Poraquê

Poraquê learns maps between the three-dimensional scalar fields of density-functional theory. For a given material the local external potential, the valence charge density and the kinetic energy density all live on one shared grid in one file format, which makes them directly comparable, composable, and usable as aligned inputs and targets for a neural operator.

Two mappings are learned:

\[V_{\mathrm{ext}} \;\longmapsto\; \rho \qquad\text{and}\qquad \rho \;\longmapsto\; \tau\]

They are not unrelated regressions. The first is the Hohenberg–Kohn map, whose existence and uniqueness is a theorem. The second is the kinetic energy density functional, the missing ingredient of orbital-free DFT. Composed, they constitute a complete orbital-free calculation from geometry alone — no wavefunctions, no self-consistency cycle.

What Poraquê provides

  • Scalar fields — a shared-grid data model for EXTCAR, CHGCAR and TAUCAR, with an analytic reconstruction of the local pseudopotential that reproduces a reference calculation to a relative \(2\times10^{-5}\).

  • Neural operators — Fourier neural operators that handle different grid shapes across materials, with physical constraints enforced by construction rather than by penalty.

  • Data sources and modular training — one dataset over a mixture of data layouts: local DFT runs, prepared caches, and bulk archives of standalone CHGCAR files. Each model trains independently, so the vast public density archives — which publish no kinetic energy density — are usable for the Hohenberg–Kohn map.

  • Energies and the ASE calculator — Kohn–Sham total-energy components integrated from the predicted fields, and an ASE calculator that runs the whole chain from an ase.Atoms object.

  • Charges and population analysis — charge-conservation checks and per-atom partial charges by Voronoi, Hirshfeld or Bader partitioning of the predicted density.

  • A code-agnostic ingestion layer: VASP is implemented, Quantum ESPRESSO and GPAW are scaffolded behind the same four-method contract.

  • Hardware acceleration on CUDA and Apple Metal, with a graceful CPU fallback.

  • A YAML-driven training pipeline that emits metrics, figures and a typeset PDF report.