AlienX Labs — pip install alienx-labs

Isomorphic Spatial Net (ISN): neural operators that operate on continuous geometric manifolds instead of fixed grids — native rotation and scale invariance, zero-shot across resolutions and Reynolds numbers.

The grid is dead. The manifold is awake.

Three pretrained operators, weights bundled in the wheel (no downloads, no setup — install and call):

Install

pip install alienx-labs

60-second tour

import torch, alienx_labs as ax

dev = "cuda" if torch.cuda.is_available() else "cpu"

# ── 1. Darcy flow: rotate the world, the operator does not notice ─────────
model = ax.load_darcy2d().to(dev)
sample = ax.data2d.generate_darcy_sample_gpu(64, dev, angle_deg=37.0, seed=7)
coords, k, gkm, gkv, p_true = sample
knn = ax.model2d.get_cached_iso_knn(64, dev)
p_pred = model(coords.unsqueeze(0), k.unsqueeze(0), gkv.unsqueeze(0),
               gkm.unsqueeze(0), knn).squeeze(0)
# p_pred is (64*64,) pressure — compare to p_true

# ── 2. Gross–Pitaevskii: complex wavefunction evolution ────────────────────
gp = ax.load_gp2d().to(dev)
psi0, psi_t = ax.gp2d.generate_gp_pair(64, dev, angle_deg=0.0, seed=1003)
d_r, d_i = gp(ax.gp2d.model_coords(64, dev).reshape(-1, 2),  # see docstring
              psi0.real.flatten().unsqueeze(0),
              psi0.imag.flatten().unsqueeze(0),
              ax.model2d.get_cached_iso_knn(64, dev), 64)
psi_pred = torch.complex(psi0.real.flatten() + d_r, psi0.imag.flatten() + d_i)

# ── 3. 3D turbulence: 32³ Taylor–Green, a Reynolds it never trained on ────
op3 = ax.load_turb3d().to(dev)      # trained on Re ∈ {300, 628, 1200}
print(op3.G)                        # 32 — pass Re it has NEVER seen

Full runnable scripts (Darcy sweep, GP rollout, 3D TGV rollout with the spectral solver as ground truth) ship inside the package: python -m alienx_labs.examples — or lift them from examples/ in the repo.

What makes it invariant (the architecture in one paragraph)

Each node lives on a spatial graph with an isotropic 24-neighbor circular stencil (radius √8 — uniform angular coverage, no cardinal spikes). A local SO(2)/SO(3) frame (gradient primary, inertia-tensor fallback with a sign_lock that makes eigh's arbitrary eigenvector sign deterministic and equivariant) makes displacements rotation-equivariant. Edge features encode the local angle as even complex harmonics (cos 2θ, sin 2θ, cos 4θ, sin 4θ) — message weights invariant under θ → θ + π. A constant physical scale depth makes the operator scale-blind by construction — exactly what produces zero-shot resolution transfer. The 3D operator runs on the QSA block: complex-valued (Hermitian-scored) attention whose phase channel carries real predictive signal — ablate it (sever_phase(True)) and zero-shot error grows 4.7×. No data augmentation. No learned geometry.

Hand-verified numbers (rerun from the bundled checkpoints)

Gradio / Spaces

The labs are live (no install needed):

• Sigil Lab 2D (Darcy): https://huggingface.co/spaces/ElBalor/AlienX-Sigil-Lab-2D
• GP Lab: https://huggingface.co/spaces/ElBalor/AlienX-GP-Lab
• Flow Lab 3D (Navier–Stokes): https://huggingface.co/spaces/ElBalor/AlienX-Flow-Lab-3D

Papers

• 2D (v3, with the Gross–Pitaevskii cross-PDE demonstration): ElBalor/AlienX-2D-Isotropic-Stencil
• 3D: ElBalor/AlienX-3D-ISN-Operator

Citation

@software{yaka2026alienx,
  author = {Yaka, Eric Heylel Danjuma},
  title  = {AlienX: Isomorphic Spatial Nets - Equivariant Neural Operators for Physical Fields},
  year   = {2026},
  url    = {https://huggingface.co/ElBalor/AlienX-2D-Isotropic-Stencil}
}

License

AGPL-3.0 — see LICENSE.

Eric Yaka (Elbàlor / The Digital Necromancer) · Capital Software · Abuja, Nigeria