Neural operators for electronic structure applications
A software framework for machine learning operators between the real-space functions of density functional theory (DFT). The model predicts the charge density and the kinetic energy density. No wavefunctions, no diagonalizations, no self-consistency cycle.
Two Physics-Informed Fourier Neural Operators (PIFNOs) do the work. EXT2CHG maps the (local) external potential to the charge (pseudo)density, the Hohenberg–Kohn map, whose existence is guaranteed by a theorem. CHG2TAU maps the charge (pseudo)density to the kinetic energy (pseudo)density, the missing ingredient of orbital-free DFT.
Vext
(local) external potential
Calculated by Poraque itself, using additional (optional) data from the POTCARs
charge density
ρ
charge density
Charge density (including PAW contribution) in CHGCAR format
kinetic energy density
τ
kinetic energy density
Kinetic energy density (TAUCAR) calculated by VASP 6.6+
What Poraquê learns
ext2chg
The Hohenberg–Kohn map
The external potential Vext fixes the ground-state density — that correspondence is a theorem, not an approximation. Poraquê learns it as a Fourier Neural Operator: no wavefunctions, no diagonalizations, no self-consistency cycle, one forward pass from a bare geometry to ρ.
Vext is computed natively from POTCAR tables
Falls back to a Gaussian pseudo-ion model when no pseudopotential is available
A physics-informed electron-count term keeps the charge density integral close to the nominal valence charge
Every predicted function (field) is written in CHGCAR format
chg2tau
The kinetic energy density map
The kinetic energy density is the ingredient that would let orbital-free DFT replace Kohn–Sham outright, and no closed form for it is known. Poraquê fits it directly against reference kinetic energy densities.
Physics-informed constraints for the Thomas-Fermi and von Weizsäcker limits.
Non-linear and non-local relationship with the charge density
An optional Sobolev (H¹) loss penalizes error in the gradient, not only the value
Symbolic distillation (PySR, optional) can fit a closed-form expression to the trained residual
A trained pair (ext2chg and chg2tau) lives in one bundle.
01
Data ingestion
A directory of VASP calculations (including CHGCAR and TAUCAR), a Materials Project download, or both at once. Every layout normalizes through one data ingestion before training ever sees it.
02
Training
Input file in YAML format. One command trains ext2chg and chg2tau together and writes a single bundle holding both.
03
Prediction
Inference of charge density and kinetic energy density solely from the material geometry (POSCAR).
