(329d) Novel Approaches to Protonic Ceramic Electrochemical Cells Digital Twin Modeling Based on Embedded Karhunen-Loève Decomposed Gaussian Processes

Protonic Ceramic Electrolytic Cells (PCECs), which involve water splitting reactions, have emerged as efficient technologies for hydrogen production due to their cost-effectiveness, moderate temperature operation, and high efficiency¹. Several publications report experimental studies on PCEC^1,2,3; however, there is significantly less work on digital twin models of PCECs that can be used to provide actionable insights based on operational data. This research aims to develop a digital twin model based on physics with embedded Gaussian Processes (GPs). The GPs will be used as a mode of estimating uncertain quantities, such as diffusivities and reaction rate constants, as implicit functions of the dynamic states, including concentrations and temperatures. The GPs replace the uncertain parameters within the physical model, which will help overcome any plant-model mismatch. This leads to computationally fast and accurate digital twins, without the loss of interpretability and extrapolability. A key shortcoming of full GP models is their cubic complexity, due to the calculation of the inverse of the covariance matrix via Cholesky decomposition. To make GPs more scalable, Karhunen-Loève (KL) decomposed GPs will be implemented with a BSS-ANOVA kernel, which reduces the complexity to O(NP²) for training and O(P) for each point of inference, where N is the number of training points and P is number of terms in the expansion. To improve the proposed method's speed further, forward variable selection will also be implemented to truncate the number of terms.

References:

(1) Tian, H.; Li, W.; Ma, L.; Yang, T.; Guan, B.; Shi, W.; Kalapos, T. L.; Liu, X. Deconvolution of Water-Splitting on the Triple-Conducting Ruddlesden–Popper-Phase Anode for Protonic Ceramic Electrolysis Cells. ACS Appl. Mater. Interfaces 2020, 12 (44), 49574–49585. https://doi.org/10.1021/acsami.0c12987.

(2) Tong, Y.; Meng, X.; Luo, T.; Cui, C.; Wang, Y.; Wang, S.; Peng, R.; Xie, B.; Chen, C.; Zhan, Z. Protonic Ceramic Electrochemical Cell for Efficient Separation of Hydrogen, ACS Appl. Mater. Interfaces 2020, 12 (23), 25809–25817. https://doi.org/10.1021/acsami.0c04024.

(3) Oh, S.; Kim, H.; Jeong, I.; Kim, D.; Yu, H.; Lee, K. T. Recent Progress in Oxygen Electrodes for Protonic Ceramic Electrochemical Cells. Korean Ceram. Soc. 2024, 61 (2), 224–249. https://doi.org/10.1007/s43207-023-00360-y.