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

2026-04-03

AI Summary

To enhance the predictive capability of digital twins, efficient acquisition of high-quality experimental data is imperative. This work proposes a novel integration of eigenvalue- and condition number-based computations into the Pyomo.DoE framework via a callback mechanism, enabling rigorous support for eigenvalue-oriented optimal design criteria such as E-optimality and ME-optimality. By establishing a unified abstraction for experimental modeling, the approach selectively targets dimensions in the parameter space that exhibit insufficient information content or numerical instability, seamlessly combining first-principles models with intrusive uncertainty quantification. The proposed method substantially broadens the range of design criteria supported by Pyomo.DoE, reduces user modeling effort, and improves both the efficiency and accuracy of constructing high-fidelity digital twins.

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.

Problem

• optimal experimental design
• eigenvalue-based criteria
• equation-oriented optimization
• digital twins
• Pyomo.DoE

Innovation

• Eigenvalue-based optimality
• Pyomo.DoE
• Equation-oriented optimization
• Digital twin
• Intrusive uncertainty quantification