Poraquê

Poraquê is a software framework for machine learning operators between the real-space fields of density functional theory. Given only a crystal geometry, it predicts the charge density and the kinetic energy density — no wavefunctions, no self-consistency cycle.

Two Fourier Neural Operators are learned: the first maps the external potential to the charge density (ext2chg), the second maps the charge density to the kinetic energy density (chg2tau). They are not two unrelated regressions — the first is the Hohenberg–Kohn map, whose existence is a theorem, and the second is the kinetic energy density functional, the missing ingredient of orbital-free DFT.

Install

pip install poraque

Or from source, which is what you want if you intend to change anything:

git clone https://github.com/seixas-research/poraque.git
cd poraque
pip install -e .

Python 3.11 or newer. Symbolic distillation is an optional extra: pip install "poraque[symbolic]". Installing registers seven console commands — poraque-train, poraque-inference, poraque-committee, poraque-active-learning, poraque-atoms, poraque-vasp and poraque-mp — which run from any directory once the environment is active. All but the last are the main() of the script of the same name under scripts/, so python scripts/poraque_train.py is equivalent to poraque-train and needs nothing installed.

Faster CPU inference (optional)

Poraquê ships a small C kernel for the spectral contraction — the one part of a Fourier layer PyTorch runs poorly at batch 1, which is the shape every prediction has. It compiles itself on first use and needs no configuration.

python -m poraque.ml.backend --benchmark    # compile now and check it

2–3.4× on whole-model CPU inference at 24–32³ (less at 96³, where the FFTs dominate). Optional in every sense: without a C compiler everything works and falls back to torch.einsum. Training is unaffected, accuracy is identical to float32 rounding, and PORAQUE_C_BACKEND=0 turns it off. See the User Guide §1.5 for the details.

Use

# 1. train one ext2chg and one chg2tau model on all structures
poraque-train --config configs/train.yaml

# 2. measure generalisation
poraque-train --config configs/train.yaml --kfold --k-folds 5

# 3. predict a structure that has never been computed. --models points at
#    the bundle step 1 wrote: models/<task.name>/<task.name>.pfno
poraque-inference new_structure/ --output predictions/new_structure \
    --models models/pt_w16_m8_l3/pt_w16_m8_l3.pfno

# 4. calibrate: does committee disagreement predict error? Run this on
#    LABELLED data first -- it costs nothing and says whether step 5 means
#    anything. Read the Spearman coefficient. --cache is the tagged
#    directory step 1 built (the tag encodes resolution and potentials).
poraque-committee --models "models/committee_*" --task ext2chg \
    --cache data/cache/res32_potcar --against models/<name>/log/<name>.json

# 5. select: which UNLABELLED structures to compute next. This one spends
#    the DFT budget, so it is the one that needs step 4 to have passed.
poraque-active-learning --models "models/committee_*" --task ext2chg \
    --pool data/pool --select 5

Steps 4 and 5 are two halves of one loop, not two ways of doing the same thing. poraque-committee runs on labelled data and asks whether the disagreement measure predicts error at all — it costs nothing and produces a Spearman coefficient. poraque-active-learning runs on an unlabelled pool and turns that measure into a spending decision. Run the first one first.

Every predicted field is written in CHGCAR format.

Configuration

Every key is optional — a file states only what the run does differently. That is why configs/train.yaml fits on half a page: of the ~80 settings a full config carries, it changes a handful.

configs/train_complete_and_commented.yaml is the reference: it lists the settings worth knowing about, each with the reasoning behind it. Read it there and copy only what you need into your own file.

One directory per model

Everything a run writes lands under models/<name>/:

models/pt_w16_m8_l3/
    pt_w16_m8_l3.pfno     the weights
    log/                  training log, metrics JSON, resolved config
    plots/                loss curves, parity, field slices
    report/               the generated PDF

A trained model is not one file: it is weights, plus the numbers that say how good they are, plus the figures behind those numbers, plus the config that produced them. Naming the run is the only thing you set — task.name — and two runs with different names cannot collide.

Each part can be switched off independently:

output:
  root: models              # null disables all output
  write_log: true
  plot_figures: true
  write_pdf_report: true
  checkpoint: true

or from the shell with --output-root DIR, --no-plots, --no-report.

Precision

Two independent settings, because they control different costs:

data:  {precision: float64}    # how fields are stored: float16 | float32 | float64
model: {precision: float32}    # what the operator computes in: float32 | float64

data.precision is memory — a 160³ field is 16 MB in double and 8 MB in single. model.precision: float64 roughly doubles time and memory and is for checking that a physical result is not a single-precision artefact; it needs training.device: cpu, since Metal has no float64 at all.

