The dataset was designed to learn the pressure-dependent mapping from structure-derived SAD fields to DFT-derived ELF fields for compact high-pressure prototype cells. Recent general-purpose potential-energy-surface resources, including MatPES, MP-ALOE, the Materials Project trajectory dataset introduced with CHGNet, and OMat24, provide broad energy, force, and stress labels for training machine-learning interatomic potentials^[40-43]. Universal and foundational interatomic-potential architectures trained across broad chemical spaces include M3GNet, CHGNet, DPA-2, NequIP, Allegro, MACE, the MACE foundation model, and GRACE^[42,44-50]. In contrast, the dataset developed in this work was assembled around volumetric ELF output. Energies, forces, and stresses were retained for quality control and possible future use, but the learning task uses the SAD arrays as inputs and the ELF arrays as targets.

The dataset construction was guided by three requirements. First, the structures had to sample a broad range of pressures rather than only equilibrium or near-equilibrium volumes. Second, the enumeration had to include small prototype cells that could be systematically populated across many elements and element pairs. Third, the coverage had to include elements that may be underrepresented in common materials datasets but are chemically relevant under pressure, including noble gases and f-block elements.

Unary structures were generated from six compact prototype families: simple cubic (SC, Pm$$ \bar{3} $$m), body-centered cubic (BCC, Im$$ \bar{3} $$m), face-centered cubic (FCC, Fm$$ \bar{3} $$m), hexagonal close-packed (HCP, P6₃/mmc), diamond cubic (DC, Fd$$ \bar{3} $$m), and a hexagonal family represented in the workflow by P6/mmm. Binary AB structures were generated from seven prototype families: CsCl (Pm$$ \bar{3} $$m), HgS (P3₂21), NaCl (Fm$$ \bar{3} $$m), NiAs (P6₃/mmc), PbO (P4/nmm), zinc blende (ZB, F$$ \bar{4} $$3m), and wurtzite (ZW, P6₃mc). These compact families were chosen to span common unary and binary coordination motifs while keeping the enumeration tractable.

The final high-pressure subset contains the following 89 elements: H through Bi, the lanthanides La–Lu, and the actinides Ac, Th, Pa, U, Np, and Pu. The AB subset covers all 3,916 unordered canonical element pairs overall, with nearly complete coverage within each binary prototype. This element coverage was chosen to support exploratory high-pressure screening beyond the chemical space that is most common in ambient-pressure materials datasets. Under compression, noble gases and rare-earth or actinide elements can participate in unusual bonding, insertion, or charge-transfer behavior. For example, high pressure stabilizes xenon oxides with mixed oxidation states and the helium-containing compound Na₂He^[38,39]. Figure 1 summarizes the resulting element coverage and frequency.

The full 89-element inventory is listed in Supplementary Table 1.

To sample compression more systematically, we used the converged fixed-lattice prototype calculations to construct a pressure-targeted lattice-multiplier grid. Within each structure/prototype/chemical-system group, final DFT pressures from the original lattice-scale calculations were summarized by the median at each scale and used to fit a monotonic non-increasing pressure–scale relation using isotonic regression^[51]. The fitted relation was then inverted to select additional lattice-scale multipliers within the usable 0-500 GPa pressure interval. This procedure produced 164,133 converged pressure-targeted multiplier structures in the final dataset; details of the fitting, interpolation, target-pressure selection, and multiplier accounting are provided in Supplementary Note 1 and Supplementary Table 2.

All final structures were obtained from PBE calculations^[52,53]. MatPES-compatible PBE input settings and PAW potentials were used throughout^[54-56]. PBE was selected instead of r²SCAN to maintain consistency with the MatPES-compatible high-throughput workflow and to make broad pressure sampling computationally tractable. Although r²SCAN can improve semilocal descriptions across diverse bonding environments^[57], the objective was broad pressure coverage with ELF output rather than a high-fidelity equilibrium-energy benchmark. Functional sensitivity was therefore evaluated empirically using the pressure-balanced PBE–r²SCAN cross-check described below.

In a pressure-balanced 96-structure cross-check (16 per pressure bin), changing the reference from PBE to r²SCAN increased the median voxel mean absolute error (MAE) only from 0.09871 to 0.10493 and the median maximum-location distance from 1.109 to 1.183 Å. ELFNet–r²SCAN screening agreement was 92.71%, 78.13%, and 87.50% at ELF thresholds of 0.75, 0.80, and 0.90, respectively; PBE–r²SCAN agreement was at least 95.83% at every threshold. These results indicate that ELFNet retains useful screening information across the change in functionality. Supplementary Table 3 provides additional summary error metrics for this cross-check.

