The relationship between diffusion coefficient and ion conductivity in solid-state electrolytes using feedforward neural networks and symbolic regression

Electrolyte materials play a crucial role in enabling ion transport without allowing electron passage, making ionic conductivity and diffusion coefficients key properties for improving technologies such as solid-state batteries. Traditional methods for relating these properties, such as the Nernst–Einstein Equation, fail to apply to solid-state electrolytes due to their assumptions of dilute systems. This study proposes a data-driven approach to bridge this gap, developing two mechanistic models to generate a dataset of 2,000 theoretical materials, focusing on solid-state electrolytes. Feedforward neural networks (FNNs) were employed to predict ionic conductivity from diffusion coefficients, achieving relative error rates below 10% for approximately 95% of cases. Conversely, FNNs also predicted diffusion coefficients from conductivity with 97.45% accuracy, improving to 98.23% when the dissociation reaction was known. Additionally, symbolic regression yielded six mathematical equations, offering a slightly less accurate alternative to the neural networks while substantially easier to implement. Both the neural networks and symbolic equations were validated against experimental data in the literature — highlighting that even though neural networks presented a higher overall accuracy, the symbolic equations presented higher consistency. This work focused on advancing the ability to predict key electrolyte properties using fewer variables, presenting a practical, experimentally feasible solution for the optimization of electrolyte materials in solid-state devices. • Developed neural networks to link diffusion and conductivity. • Conductivity predictions achieved error below 10% in 95% of cases. • Diffusion coefficients at proper magnitude in 97.5% cases without dissociation data. • Neural networks showed higher accuracy when validated with literature data. • Symbolic regression excelled in extrapolation despite marginally lower accuracy.