Discovery of Science Juan Meza Lawrence Berkeley National Laboratory http://www.nersc.gov/~meza

  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. 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 • 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 Heater zones Silicon wafers (200 mm dia.) Thermocouple Quartz pedestal

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

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

More Related