(193g) Pyomo.Doe 2.0: Improved Usability and Computational Efficiency for Science-Based Design of Experiments (SBDoE)

Experimental data and observations are the foundation for hypothesizing, discovering, and validating scientific phenomena and corresponding mathematical models. In engineering, there has been significant interest in utilizing digital twins to describe complex systems (i.e., chemical production processes) for designing feasible processes [1, 2] and enhancing product quality and throughput via design [1, 2] and control [2]. However, digital twins that accurately describe such systems require data that is both high quality and in sufficient quantity [3]. In many fields, such as specialty chemical manufacturing (e.g., pharmaceuticals), the material cost, labor cost, or equipment cost to collect experimental data can be prohibitive.

For this reason, choosing which experiments should be run to construct a useful digital twin without exceeding an experimental budget becomes the key question during experimental campaign design. For this task, design of experiments (DoE) can leverage statistical measures to inform which experiments would be most beneficial to develop an accurate model, outperforming less sophisticated one-variable-at-a-time approaches widely adopted today [4]. In many science and engineering domains, the form of equations that dictate system behavior is known subject to a set of unknown model parameter values (i.e., reaction kinetics, membrane separation coefficients, etc.). With this in mind, science-based DoE (SBDoE) leverages the model structure and poses an optimization problem to inform which experiment(s) should be performed to maximize information gain, i.e., the accuracy of the digital twin [5]. However, efficient and accurate SBDoE requires formulating both the parameter estimation and design of experiments problems. These problems are very similar in structure and, for the DoE problem, require error-prone modeling (i.e., constructing a sensitivity matrix for experimental inputs with respect to unknown model parameters). To address this problem, Pyomo.DoE was developed to automate the sequence of design-optimize-evaluate for SBDoE [5].

In this work, we present a new modeling abstraction to unify the design of experiments (Pyomo.DoE) and parameter estimation (ParmEst) problems within the Pyomo ecosystem. Ultimately, the organization of ParmEst and Pyomo.DoE has shifted away from a model-based paradigm and instead encompasses the idea of an experiment. Each experiment has a set of experimental inputs and outputs. Inputs are conditions that change for each experiment, and outputs are the states that correspond to experimental measurements. Finally, a model is associated with each experiment. Experimental inputs, experimental outputs, and unknown model parameters are labeled within the model object, each in their own group. In this way, Pyomo can construct vital components of the parameter estimation or DoE model directly. For instance, the objective function for parameter estimation can be constructed automatically using the labels for experimental outputs, and the sensitivity matrix used to construct information matrices in DoE can be compiled from the experimental inputs and unknown model parameters.

Since many experiments can be conducted during parameter estimation, the software framework can also appropriately group these experiments for simultaneous optimization. The refactored framework more readily facilitates automated workflows, e.g., DoE for self-driving laboratories. For ParmEst, the new modeling abstraction promotes complex workflows for both top-down and bottom-up approaches for model discrimination in systems where many candidate mechanisms should be evaluated separately (i.e., crystallization). ParmEst can also reuse models that are already built to avoid rebuilding a model many times during repetitive tasks (especially useful in cases where large models need to be initialized). Also, the refactored framework utilizes “grey box” capabilities within Pyomo to perform sensitivity calculations during IPOPT callbacks [6], removing the need to model matrix factorizations explicitly and subsequently reducing the complexity of the DoE optimization problem. Given the scenario-based structure of DoE and parameter estimation, parallel computing approaches to improve computational efficiency will also be discussed. The redeployment of Pyomo.DoE through the refactoring (i) improves user experience, (ii) streamlines automation for self-driving labs and other applications, and (iii) improves computational efficiency for SBDoE. Pyomo.DoE is available in its current version as a contributing package to Pyomo at https://github.com/Pyomo/pyomo.

Disclaimer: This project was funded by the U.S. Department of Energy (DOE) National Energy Technology Laboratory, an agency of the United States Government, through a 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.

Acknowledgments: This work was supported as part of the Carbon Capture Simulation for Industry Impact (CCSI2) project, funded through the U.S. DOE Office of Fossil Energy and Carbon Management. This effort was funded in part 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.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

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