The final dataset contains 326,009 structures, including 7,423 unary and 318,586 binary structures. It is nearly balanced between the fixed absolute-lattice and pressure-targeted multiplier generation routes. The achieved pressures span -49.983 to 499.997 GPa, with a median of 83.26 GPa and a mean of 149.12 GPa. The median force magnitude is zero because many one-site and two-site high-symmetry prototypes have symmetry-cancelled forces; this does not imply zero stress or zero electronic response. Additional dataset statistics are provided in Supplementary Table 4, and the distributions of cohesive energy, force magnitude, and achieved pressure are summarized in Figure 2.

Negative achieved pressures arise only from expanded fixed-lattice configurations and represent DFT tensile-stress states.

ELFNet is a full-grid neural operator

(3) $$ \begin{aligned} f_{\theta}:\; &\mathbb{R}^{1\times D\times H\times W} \rightarrow [0,1]^{1\times D\times H\times W},\\ &\rho _{\mathrm{SAD}} \longmapsto \widehat{y}=f_{\theta}(\rho _{\mathrm{SAD}}), \end{aligned} $$

where $$ \widehat{y} $$ is the predicted ELF field. It processes the complete unit-cell SAD grid in one same-resolution forward pass and returns one sigmoid-bounded ELF grid.

The production model uses one input SAD channel, one output ELF channel, a base width of 32, 16 same-resolution flat residual blocks, a kernel size of five, and three-dimensional convolutional block attention module (CBAM) after every four residual blocks. The stem applies a circularly padded 3 × 3 × 3 convolution, GroupNorm, and Gaussian error linear unit (GELU) activation. Each residual block contains two circularly padded 5 × 5 × 5 convolutions with GroupNorm, GELU, and squeeze-excitation (SE). A CBAM module follows blocks 4, 8, 12, and 16^[59-63].

After the residual body, a further circularly padded 5 × 5 × 5 convolution and GroupNorm are combined with a long skip connection from the stem, followed by GELU activation. A 1 × 1 × 1 convolution and sigmoid activation then produce the one-channel ELF field. The bundled checkpoint contains 4,232,989 trainable parameters. This same-grid design preserves the image-to-image character of the SAD-to-ELF mapping while avoiding the memory overhead of multi-resolution feature maps and patch reconstruction. Figure 3 summarizes the implemented data flow.

The training loader yields complete unit-cell SAD/ELF pairs. Samples are bucketed by grid shape to avoid unnecessary padding, so the production model trains on native full-grid arrays rather than extracted patches.

The 326,009 paired full-grid SAD/ELF samples were divided deterministically at the sample level into 309,709 training samples and 16,300 validation samples using a validation fraction of 0.05 and a random seed of 42. The independent 50,000-structure hydride-derived template set was not used for training, validation, checkpoint selection, or hyperparameter tuning.

The production model was trained for 80 epochs using the AdamW optimizer with a maximum learning rate of 1 × 10^-4, a weight decay of 1 × 10^-4, and a OneCycleLR learning-rate schedule. The batch size was 16 per distributed process, with two gradient-accumulation steps and gradient-norm clipping at 1.0. Training used mixed bfloat16 precision on eight distributed ranks across two compute nodes, each equipped with four NVIDIA A100 80 GB GPUs.

The full bfloat16 production run completed all epochs and optimizer steps with finite training and validation losses, no NaN or Inf events, and finite model and optimizer tensors in the final checkpoint.

ELFNet does not explicitly enforce point-group or space-group symmetry beyond the periodic boundary conditions built into the convolutional layers. Recent equivariant atomistic and electronic-field models demonstrate how rotational covariance can be incorporated directly into learned three-dimensional representations^{[32,34,35,46]}. In principle, crystallographic symmetry could also be incorporated by averaging predictions or intermediate feature fields over space-group operations written in Seitz form, g = {R|t}, where R is a rotation and t is a fractional translation. For a grid-based convolutional neural network (CNN), however, this would require resampling feature tensors under multiple symmetry operations and averaging the transformed copies. This would increase memory use and wall time, especially for full-grid ELF learning in high-symmetry cells.

This choice is consistent with the intended screening task. ELFNet is designed to identify candidate templates before more expensive DFT calculations, not to replace final electronic-structure analysis. Circular padding ensures that local neighborhoods wrap across unit-cell boundaries, preserving periodicity in the learned representation. For template screening, the most important requirement is to recover the presence, approximate magnitude, and spatial location of high-ELF maxima. A prediction with small symmetry-breaking artifacts can still be useful if it identifies the same interstitial localization basins that would motivate follow-up DFT calculations. Explicit symmetry averaging remains a useful future extension, but it is omitted here to prioritize memory efficiency and full-grid throughput.

Across 117 Fm$$ \bar{3} $$m structures, symmetry averaging produced a raw-to-averaged field MAE of 0.01672 and reduced the median DFT-referenced maximum-location error by 0.185 Å. The 0.640 Å single-voxel argmax change reflects switching among near-degenerate maxima rather than physical displacement of an ELF feature. Small field and peak-amplitude changes indicate that raw predictions are already close to their symmetrized counterparts, but averaging is advisable when exact space-group consistency is required. Results are reported in Supplementary Table 5.

