Fitting Pair Distribution Function with Backpropagation

Pair distribution function (PDF) analysis is a powerful technique for characterizing both long-range structures and local distortions in materials, gaining significant importance in materials science. However, conventional PDF modeling approaches—including real-space Rietveld refinement for small-box models and Reverse Monte Carlo (RMC) for big-box models—often suffer from efficiency limitations. We propose a novel approach us- ing backpropagation algorithms to fit neutron and X-ray PDF data of ferroelectric perovskites. Our results demonstrate that this method achieves fitting accuracy comparable to RMC while offering potential efficiency advantages across various temperature ranges. By simultaneously optimizing tens of thousands of parame- ters, our approach can overcome unstable convergence inherent in RMC’s random perturbation. This method shows particular promise for determining local structures in materials with correlated disorder and illustrates the broader potential of integrating physical formulas within neural network frameworks for materials analysis.