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Computationally Efficient Atmospheric Chemical Kinetic Modeling By Means of High Dimensional Model Representation (HDMR) Presented at the 3rd International Conference on Large Scale Scientific Computations (LSSC01) June 7th, 2001, Sozopol, Bulgaria by S.W. Wang*, P. G. Georgopoulos* and G. Li**, H. Rabitz** *Environmental and Occupational Health Sciences Institute 170 Frelinghuysen Road, Piscataway, NJ 08854 **Department of Chemistry, Princeton University Princeton, NJ 08542 LSSC-2001

Computational Chemodynamics Laboratory EOHSI

OUTLINE

• introduction and rationale - computational burden of chemical kinetics in 3-D models • approach - the HDMR technique • case study - alkane photochemistry • conclusion and future efforts

LSSC-2001

Computational Chemodynamics Laboratory EOHSI

INTRODUCTION AND RATIONALE • Chemical kinetics calculations often consume 90% of the total CPU time in 3-D atmospheric chemistry-transport model simulations • Traditionally, mechanism reduction is pursued through semi-empirical (diagnostic) lumping approaches including: – the “lumped structure” approach (CBM IV) – the “lumped molecule” approach (SAPRC93) • An alternative is to develop explicit functions or look-up tables to parameterize the reaction mechanism: – exponentially growing difficulty of sampling effort – interpolation difficulty in high dimensional space • The HDMR approach has the ability to resolve these high dimensional mapping problems • Fast Equivalent Operational Model (FEOM) can be valuable when there is a need to perform multiple simulations with the model (such as for Monte Carlo type of uncertainty analysis, etc.) LSSC-2001

Computational Chemodynamics Laboratory EOHSI

APPROACH: THE HDMR TECHNIQUE I

SYSTEM

O

• System (a mathematical model): – Input I: x = {x1 , x2, . . . , xn} – Output O: f (x) = f (x1 , x2 , . . . , xn ) • The HDMR method expresses a model output as a expansion of correlated functions: f (x) = f0 +

n
i=1

fi(xi ) +




fij (xi , xj ) + · · ·

1≤i