Or drive it from ASE:

from ase.build import bulk
from poraque.calculator import Poraque

atoms = bulk("Pt", "fcc", a=3.92, cubic=True)
atoms.calc = Poraque("models/poraque_models.pfno", potcar_dir="POTCARs")

rho = atoms.calc.get_charge_density(atoms)   # ChargeDensity, e/Ang^3
print(rho.electron_count())                  # 44.0, the valence count
rho.write("CHGCAR_pred")                     # readable by any DFT tool

charges = atoms.get_charges()                # net charge per atom, +e
print(atoms.calc.charge_analysis)            # populations, valence, method

potcar_dir is a POTCAR library — one subdirectory per element, <potcar_dir>/Pt/POTCAR — not a single POTCAR file. The entries for whatever elements the Atoms happens to contain are assembled on demand, which is what lets one calculator serve arbitrary compositions.

Forces and stress are not implemented, so this is single points, not relaxations.

Training on the Materials Project

poraque-mp turns a chemical space — a set of elements — into a local dataset of charge densities. Size it first; over a chemical space the estimate is exact, because charge densities are objects in a public S3 bucket and their sizes are read with HEAD requests that transfer no payload:

# a pure dry run: prints to the console and writes nothing at all
poraque-mp --elements Pt Pd Ni --estimate

# download into ./data/MP, skipping anything over 20 MB
poraque-mp --elements Pt Pd Ni --output data/MP --max-size-mb 20

--output (or --outdir) defaults to the current directory, so a command that writes hundreds of megabytes puts them where you ran it. Files stay gzipped; Poraquê reads compressed volumetric files in place.

The per-object size cap has two spellings and they are the same cap: --max-size-mb and --max-size-gb, a decimal factor of 1000 apart, matching every size this tool prints. One CHGCAR is an MB-scale object and a whole download is a GB-scale one, so which unit reads naturally depends on which of the two you are thinking about. Passing both is refused rather than resolved.

The whole database is --all, stated explicitly. It selects every material the index says has a charge density — one server-side query rather than 2ⁿ chemical systems — and the search filters still apply under it, which is how a subset of everything is taken. Omitting --elements is not a second spelling of it: a command naming neither is refused, since a forgotten flag would otherwise become a multi-terabyte transfer.

--sample N is what makes --all usable. It draws N materials at random and those become the working set — with --estimate it sizes exactly those N, and without --estimate it downloads them. Everything the run writes into --output describes that subset, summary and CIFs included, so a sampled directory never carries an index of a set it does not hold.

# what would 20 random materials from the whole database cost?
poraque-mp --all --estimate --sample 20

# fetch exactly those 20
poraque-mp --all --sample 20 --output data/MP

# the trainable subset of it, as compressed HDF5
poraque-mp --all --num-sites 1 12 --max-size-mb 20 \
    --output data/MP --hdf5 --compression gzip

A sampled estimate still projects to the whole set — the sample mean times the number advertised — on its own line and labelled as a projection, because sizing the database is what you usually want to know before deciding to fetch a piece of it. Both numbers are printed; one alone would be read as the other.

--seed decides which subset, and it is a set rather than a lottery: the same seed selects the same materials, so an interrupted sampled download resumes onto the same subset instead of fetching N more beside it. Sizes are also strongly right-tailed, so two draws of twenty can differ by tens of percent, and a projection that moved on every run could not be planned against.

A download is one directory per material, named by its id — the shape of a VASP run, and the shape data.data_paths already reads:

data/MP/
    summary.csv  manifest.json  manifest.csv
    structures/mp-124.cif
    mp-124/{CHGCAR.gz, INCAR, KPOINTS, POSCAR, mp.json}
    mp-81/ {CHGCAR.gz, INCAR, KPOINTS, POSCAR, mp.json}
    mp-126/{fields.h5, ...}    # with --hdf5

The three VASP inputs reconstruct the calculation, so a material directory is one VASP can be pointed at. INCAR and KPOINTS come from the task record the density belongs to — MP's standard static set fills in when a record cannot be read, and the file says which. The POSCAR comes from the density's own header: that is the geometry it was computed at, and taking it from anywhere else is how a directory ends up with a structure and a density that disagree.

None of them is training data. The loader records the density and nothing else, and the external potential stays computed — mp.json is what keeps the directory from being mistaken for a VASP run now that it looks like one. --no-vasp-inputs skips the three.

--hdf5 keeps everything, and VASP still cannot read it

--hdf5 writes each density as a chunked, compressed field store instead of a CHGCAR. It is a re-encoding rather than a conversion — pymatgen already holds ρ·Ω, which is what the store keeps — and it carries everything the text file does: the magnetisation block of a spin-polarised density, and the PAW augmentation records, the one-centre terms ICHARG = 1 will not restart without.

What no store can do is be opened by VASP, so a run needs the density written back out:

poraque-vasp chgcar data/MP/mp-124/fields.h5 --output CHGCAR

# or straight into a deck, which converts rather than copies
poraque-vasp energy data/MP/mp-124/fields.h5 --like <run> --copy-density

Every mode takes a store where it takes a CHGCAR — address one field as fields.h5::CHGCAR when the store holds several. A text source is copied byte for byte rather than parsed and re-emitted: re-rendering a file that was already correct can only lose digits or shift a column, and the density block is a column-positional Fortran read.

