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Efficient sensitivity/uncertainty analysis using the combined stochastic response surface method and automated
S S Isukapalli1, A Roy, P G Georgopoulos
1Rutgers University & University of Medicine and Dentistry of New Jersey, Piscataway 08854, USA.
Summary
Estimating model uncertainties is crucial. A new method combining Stochastic Response Surface Method (SRSM) and Automatic Differentiation of FORTRAN (ADIFOR) significantly reduces computational cost for uncertainty propagation in complex models.
Area of Science:
- Environmental modeling
- Biological modeling
- Computational science
Background:
- Estimating prediction uncertainties is vital for environmental and biological models.
- Traditional uncertainty propagation methods (e.g., Monte Carlo, Latin Hypercube Sampling) are computationally expensive for complex models.
Purpose of the Study:
- To develop and present a computationally efficient framework for uncertainty propagation.
- To couple the Stochastic Response Surface Method (SRSM) with Automatic Differentiation of FORTRAN (ADIFOR).
Main Methods:
- SRSM uses series expansions of model inputs/outputs with standard random variables.
- ADIFOR transforms model code to compute output derivatives with respect to inputs.
- Coupled SRSM-ADIFOR uses calculated outputs and derivatives to approximate series expansion coefficients.
Main Results:
- The coupled SRSM-ADIFOR framework was successfully developed and tested.
- Case studies included a pharmacokinetic model and an atmospheric photochemical model.
- Results closely matched traditional methods but reduced simulations by ~100-fold.
Conclusions:
- The coupled SRSM-ADIFOR method offers a computationally efficient approach to uncertainty propagation.
- This method significantly reduces the number of simulations needed for complex models.
- The approach is validated by its close agreement with established uncertainty estimation techniques.