Convolutional Neural Networks to Assist the Assessment of Lattice Parameters from X-ray Powder Diffraction

This article presents the development of convolutional neural networks (CNNs) for the estimation of lattice parameters in organic compounds across various crystal systems. A comprehensive collection of 92,085 organic compounds was utilized to train the CNNs, encompassing crystals with unit cells containing up to 512 atoms and a maximum unit cell volume of 8000 ų. Simulated diffraction patterns were generated for each compound, comprising four diffraction patterns with different crystal sizes. These diffraction patterns were generated within a 2θ window of 3-60°, employing a step size of 0.02051°. Two distinct CNN architectures were developed with differing input data. The first CNN, referred to as XRD-CNN, was trained solely on diffraction patterns. In the test set, XRD-CNN demonstrated a mean absolute percentage error (MAPE) of 11.04% for unit cell vectors, 7.40% for angles, and 26.83% for unit cell volume. The second CNN, XRDElem-CNN, incorporated a binary representation of atoms within the unit cell as an additional input. XRDElem-CNN achieved improved performance, yielding MAPE values of 4.73% for unit vectors, 6.49% for angles, and 6.05% for the unit cell volume. To validate the performance of XRDElem-CNN, real diffraction patterns obtained from a conventional laboratory diffractometer (Cu Kα wavelength) were employed. Various representations of atoms within the unit cell were proposed, which were computationally efficient for evaluation with the CNNs. The assessed lattice parameters by XRDElem-CNN were validated using the Lp-search method, showing agreement with the reported values.