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Machine learning has emerged as a potent computational tool for expediting research and development in solid oxide fuel cell electrodes. The effective application of machine learning for performance prediction requires transforming electrode microstructure into a format compatible with artificial neural networks. Input data may range from a comprehensive digital material representation of the electrode to a selected set of microstructural parameters. The chosen representation significantly influences the performance and results of the network. Here, we show a novel approach utilizing persistence representation derived from computational topology. Using 500 microstructures and current-voltage characteristics obtained with 3D first-principles simulations, we have prepared an artificial neural network model that can replicate current-voltage characteristics of unseen microstructures based on their persistent image representation. The artificial neural network can accurately predict the polarization curve of solid oxide fuel cell electrodes. The presented method incorporates complex microstructural information from the digital material representation while requiring substantially less computational resources (preprocessing and prediction time approximately 1 min) compared to our high-fidelity simulations (simulation time approximately 1 hour) to obtain a single current-potential characteristic for one microstructure., Comment: 20 pages, 12 figures, submitted to Energy and AI

Uncovering microstructure evolution mechanisms that accompany the long-term operation of solid oxide fuel cells is a fundamental challenge in designing a more durable energy system for the future. To date, the study of fuel cell stack degradation has focused mainly on electrochemical performance and, more rarely, on averaged microstructural parameters. Here we show an alternative approach in which an evolution of three-dimensional microstructural features is studied using electron tomography coupled with topological data analysis. The latter produces persistent images of microstructure before and after long-term operation of electrodes. Those images unveil a new insight into the degradation process of three involved phases: nickel, pores, and yttrium-stabilized zirconium., Comment: 16 pages, 19 figures, original research

One of the most common and universal problems in science is to investigate a function. The prediction can be made by an Artificial Neural Network (ANN) or a mathematical model. Both approaches have their advantages and disadvantages. Mathematical models were sought as more trustworthy as their prediction is based on the laws of physics expressed in the form of mathematical equations. However, the majority of existing mathematical models include different empirical parameters, and both approaches inherit inevitable experimental errors. At the same time, the approximation of neural networks can reproduce the solution extremely well if fed with a sufficient amount of data. The difference is that an ANN requires big data to build its accurate approximation whereas a typical mathematical model needs just several data points to estimate an empirical constant. Therefore, the common problem that developer meet is the inaccuracy of mathematical models and artificial neural network. An another common challenge is the computational complexity of the mathematical models, or lack of data for a sufficient precision of the Artificial Neural Networks. In the presented paper those problems are addressed using the integration of a mathematical model with an artificial neural network. In the presented analysis, an ANN predicts just a part of the mathematical model and its weights and biases are adjusted based on the output of the mathematical model. The performance of Integrated Mathematical modeling - Artificial Neural Network (IMANN) is compared to a Dense Neural Network (DNN) with the use of the benchmarking functions. The obtained calculation results indicate that such an approach could lead to an increase of precision as well as limiting the data-set required for learning.

In the paper a mathematical model of the PEN structure (positive electrode - electrolyte - negative electrode) of the Solid Oxide Fuel Cell (SOFC) is analyzed. It is proved that classical formulation of the problem leads inevitably to locally unphysical effects related to negative values of the activation overpotential. Moreover, the active layers' thicknesses are shown to be components of solution and cannot be predefined in an arbitrary way. A modified mathematical formulation of the problem is proposed which includes this novelty alongside an amended definition of the activation overpotential. A dedicated computational scheme is developed for the cathode sub-problem. The accuracy of computations is investigated by means of a newly introduced analytical benchmark example. The numerical results obtained for LSCF cathode are used to discuss certain aspects of the modified formulation and the active layer thickness. The new modelling approach is validated by comparison with experimental data.