dtsdts/multifidelity-dft-deltas

Multi-fidelity DFT delta corrections for crystal structures

Dataset Description

This dataset contains ~60,000 crystal structure relaxations from the NOMAD repository, computed with the all-electron DFT code FHI-aims 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)

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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

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Loading Examples

Tabular data (Parquet)

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)

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"

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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

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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

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Citation

If you use this dataset, please cite:

@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},
}

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License

Creative Commons Attribution 4.0 International (CC BY 4.0)

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Training Code

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