cluster-03-potential-flow-pinn

Cluster 3 Potential Flow PINN

A Physics-Informed Neural Network predicting velocity potential (φ) and stream function (ψ) for 2D potential flow around a rotating cylinder — the pre-image, under the exact Joukowski conformal map, of a Joukowski airfoil — at any angle of attack. Trained as part of the 9-cluster Scientific AI Cluster Orchestration Framework, which pairs this network with an exact symbolic ("Symetria") Joukowski solver and two physics-grounded safety audits under LangGraph supervision.

Architecture

The network predicts only the smooth, single-valued doublet+uniform-flow part of φ (plus ψ). The multi-valued vortex/circulation contribution to φ — (Γ(α)/2π)·θ, a genuine topological feature of point-vortex potentials that no smooth feedforward network can represent without corrupting its local gradient near the branch cut — is added analytically instead, so the network is only ever asked to learn the smooth part it can actually represent.

Quickstart

import torch
from huggingface_hub import hf_hub_download
from modeling import PotentialFlowPINN

ckpt_path = hf_hub_download("dave1368/cluster-03-potential-flow-pinn", "potential_flow_pinn.pt")
# weights_only=False: the checkpoint is a dict with metadata (model_state_dict
# plus training info), not a bare tensor, so torch's default-safe loader can't
# be used as-is. Only do this for checkpoints you trust the source of.
checkpoint = torch.load(ckpt_path, map_location="cpu", weights_only=False)

model = PotentialFlowPINN()
model.load_state_dict(checkpoint["model_state_dict"])  # checkpoint also carries training-time loss history, see training_metrics.json
model.eval()

# coords: (x, y, angle_of_attack_degrees)
coords = torch.tensor([[1.5, 0.5, 5.0]])
phi_psi = model(coords)
print(phi_psi)  # tensor([[phi, psi]])

Training data

Exact closed-form labels — no synthetic correlation needed. For each sampled (r, θ, α), the exact potential-flow-around-a-rotating-cylinder solution (uniform flow + doublet + circulation, with circulation set by the Kutta condition at the trailing edge) provides the ground-truth (φ, ψ):

• 60,000 training points, 10,000 validation points
• Domain: r ∈ [1, 5·R], θ ∈ [-π, π], α ∈ [-10°, 25°]
• Final train loss: 3.80e-05 · Final val loss: 3.76e-05 (MSE, 3000 epochs)

Validated against classical sources (post-deployment finding)

Cross-checked against Euler (1757), d'Alembert (1752), and Joukowski (1910) — the papers cited in this cluster's Master Specification. Full data tables in the Space README. This network's drag error, correctly measured in the flow-aligned frame, is small and roughly constant across the full AoA range (0.13–0.35) rather than growing with angle.

Limitations

• Pointwise accuracy degrades near the airfoil surface (r ≈ R), especially right at the stagnation point — the region of steepest field curvature.
• Inviscid potential flow cannot represent boundary layers, separation, or stall — by construction (this is the content of d'Alembert's Paradox).
• The d'Alembert audit doesn't really grade how well this model learned the physics — a barely-trained version of this network, whose output changes very little from point to point, would also pass, since it too produces near-zero drag. What the audit is actually good at is catching a badly broken model, not measuring how accurate a working one is.

Related

• Space (interactive demo)