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

TL;DR

This paper enhances Pyomo.DoE with eigenvalue-based criteria for optimal experimental design, enabling more effective data collection for digital twins through advanced model-based optimization techniques.

Contribution

It introduces callback-based eigenvalue computation capabilities and a new modeling abstraction, expanding Pyomo.DoE's functionality for digital twin workflows.

Findings

Enables eigenvalue-based metrics within equation-oriented optimization.

Reduces modeling effort with new abstraction for uncertainty quantification.

Improves experimental design focus on poorly informed parameters.

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.