Simultaneous solution approach to model‐based experimental design

Abstract

A model‐based experimental design is formulated and solved as a large‐scale NLP problem. The key idea of the proposed approach is the extension of model equations with sensitivity equations forming an extended sensitivities‐state equation system. The resulting system is then totally discretized and simultaneously solved as constraints of the NLP problem. Thereby, higher derivatives of the parameter sensitivities with respect to the control variables are directly calculated and exact. This is an advantage in comparison with proposed sequential approaches to model‐based experimental design so far, where these derivatives have to be additionally integrated throughout the optimization steps. This can end up in a high‐computational load especially for systems with many control variables. Furthermore, an advanced sampling strategy is proposed which combines the strength of the optimal sampling design and the variation of the collocation element lengths while fully using the entire optimization space of the simultaneous formulation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4169–4183, 2013

Dynamic parametric sensitivity optimization using simultaneous discretization in JModelica.org

“…When employing simultaneous discretization, an initial guess is needed for all system variable trajectories, not only those generating degrees of freedom (inputs). With the augmented problem formulation (11), this includes the parametric sensitivities of the state and algebraic variables. To generate such initial guesses, the system is simulated in JModelica.org with CVODES (as described in Section II-D) with the constant inputs u 1 = 0.1 and u 2 = 15g/L.…”

“…The second contribution is an open-source toolchain for OED using Modelica. Recent and related work in these directions is [11] and [12].…”

Component Characterization in a Growth-Dependent Physiological Context: Optimal Experimental Design

“…OED techniques are especially promising when coupled with optogenetic or microfluidic techniques, which allow for a broad range of dynamic perturbations in vivo [30]. Here, we employ optimal experimental design algorithms originally demonstrated for chemical and bioprocess engineering applications [31][32][33] for the characterization of a genetic component from simulated data.…”

A differentiable reformulation for E-optimal design of experiments in nonlinear dynamic biosystems

“…The formulation of optimal experiment design using single shooting [20], multiple shooting [21] or orthogonal collocation [22] has been discussed in depth in these papers. A severe issue is that for nonlinear dynamic systems, the design depends on the current best guess for the parameter value.…”