(150a) Scalable Computational Methods for Sequential, Science-Based Design of Experiments Using Pyomo.Doe

In science, experimental data are foundational for scientific hypotheses to be tested and validated oftentimes with a corresponding mathematical model. There has been significant interest in building predictive models, or digital twins, to describe complex systems (i.e., control systems, chemical production processes, biological systems) to enhance product quality and accelerate scientific discovery (e.g., self-driving labs) [1, 2, 3]. Ensuring a mathematical model is of high quality and has predictive capabilities requires a sufficient amount of high-quality data [3]. However, in many fields, the material cost (e.g., pharmaceuticals), time commitment (e.g., biological systems), or equipment cost (e.g., atomic discovery) can be prohibitive.

Therefore, optimally designing the set of experiments that should be run to give the most important information with a limited budget (e.g., fiscal, time, equipment) is vital to a successful experimental campaign. Existing methods for experimental design typically identify a set of experiment design variables and use space-filling paradigms (e.g., factorial design, one-variable-at-a-time [4]) and are limited to predetermined experimental conditions, oftentimes missing key information. With this in mind, design of experiments (DoE) [5] leverages statistical measures of information content to dictate which set of experiments will develop the most predictive model. To accomplish this goal, we utilize the newly refactored Pyomo.DoE in conjunction with Pyomo’s contributed parameter estimation package, ParmEst, to perform closed-loop, optimal experimental design [6, 7].

In the past, we would sequentially optimize one experiment at a time, gather the data for that experiment, and use that data to refine the model. However, in many instances, an experimental plan would be more efficient when multiple experiments are proposed in a batch-wise fashion. Optimally designing a batch of multiple experiments increases the complexity of the optimal DoE problem greatly (e.g., 5 experiments require 5 instances of the optimal DoE to be solved simultaneously). This presents a tradeoff between batch experimental campaign optimization and computational tractability. Fortunately, each instance of the optimal DoE problem is loosely coupled (i.e., only in the objective function), allowing us to exploit problem structure to decompose optimal batch experimental campaigns to be solved tractably.

In this work we present decomposition methods that enable tractable optimization of batch experimental campaign design. We then compare three different methodologies using the existing methodology and using this decomposition strategy on an automated system, the “temperate control lab” (TC Lab). First, we use the existing approach to optimize each experiment individually. Second, we use the decomposition strategy to optimize a new batch of experiments. And finally, we utilize the decomposition strategy to optimize batches of experiments but now re-optimizing after each experiment. Each strategy employs closed-loop model refinement and acts as a fully automated self-driving system (e.g., automated experiments, automated parameter estimation, and automated optimal experimental design). With this in mind, Pyomo.DoE is also being leveraged to automate membrane cascade design to explore technology viability for critical minerals separations and recycling applications.

Acknowledgements: The authors graciously acknowledge funding from the U.S. Department of Energy, Office of Fossil Energy and Carbon Management, through the Carbon Capture Program. This effort was funded by the U.S. Department of Energy’s Process Optimization and Modeling for Minerals Sustainability (PrOMMiS) Initiative, supported by the Office of Fossil Energy and Carbon Management’s Office of Resource Sustainability.

Disclaimer: This project was funded by the Department of Energy, National Energy Technology Laboratory an agency of the United States Government, through a site support contract. Neither the United States Government nor any agency thereof, nor any of its employees, nor the support contractor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, or any of their contractors.

References

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