EviDTB adds uncertainty to DFT Hamiltonian prediction: dropping the 15% most uncertain structures cuts the error's 99th percentile from 16.63 to 3.72 eV²

EviDTB gives a universal DFT Hamiltonian model a structure-level reliability score alongside each prediction, without training several models per structure or repeating stochastic passes. Deep ensembles estimate uncertainty from disagreement among independently trained models, and Monte Carlo dropout needs repeated stochastic forward passes; both require four network evaluations at inference, and the ensemble costs about four times a single model during training. On a 5,000-structure subset, the Spearman rank correlation between EviDTB's mean uncertainty per atom and the mean local squared prediction error is comparable to the four-member deep ensemble and higher than mean-variance estimation and Monte Carlo dropout; EviDTB attains the highest ROC-AUC for detecting high-error structures, above the ensemble, while its Hamiltonian prediction error is slightly higher than the ensemble's.

The uncertainty score can screen out high-risk candidates directly, leaving first-principles verification for structures more likely to be accurate. Without screening, the full 5,478 held-out structures have a mean local squared prediction error of 1.47 eV² and a 99th percentile of 16.63 eV², a heavy high-error tail. Removing the 15% of structures with the highest mean uncertainty per atom lowers the mean local squared prediction error to 0.62 eV² and its 99th percentile to 3.72 eV², a 78% reduction; removing 10% and 20% lowers the 99th percentile to 4.94 and 2.93 eV² respectively.

The model learns the residual of the converged Hamiltonian relative to a reference Hamiltonian at the initial density, rather than the full Hamiltonian matrix. Self-consistent DFT calculations commonly start from a superposition of atomic charge densities, and the Hamiltonian at that initial density can be constructed without self-consistent iterations, serving as a structure-dependent reference term. In the OpenMX PBE nonmagnetic calculations, spin-orbit coupling enters through fully relativistic nonlocal pseudopotentials and stays unchanged during self-consistent iterations; the density-dependent Hartree and exchange-correlation correction contributes only to the real parts of the spin-diagonal blocks, so the network learns only a real symmetric residual matrix.

Uncertainty comes from evidential deep regression in one deterministic forward pass, with no sampling. Evidential deep regression does not output a variance directly; it predicts the parameters of a normal-inverse-gamma distribution, from which the predictive mean and uncertainty are obtained analytically. In the implementation, scalar channels at each source node give the normal-inverse-gamma parameters, the scale is obtained by summing squared scales predicted from the node and its outgoing-edge features, and the total predictive variance is computed directly under an effective-subspace model whose effective dimension is set to 5 as a hyperparameter.

The demonstrated scope is PBE nonmagnetic DFT Hamiltonians with spin-orbit coupling in OpenMX, with training and test structures from the Materials Project and a separate external evaluation on 636 structures generated by CrystalFormer and relaxed with MatterSim without retraining. The intended readers are researchers working on high-throughput electronic-structure screening and machine-learned Hamiltonian models.

Deep evidential regression is often described as separating epistemic from aleatoric uncertainty, but that interpretation remains under debate, so only the combined per-atom uncertainty score is evaluated and the two components are not validated separately. The structures come from the Materials Project, and applicability to other screening scenarios such as two-dimensional materials and high-pressure structures requires further validation; the calculations assume all structures are nonmagnetic, so the model is restricted to nonmagnetic DFT Hamiltonians.