For each template, the DFT and ELFNet ELF grids were reduced to two screening metrics: the value of the global ELF maximum and the real-space distance between the predicted and DFT maximum locations. The maximum-value metric tests whether ELFNet recovers the amplitude of the strongest localization feature. The maximum-location metric tests whether that feature appears in the same region of the unit cell as the DFT reference. These metrics are complementary because a prediction can closely match the maximum ELF value while placing it in a different local basin, or it can place the maximum near the DFT reference location while under- or overestimating its value.

Figure 5 summarizes the template screening evaluation. The left panel compares the predicted and reference global ELF maxima, and the right panel compares maximum-value absolute error with maximum-location distance. The high density of structures with small value errors and small location distances shows that many templates are suitable for first-stage ranking, while the broader tails identify lower-confidence cases that should be prioritized for direct DFT validation if they appear chemically promising.

Across the 50,000-template set, the median absolute error in the global ELF maximum was 0.0268, and the median maximum-location distance was 0.895 Å. The corresponding 95th-percentile values were 0.1577 and 2.845 Å, respectively. At the thresholds shown in Figure 5, 93.57% of structures had both a maximum-value error no greater than 0.20 and a maximum-location distance no greater than 3 Å. These results show that the selected set is concentrated in the low-error region relevant to first-stage screening, while the remaining tail identifies lower-confidence cases for direct DFT validation. Large location errors should not necessarily be interpreted as complete field failures because the global maximum can shift between nearly equivalent localization basins. Additional percentile statistics and screening-threshold region counts are provided in Supplementary Table 10.

Pressure-stratified medians remained within the screening thresholds in every bin, with maximum-value errors no greater than 0.0361 and maximum-location distances no greater than 1.296 Å. The 160 GPa bin had the largest median location distance and the 300 GPa bin the largest median maximum-value error, but both remained within threshold; the aggregate result is therefore not solely a 200 GPa effect. Results are reported in Supplementary Table 11.

Among the 3,214 threshold failures, 1,515 exceeded only the maximum-value threshold, and 1,699 exceeded only the maximum-location threshold. No structure exceeded both thresholds. Pressure-stratified failure rates ranged from 2.36% at 100 GPa to 13.56% at 160 GPa. Failure rates also rose with structural and spatial complexity: from approximately 4% for one- or two-metal-site structures to 13.17% for eight-site structures and 26.57% for twelve-site structures, and from 3%-5% in the two smallest grid-volume quartiles to 9%-10% in the two largest. This pattern is consistent with increasing peak-location ambiguity. Element enrichments were confounded by pressure, scaffold, space group, and co-occurring elements and should not be interpreted as causal. Supplementary Tables 10 and 11 provide additional threshold-region counts and pressure-stratified summaries.

To test whether ELFNet provides a practical timing advantage for screening, we compared fixed-geometry DFT ELF generation and ELFNet prediction for the same 50,000-structure evaluation set. For VASP, the final Total CPU time used (sec) and Elapsed time (sec) fields were parsed from each OUTCAR. The VASP calculations excluded ionic relaxation. Each calculation used eight MPI ranks, with up to six calculations running concurrently within a 48-task allocation on Intel Xeon Gold 6342 CPU nodes.

The ELFNet benchmark measured per-structure elapsed time from reading the benchmark input/reference ELFCAR through SAD construction, model inference, and writing the predicted ELFCAR. The input read supplied structure and grid metadata for the benchmark; a deployment workflow can instead begin from a structure file. Inference used one node containing four NVIDIA A100-SXM4-80GB GPUs and 32 CPU cores, with the evaluation set divided among four single-GPU processes. Because both workflows used concurrent execution, the reported totals are sums of per-structure timer values rather than the elapsed wall time of either complete campaign.

Summed over the evaluation set, the VASP Total CPU time used fields were 922.6 h and the VASP Elapsed time fields were 935.3 h. The 922.6 h quantity is a sum of VASP timer fields and is not scheduler-accounted core-hours. The full ELFNet inference-through-write pipeline required 2.67 h of summed per-structure elapsed time. Using elapsed time consistently, the mean per-structure values were 67.34 s for VASP ELF generation and 0.192 s for the complete ELFNet pipeline. Their ratio corresponds to an approximately 350-fold reduction in summed per-structure elapsed time on the specified CPU and GPU systems. This is a hardware-specific timing ratio rather than a hardware-normalized compute-efficiency metric or a measured full-campaign wall-clock speedup.

The model forward pass accounted for 18.5 min of aggregate processing time; much of the end-to-end pipeline time arose from input/output and preprocessing. In a production screening workflow, maxima could be evaluated directly from predicted tensors, with full ELFCAR files written only for selected candidates. Additional timing definitions and values are provided in Supplementary Table 12.