---
license: cc-by-4.0
task_categories:
  - other
tags:
  - materials-science
  - dft
  - crystal-structures
  - multi-fidelity
  - gnn
  - delta-learning
pretty_name: "Multi-fidelity DFT delta corrections for crystal structures"
size_categories:
  - 10K<n<100K
---

# Multi-fidelity DFT delta corrections for crystal structures

## Dataset Description

This dataset contains ~60,000 crystal structure relaxations from the
[NOMAD repository](https://nomad-lab.eu), computed with the all-electron DFT
code [FHI-aims](https://fhi-aims.org) at multiple levels of numerical precision
(basis set size × k-point density). For each pair of a low-fidelity and a
high-fidelity calculation on the same structure, we provide the **delta
corrections** — the difference in key physical observables between the two
settings.

The dataset was constructed to train and evaluate machine-learning models that
predict the correction needed to "upgrade" a cheap DFT calculation to a more
expensive one, without running the expensive calculation.

### Key quantities

| Symbol | Column | Description |
|--------|--------|-------------|
| ΔE | `delta_total_energy_per_atom` | Energy delta (eV/atom) |
| ΔE_g | `delta_homo_lumo_gap` | HOMO–LUMO gap delta (eV) |
| ΔV | `delta_final_volume_per_atom` | Volume delta (ų/atom) |

---

## Files

| File | Format | Size | Description |
|------|--------|------|-------------|
| `data.parquet` | Parquet (snappy) | ~92 MB | Tabular delta corrections + DFT settings + features |
| `graph_data.pt` | PyTorch `torch.save` | ~352 MB | Pre-processed graph dataset for GNN training |

---

## Loading Examples

### Tabular data (Parquet)

```python
import pandas as pd

df = pd.read_parquet("data.parquet")
print(df.shape)          # (59235, 175)
print(df["basis_size"].value_counts())
print(df["delta_total_energy_per_atom"].describe())
```

### Graph data (PyTorch / PyG)

```python
import torch

graphs = torch.load("graph_data.pt", map_location="cpu")
# graphs is a list of torch_geometric.data.Data objects
g = graphs[0]
print(g.x.shape)          # atom features
print(g.edge_index.shape) # connectivity
print(g.pos.shape)        # fractional / Cartesian positions
# g.split  →  "train" | "val" | "test"
```

---

## Column Dictionary

### Identifiers & DFT settings

| Column | Type | Description |
|--------|------|-------------|
| `compound_name` | str | Chemical formula + ICSD index label |
| `formula` | str | Reduced chemical formula |
| `ICSD_number` | int | ICSD database entry number |
| `uid` | str | Unique structure–setting identifier |
| `split` | str | `train` / `val` / `test` (80/10/10 by structure) |
| `basis_size` | str | FHI-aims basis tier: `minimal`, `standard`, `tier1`, `tier2` |
| `k_point_density` | int | Monkhorst–Pack k-point density parameter (2, 4, or 8) |
| `functional` | str | XC functional (PBE throughout) |
| `relaxation` | str | Relaxation protocol identifier |

### Primary delta targets

| Column | Unit | Description |
|--------|------|-------------|
| `delta_total_energy_per_atom` | eV/atom | Total energy difference (low→high fidelity) |
| `delta_homo_lumo_gap` | eV | HOMO–LUMO gap difference |
| `delta_final_volume_per_atom` | ų/atom | Cell volume difference |
| `delta_relaxed_a_len` | Å | Lattice parameter *a* difference |
| `delta_relaxed_b_len` | Å | Lattice parameter *b* difference |
| `delta_relaxed_c_len` | Å | Lattice parameter *c* difference |

### Structure geometry (low-fidelity baseline)

| Column | Unit | Description |
|--------|------|-------------|
| `original_volume` | ų | Unit cell volume before relaxation |
| `final_volume` | ų | Unit cell volume after low-fidelity relaxation |
| `original_a_len`, `_b_len`, `_c_len` | Å | Pre-relaxation lattice parameters |
| `relaxed_a_len`, `_b_len`, `_c_len` | Å | Post-relaxation lattice parameters (low-fidelity) |
| `original_atom_positions` | str | Fractional positions (JSON-encoded) |
| `relaxed_atom_positions` | str | Relaxed fractional positions (low-fidelity) |

### Elemental features (statistics over atoms in unit cell)

Columns follow the pattern `{stat}_{feature}` where `stat` ∈ {`max`, `min`, `mean`, `mad`}:

| Feature suffix | Description |
|----------------|-------------|
| `atomic_EA_half` | Electron affinity (half-electron, eV) |
| `atomic_IP_half` | Ionisation potential (half-electron, eV) |
| `atomic_HOMO` / `atomic_LUMO` | HOMO/LUMO energy of isolated atom (eV) |
| `atomic_rs/rp/rd/rf` | Orbital radii (Bohr) |
| `monomer_total_energy_per_atom` | Free-atom reference energy (eV/atom) |
| `monomer_volume_per_atom` | Free-atom reference volume (ų/atom) |
| `monomer_bandstructure_gap` | Free-atom band gap proxy (eV) |
| `valence_electrons` | Number of valence electrons |
| `basis_functions` | Number of basis functions per atom |

---

## Dataset Statistics

- **Total rows:** 59,235
- **Unique structures:** ~14,500
- **Basis sizes:** `minimal`, `standard`, `tier1`, `tier2`
- **k-point densities:** 2, 4, 8
- **Elements covered:** H through Bi (excluding lanthanides/actinides; a small number of heavy-element structures are filtered)
- **Train / val / test split:** 80 / 10 / 10 by unique crystal structure

---

## Citation

If you use this dataset, please cite:

```bibtex
@inproceedings{speckhard2026multifidelity,
  title     = {Multi-fidelity {DFT} delta corrections for crystal structures},
  author    = {Speckhard, Daniel and others},
  booktitle = {ICML 2026 Workshop on Machine Learning for Materials},
  year      = {2026},
}
```

---

## License

[Creative Commons Attribution 4.0 International (CC BY 4.0)](https://creativecommons.org/licenses/by/4.0/)

---

## Training Code

The GNN and Random Forest training code used with this dataset is available at:  
**https://gitlab.mpcdf.mpg.de/dansp/errorbar_modelling**