(603b) Recent Advances in Kinetic Parameter Estimation Toolkit (KIPET) with Spectra

Developed over the past four years, the Kinetic Parameter Estimation Toolkit (KIPET), is an open-source toolbox for the determination of kinetic parameters from a variety of experimental datasets including spectra and concentrations. KIPET seeks to overcome limitations of standard parameter estimation packages by applying a unified optimization framework based on maximum likelihood principles and large-scale nonlinear programming strategies for solving estimation problems with nonlinear differential algebraic equations (DAEs). The software package includes tools for data preprocessing, determination of parameter confidence levels for a variety of problem types, and informative wavelength selection to improve the lack of fit (Schenk et al., 2020). All these features have been implemented in Python with the algebraic modeling package Pyomo. KIPET exploits the flexibility of Pyomo to formulate and discretize the dynamic optimization problems that arise in the parameter estimation algorithms. Solutions of these optimization problems are obtained with the nonlinear solver IPOPT and confidence intervals are obtained through the use of either sIPOPT or a newly developed tool, k_aug.

In this talk, we discuss a recently enhanced KIPET package (Short et al., 2020) that considers multiple experiments with potentially different reactants and kinetic models, different dataset sizes with shared or unshared individual species' spectra, leading to fast parameter estimation and confidence intervals based on the NLP sensitivities. In addition, we present a new variance estimation technique based on maximum likelihood derivations for unknown covariances from two sample populations. This approach leads to a straightforward deconvolution of variances between noise in model variables and in spectral measurements. Moreover, we discuss a new estimability analysis approach that systematically determines a ranked subset of kinetic parameters with well-defined confidence intervals (Chen and Biegler, 2020). With nonlinear kinetic models and limited measurements, it is often difficult to correctly estimate all the parameters, due to linear dependence and low correlation among the parameters. A common approach is to estimate a subset of the parameters by fixing the others at reasonable (often literature) values. However, it is often challenging to determine which parameters can be properly estimated. In this talk we present an efficient approach that ranks the estimable parameters, and discards those that cannot be estimated accurately. Based on reduced the reduced Hessian information with simple Gauss-Jordan elimination, the proposed approach leads to fast parameter selection and estimation within a simultaneous collocation framework. This approach becomes much more efficient for large problems than competing approaches based on multiple eigenvalue decompositions (Quaiser and Mönnigmann, 2009). Several case studies with increasing complexity are presented to demonstrate the performance of this proposed approach.

1. W. Chen, L. Biegler, “Reduced Hessian Based Parameter Selection and Estimation with Simultaneous Collocation Approach,” submitted for publication (2020)
2. Schenk, M. Short, J. S. Rodriguez, D. Thierry, L. T. Biegler, S. Garcia-Munoz, W. Chen, “Introducing KIPET: A novel open-source software package for kinetic parameter estimation from experimental datasets including spectra," Computers and Chemical Engineering, 134(4), 106716 (2020)
3. Short, L. T. Biegler, S. Garcia-Munoz, W. Chen, "Estimating Variances and Kinetic Parameters from Spectra Across Multiple Datasets Using KIPET," Chemometrics and Intelligent Laboratory Systems, to appear (2020)
4. Quaiser, T., Mönnigmann, M. “Systematic identifiability testing for unambiguous mechanistic modeling-application to JAK-STAT, MAP kinase, and NF-κB signaling pathway models,” BMC Systems Biology, 3,50 (2009).