Then train. data_paths is the only key that names a dataset, and a download goes in it exactly as a run tree does — every entry is a directory of per-material subdirectories, and nothing says which is which:

task: ext2chg              # MP publishes no tau, so chg2tau is not trainable
data:
  data_paths:
    - data/MP              # mp-124/, mp-81/, ...
    - data/vasp/structures # optional: your own runs, pooled into the same set
  potcar_dir: /opt/vasp/potpaw_PBE     # see below
  resolution: 32

TAUCAR is optional per material, so type: all on a mixture trains ext2chg on everything and chg2tau on whichever materials have a τ.

poraque-train --config configs/train_materialsproject.yaml

Set potcar_dir. An MP download has a structure and a density and no pseudopotentials, and the external potential — the model's input — cannot be built exactly without them. Point at the POTCAR library that generated the data (MP uses the VASP PBE set) and V_ext is VASP's tabulated local potential, accurate to a relative 2×10⁻⁵. Leave it out and the Gaussian pseudo-ion model stands in: on the Ag–Pt–Pt set the two differ by 0.38 relative L2 — they are different fields, not different roundings of one. Missing entries warn and fall back per element rather than failing the run.

The structure itself needs nothing extra: a CHGCAR carries its own POSCAR in its first lines.

What is in here

Design points

• The external potential is computed natively. Poraquê reconstructs it from the POTCAR tables on any standard VASP output, matching a reference potential to a relative 5×10⁻⁵. There is no option to import one: the training input must be exactly what inference produces. Where the data ships no pseudopotentials — a public density archive, or a run whose POTCAR was stripped — potcar_dir supplies them and the same exact construction is used; failing that, a Gaussian pseudo-ion model stands in, and the run says which of the two it used.
• Grids may differ between materials. One model serves all of them: the operator's weights live in Fourier-mode space, and batches are bucketed by grid shape.
• Constraints are structural where possible. For chg2tau, τ = τ_vW[ρ] + softplus(·) makes the Hoffmann-Ostenhof bound hold by construction rather than by penalty.
• Resampling is spectral. Fourier truncation is the exact band-limited projection for a plane-wave field; interpolation would alias and shift the electron count.
• CUDA, Apple Metal and CPU, selected automatically.

Status

Seventeen platinum supercells — ten 27-atom cells and seven 32-atom cells, spanning four grid shapes. A single 80/20 split at 32³ working resolution, 300 epochs with early stopping, whole structures held out (seed=42):

R² on the held-out structures is 0.9976 (ext2chg) and 0.9953 (chg2tau). The ± is the spread across the three validation structures, not a cross-validation error bar — see the caveat below.

The learned kinetic functional beats the analytic orbital-free functionals by a wide margin on this system — on the same held-out fields Thomas-Fermi scores 1.347 and von Weizsäcker 0.738, so chg2tau is 26× and 14× better respectively.

What this split can and cannot tell you. With valid_fraction = 0.2 and 17 structures, the held-out set is three structures — and at seed=42 all three (struct_011, struct_012, struct_016) happen to be 32-atom cells. So the headline numbers describe the harder subset only, there is no held-out 27-atom measurement at all, and three structures is too thin a base for a meaningful error bar. Earlier 5-fold cross-validation on the 12-structure dataset put 32-atom cells at roughly twice the error of 27-atom ones; the number above is consistent with that, and is better than the 0.0445 that subset scored then, which is what four 32-atom cells in training rather than one should buy. Use --kfold for a figure that covers every structure.

Still one element. These numbers measure interpolation between geometries of platinum and now, weakly, extrapolation across cell size. They say nothing about transfer to other chemistry. Growing the dataset remains the main open item — see docs/notes/roadmap.md.

Energies are not there yet. The total energy is a sum of terms of order 10⁴ eV whose physically relevant variation is a fraction of an eV per atom — a relative ~10⁻⁴ — and a field-level error of 2×10⁻² cannot survive that cancellation. The last full measurement, on the earlier 12-structure dataset, put the true spread at 0.27 eV/atom against an error on predicted differences of 0.29 eV/atom — a ratio of 1.06 with correlation r ≈ −0.1. Those figures have not been re-measured on the current 17-structure dataset, and the verdict they support is unchanged either way: an error equal to the signal and no correlation means the predicted energy ordering carries no information. The energy module itself is validated against exact Madelung constants and uniform-electron-gas limits; it is the fields that are not yet accurate enough. See docs/source/energy/index.md.

License

Poraquê is released under the MIT License. Copyright © 2026 Leandro Seixas Rocha.

Acknowledgements

We thank financial support from INCT Materials Informatics (Grant No. 406447/2022-5).