Discussion: “Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions” (Pandita, P., Bilionis, I., and Panchal, J., 2019. ASME. J. Mech. Des. 141(10): 101404)

The authors of the discussed paper simplified the information-based acquisition on estimating statistical expectation and developed analytical computation for each involved quantity under uniform input distribution. In this discussion, we show that (1) the last three terms of the acquisition always add up to zero, leaving a concise form with a much more intuitive interpretation of the acquisition; (2) the analytical computation of the acquisition can be generalized to arbitrary input distribution, greatly broadening the application of the developed framework.

Optimal design of experiments for effective modeling of atrazine degradation in soils

<p>The natural degradation pathways of the herbicide atrazine (AT) are highly complex. These pathways involve the metabolic activity of several bacterial guilds (that use AT as a source of carbon, nitrogen or both) and abiotic degradation mechanisms. The co-occurrence of multiple degradation pathways, combined with challenges in quantifying bacterial guilds and relevant intermediate metabolites, has led to the development of competing model formulations, which all represent valid descriptions of the fate of AT. A proper understanding of the fate of this complex compound is needed to develop effective management and mitigation strategies.</p><p>Here, we propose a model discrimination process in combination with prospective optimal design of experiments. We performed Monte-Carlo simulations using a first-order model that reflects a simple reaction chain of complete AT degradation and a set of Monod-based model variants that consider different bacterial consortia and degradation pathways. We used a Bayesian statistical analysis of these simulation ensembles to simulate virtual degradation experiments and chemical analysis strategies, thus obtaining predictions on the utility of experiments to deliver conclusive data for model discrimination. To do so, we defined different experimental protocols including a combination of: i) the metabolites to measure (AT, metabolites and CO<sub>2</sub>), ii) sampling frequency (sampling every day, every two days and every four days), iii) features difficult to quantify (specific bacterial guilds). As a statistical metric to measure the conclusiveness of these virtual experiments, we used the so-called energy distance.</p><p>Our results show that simulated AT degradation pathways following first-order reaction chains can be clearly distinguished from simulations using Monod-based models. Within the Monod-based models, we detected three clusters of models that differ in the number of bacterial guilds involved in AT degradation. Experimental designs considering main AT metabolites and sampling frequencies of once every two or four days at durations of 50 or 100 days provided the most informative data to discriminate models. Including measurements of bacterial guilds only slightly improved model discrimination. Our study highlights that environmental fate studies should prioritize measuring metabolites to elucidate active AT degradation pathways in soil and identify robust model formulations supporting risk assessment and mitigation strategies. </p>

Quantum-state estimation problem via optimal design of experiments

In this paper, we study the quantum-state estimation problem in the framework of optimal design of experiments. We first find the optimal designs about arbitrary qubit models for popular optimality criteria such as [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-optimal designs. We also give the one-parameter family of optimality criteria which includes these criteria. We then extend a classical result in the design problem, the Kiefer–Wolfowitz theorem, to a qubit system showing the [Formula: see text]-optimal design which is equivalent to a certain type of the [Formula: see text]-optimal design. We next compare and analyze several optimal designs based on the efficiency. We explicitly demonstrate that an optimal design for a certain criterion can be highly inefficient for other optimality criteria.

Identification of model uncertainty via optimal design of experiments applied to a mechanical press

In engineering applications almost all processes are described with the help of models. Especially forming machines heavily rely on mathematical models for control and condition monitoring. Inaccuracies during the modeling, manufacturing and assembly of these machines induce model uncertainty which impairs the controller’s performance. In this paper we propose an approach to identify model uncertainty using parameter identification, optimal design of experiments and hypothesis testing. The experimental setup is characterized by optimal sensor positions such that specific model parameters can be determined with minimal variance. This allows for the computation of confidence regions in which the real parameters or the parameter estimates from different test sets have to lie. We claim that inconsistencies in the estimated parameter values, considering their approximated confidence ellipsoids as well, cannot be explained by data uncertainty but are indicators of model uncertainty. The proposed method is demonstrated using a component of the 3D Servo Press, a multi-technology forming machine that combines spindles with eccentric servo drives.