Parameter Estimation from Experimental Data and Finer Scale Models

Parameter Estimation from Experimental Data and Finer Scale Models 

One question that arises is if one uses multiscale simulation to predict systems behavior from first principles, then why does one need to carry out parameter estimation from experimental data The fact is that model predictions using even the most accurate QM techniques have errors. In the foreseeable future, one would have to refine parameters from experiments to create a fully quantitative multiscale model. Furthermore, for complex systems, QM techniques may be too expensive to carry out in a reasonable time frame. As a result, one may rely on estimating parameters from experimental data. Finally, an important, new class of problems arises when one has to estimate parameters of 

Rawlings and co-workers proposed to carry out parameter estimation using Newton s method, where the gradient can be cast in terms of the sensitivity of the mean (Haseltine, 2005). Estimation of one parameter in kinetic, well-mixed models showed that convergence was attained within a few iterations. As expected, the parameter values fluctuate around some average values once convergence has been reached. Finally, since control problems can also be formulated as minimization of a cost function over a control horizon, it was also suggested to use Newton s method with relatively smooth sensitivities to accomplish this task. The proposed method results in short computational times, and if local optimization is desired, it could be very useful. 

The first application of hierarchical SA for parameter estimation included refinement of the pre-exponentials in a surface kinetics mechanism of CO oxidation on Pt (a lattice KMC model with parameters) (Raimondeau et al., 2003). A second example entailed parameter estimation of a dual site 3D lattice KMC model for the benzene/faujasite zeolite system where benzene-benzene interactions, equilibrium constants for adsorption/desorption of benzene on different types of sites, and diffusion parameters of benzene (a total of 15 parameters) were determined (Snyder and Vlachos, 2004). While this approach appears promising, the development of accurate but inexpensive surfaces (reduced models) deserves further attention to fully understand its success and limitation. 

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