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 Å3. 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.