Fig. 2: Comparison of the experimental and simulated data.

a The scattering function S^exp(Q) for the Dy₂Ti₂O₇ crystal at 680 mK. b The same experimental data after being filtered by the autoencoder, \(S_{{\mathrm{AE}}}^{{\mathrm{exp}}}({\mathbf{Q}})\). c Simulated scattering data from the optimal model spin Hamiltonian, \(S_{{\mathrm{opt}}}^{{\mathrm{sim}}}({\mathbf{Q}})\). In going from (a) to (b), the autoencoder has filtered out experimental artifacts such as the red peaks, the missing data at the dark patches, etc. Using both scattering and heat capacity data, we determine the optimal spin Hamiltonian couplings to be J₂ = 0.00(6) K, J₃ = 0.014 (16) K and \(J_{3^\prime}\) = 0.096(12) K with J₁ = 3.41 K and D = 1.3224 K having been fixed in prior work¹⁷.