Topology-Informed Machine Learning for Efficient Prediction of Solid Oxide Fuel Cell Electrode Polarization

TL;DR

The paper addresses predicting solid oxide fuel cell electrode polarization curves directly from microstructure by encoding complex 3D architectures with persistence images derived from persistent homology. It introduces a three-branch neural network that consumes persistence diagrams from three phases (nickel, YSZ, and pores) across multiple topological degrees, coupled with current density, to predict the current–voltage characteristics. A representative model with PI parameters $m=50$, $C=3$, $p=1$ achieves a mean squared error of $3.3156\times10^{-5}$ and a Pearson correlation of $0.9915$ on a test set, demonstrating high fidelity in capturing structure–property relationships. The results show that high-resolution topological descriptors can deliver robust predictions even with relatively small training datasets, highlighting the practical value of topological data analysis for rapid SOFC electrode design and optimization.

Abstract

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.

Figures (12)

• Figure 1: Graphical representation of first four simplices and a simplicial 3-complex with Betti numbers
• Figure 2: Comparison of PI results for different weight functions
• Figure 3: The pipeline of creating Persistence Image.The pipeline for creating PI from source data consists of several consecutive transformations. Filtration $\mathcal{F}$ generates birth-death pairs that constitute PD. The linear transformation $T$ is responsible for the transition to birth-persistence coordinates. Then with \ref{['eq:persistence_surface']} Persistence Surface is created and then discretized to the topological descriptor - Persistence Image
• Figure 4: Achitecture of ANN used in this research. ANN used in this research consists of $3$ branches and current density $J$ input. Each branch consists of three inputs corresponding to the $k$th Persistence Diagram $PD_k$ for all of the SOFC phases: nickel, YSZ and pores. Given then, ANN have $10$ inputs
• Figure 5: Model performance and generated PI based on weight function parameters $C$ and $p$