The AXS algorithm is also tested on experimental XRD patterns. While in the benchmarking dataset, the XRD patterns correspond exactly to DFT-optimized unit cells of known structure, this is not the case for experimental patterns. We use the AXS algorithm to solve the structure of three lithium containing compounds whose lattice parameters, space groups, and stick patterns are available in the Powder Diffraction File (PDF) from the International Centre for Diffraction Data (ICDD, 2021): Li 8 HfO 6 (PDF 00-026-0847), Li 3 CrO 4 (PDF 00-045-0347), and LiFeO 2 (PDF 00-052-0698). Li 8 HfO 6 (R-3) has been proposed to be isomorphic to Li 8 ZrO 6 , and atomic positions have been solved for slightly different lattice parameters with POWD-12++ (PDF 04-022-5097). Li 3 CrO 4 (Pmn2 1 ) is thought to be isostructural to high temperature γ Li 3 PO 4 . LiFeO 2 (Pnma) has no proposed structure solution. We choose H = 2 Å-1 and d tol = 1.5 Å as structure search parameters. The atomic positions for the 100 structures with best-matching XRD patterns are optimized using DFT. The energies of the DFT results are used to determine the stability of these theoretical structures and are shown in Figure . For Li 8 HfO 6 , we find a structure that is 0.005 eV/atom above the stability hull as defined in the Materials Project. Interestingly, structures with slightly higher R-values in this space tend to relax to lower energy structures. The lowest R-value structures are caught in local minima demonstrating the importance of sampling a range of structures with low R-value. More dramatically for Li 3 CrO 4 , the AXS framework produces a structure which is 0.344 eV/atom below the stability hull as seen in Figure . For the LiFeO 2 structure, AXS finds a structure which is approximately 0.0816 eV per atom below the hull after DFT relaxation with fixed lattice parameters. These structures, shown in Figure , Figure , and Figure , represent previously unknown phases which lie near or below the energetic hull and qualitatively match the experimental powder diffraction patterns. In addition, the final Li 6 HfO 8 structure found through the AXS algorithm is within a normalized RMS distance of 0.01 of the structure in the ICDD while the final Li 3 CrO 4 structure is within a normalized RMS distance of 0.08 of the proposed isostructural Li 3 PO 4 structure with a rescaled lattice. While it is uncertain if these represent the experimentally synthesized solutions of these compounds, the AXS algorithm has generated energetically plausible structures to be further analyzed. These structures are provided as CIF files in our Supplementary Materials.