Risk-Controlled DFT Selection for Machine-Learned Interatomic Potentials
Organizations: Pritzker School of Molecular Engineering, The University of Chicago · Department of Statistics, The University of Chicago · Department of Material Science and Engineering, National University of Singapore
Abstract
Automated materials discovery requires evaluating large pools of candidate configurations, with density functional theory (DFT) as a major throughput bottleneck. Pretrained machine-learned interatomic potentials (MLIPs) approximate DFT cheaply, but their errors vary by orders of magnitude across configurations, making it difficult to decide when to trust the MLIP predictions and when to fall back to DFT. We frame this decision as a risk-controlled selection problem and solve it within a conformal risk control (CRC) framework. Each configuration is mapped from atomic numbers and Cartesian coordinates to a fixed geometric descriptor, which a lightweight predictor uses to estimate an MLIP-DFT disagreement score in energy, average force, and maximum force. CRC then calibrates this score into a selection threshold for DFT labeling such that the MLIP error on the unselected configurations, which keep their MLIP labels, stays below a user-chosen fraction of the expected error. Under an identical guarantee across eight dataset-MLIP pairs, our predictor routes 7% and 14% fewer configurations to DFT at than committee baselines. Because committee disagreement overlooks errors the MLIPs share, our gains are largest when the DFT labels and MLIP training data differ in DFT functional and basis set, and narrow when the two agree. Without model access, the structure-only predictor also ranks errors as well as the target MLIP's latent representation and outperforms widely used descriptors such as Smooth Overlap of Atomic Positions (SOAP) and Atom-Centered Symmetry Functions (ACSF).
Figures & tables
| Dataset | # configs. | # identities | # atoms (mean) | elements |
|---|---|---|---|---|
| COMP6-GDB07to09-FULL [ Smith et al., 2018 ] | 36,000 | 1,500 | 7–27 (17.0) | H, C, N, O |
| MACE-OFF23-FULL [ Eastman et al., 2023 ] | 50,195 | 15,769 | 3–150 (30.9) | H, C, N, O, F, P, S, Cl, Br, I |
| QCML-6950-9 [ Ganscha et al., 2025 ] | 62,550 | 6,950 | 2–23 (11.0) | H, C, N, O, F, P, S, Cl, Br, I |
Appendix figures & tables34 assets
Supplementary material from the paper’s appendix.
Appendix
| Feature family | Dim. | Type | Description |
|---|---|---|---|
| 10 | Discrete | Global counts of the allowed elements. | |
| 52 | Discrete | Element-resolved proximity-graph coordination states. | |
| 156 | Discrete | Element-pair contacts classified as compressed, near nominal separation, or elongated. | |
| 21 | Continuous | Atomic-number-weighted severity of short interatomic contacts. | |
| 12 | Continuous | Most severe local proximity, strain, and angular-distortion environments. | |
| 18 | Continuous | Smooth multiscale pair-distance channels with global and local pooling. |
| dataset | evaluation reference | target MLIP | MLIP training reference |
|---|---|---|---|
| COMP6 | B97X/6-31G(d), Gaussian 09 | MACE-OFF23(M) | B97M-D3(BJ)/def2-TZVPPD |
| AIMNet2 | B97M-D3/def2-TZVPP | ||
| AceFF-2 | B97M-V/def2-TZVPPD, VV10 | ||
| QCML | PBE0, FHI-aims | MACE-OFF23(M) | B97M-D3(BJ)/def2-TZVPPD |
| AIMNet2 | B97M-D3/def2-TZVPP | ||
| AceFF-2 | B97M-V/def2-TZVPPD, VV10 |
| at | committee vs. ours at matched resources | ||||||
|---|---|---|---|---|---|---|---|
| Method | MLIP evals | DFT [%] | DFT saved [pp of pool] | rel.-energy MAE [meV] | selection success [pp] | ||
| Ours | 1 | 0.808 | 57.8 | 0.289 | — | — | — |
| Raw committee | 3 | 0.497 | 61.9 | 0.282 | |||
| Supervised committee | 3 | 0.341 | 67.5 | 0.251 | |||
| Random | 1 | 0.000 | 71.6 | 0.284 | — | — | — |
| Oracle (retrospective) | — | 1.000 | 54.4 | 0.288 | — | — | — |
| primary scores | label-free controls | |||||
|---|---|---|---|---|---|---|
| Cell | Ours | Raw | Supervised | kNN-1 | kNN-5 | Max-force |
| COMP6 MACE-OFF23(M) | 0.879 | 0.223 | 0.274 | 0.261 | 0.267 | 0.134 |
| COMP6 AIMNet2 | 0.822 | 0.237 | 0.255 | 0.236 | 0.244 | 0.131 |
| COMP6 AceFF-2 | 0.888 | 0.136 | 0.183 | 0.226 | 0.232 | 0.079 |
| QCML MACE-OFF23(M) | 0.820 | 0.910 | -0.278 | 0.362 | 0.385 | 0.245 |
| QCML AIMNet2 | 0.748 | 0.529 | 0.395 | 0.371 | 0.389 | 0.322 |
| (a) Matched-resource comparisons | |||||||
|---|---|---|---|---|---|---|---|
| Dataset | MLIP | DFT saving [pp] | MAE change [meV] | Success change [pp] | |||
| Raw | Sup. | Raw | Sup. | Raw | Sup. | ||
| COMP6 | MACE-OFF23(M) | +5.85 | +5.28 | -16.12 | -16.60 | +2.19 | +2.73 |
| AIMNet2 | +5.01 | +4.77 | -14.13 | -14.40 | +2.10 | +2.51 | |
| AceFF-2 | +6.47 | +5.94 | -14.63 | -15.43 | +2.67 | +2.91 | |
| QCML | MACE-OFF23(M) | -2.51 | +8.45 | +16.13 | -36.87 | -1.19 | +3.93 |
| Dataset | MLIP | Gini | Top 10% | Med. | ||||
|---|---|---|---|---|---|---|---|---|
| COMP6 | MACE-OFF23(M) | 0.18 | 0.16 | 24 | 3.4 | 45.4 | 139 | 516 |
| AIMNet2 | 0.16 | 0.15 | 24 | 2.2 | 46.4 | 132 | 474 | |
| AceFF-2 | 0.16 | 0.15 | 24 | 2.1 | 47.4 | 132 | 443 | |
| QCML | MACE-OFF23(M) | 1.00 | 1.00 | 9 | 48.2 | 158.5 | 485 | 3,895 |
| AIMNet2 | 0.45 | 0.40 | 9 | 34.3 | 122.6 | 126 | 839 | |
| AceFF-2 | 0.46 | 0.40 | 9 | 11.0 | 42.4 | 202 | 1,151 |
Selective Prediction
Selective prediction lets models answer only when sufficiently reliable, trading coverage for lower error through abstention, referral, or extra evidence gathering.
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