Optimal Experimental Design using Eigenvalue-Based Criteria with Pyomo.DoE

Abstract

Digital twins require high-quality data to achieve predictive capability, but time and resource limitations make efficient experiment design essential. Model-based design of experiments can address this challenge, especially when coupled with equation-oriented optimization and first-principles models. Pyomo.DoE is a software package for optimal experimental design of high-fidelity, equation-oriented models; however, embedding linear algebra operations such as matrix inversion and eigenvalue computation within these optimization problems remains difficult. This work extends Pyomo.DoE with callback-based capabilities that enable rigorous computation of eigenvalue-based design metrics, including minimum eigenvalue optimality (E-optimality) and condition number optimality (ME-optimality), within equation-oriented optimization frameworks. These additions allow experimental design to focus directly on poorly informed or numerically problematic parameter directions. We also present a new experiment-creation modeling abstraction for intrusive uncertainty quantification in Pyomo that reduces user modeling effort by aligning model and software abstractions across the digital twin workflow. In addition, a brief tutorial on experimental design metrics is provided in the methodology and supplementary information. Overall, this work expands the range of practical optimal design criteria available in Pyomo.DoE and improves the workflow for building and refining high-value digital twins.

Figures (12)

• Figure 1: General workflow for model building and identification using Pyomo, parmest, and Pyomo.DoE. This work focuses on equation-oriented modeling in Pyomo and optimally designing experiments for parameter precision (boxes highlighted in blue).
• Figure 2: Parallelism between the physical experiment that a scientist performs with the digital Experiment that enables the model building workflow from Figure \ref{['fig:workflow']} within Pyomo.
• Figure 3: Example connecting the elements of a small model (in Case Study 1, Eq. \ref{['eq:batch-reaction']}) to the code required to label the important components of the model using the label_model function of an Experiment object.
• Figure 4: Objective function values, $\Psi$ (D-, E-, ME-, A-opt), and related values (maximum eigenvalue and trace of the FIM) plotted as a function of the experimental design decision, sample time (days). The star represents the optimal point found for each criterion using Pyomo.DoE with a Grey Box objective.
• Figure 5: Data for the sine wave (left) and step test (right) experiments using the TCLab system. Measured data (orange points), predicted profile using optimal parameters (solid blue line), and predicted heater temperature (dashed red line) are shown on the top of each subplot where the heater input is shown as a solid red line on the bottom of each subplot.