dave1368/cluster-05-compressible-euler-pinn

Cluster 5 Compressible Euler PINN

A Physics-Informed Neural Network predicting the compressible Euler flow field (P, ρ, u, v) across a stationary normal shock, at any upstream Mach number. Trained as part of the 9-cluster Scientific AI Cluster Orchestration Framework, which pairs this network with an exact symbolic ("Symetria") Rankine- Hugoniot shock solver and a Second Law (entropy) safety audit under LangGraph supervision.

Architecture

Input	(x, y, z, M1) — 4 features
Output	(P, ρ, u, v) — pressure, density, streamwise/spanwise velocity
Hidden layers	5 × 128 neurons, Tanh activation
Parameters	~67,000
Output scaling	log10(P/P1) (spans 2 orders of magnitude); ρ, u, v kept linear/normalized

Quickstart

import torch
from huggingface_hub import hf_hub_download
from modeling import CompressibleEulerPINN

ckpt_path = hf_hub_download("dave1368/cluster-05-compressible-euler-pinn", "compressible_euler_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 = CompressibleEulerPINN()
model.load_state_dict(checkpoint["model_state_dict"])  # checkpoint also carries training-time loss history, see training_metrics.json
model.eval()

# coords: (x, y, z, upstream_mach_number) -- x=0.5 is the shock location
coords = torch.tensor([[0.95, 0.5, 0.5, 3.0]])
p_rho_u_v = model(coords)
print(p_rho_u_v)  # tensor([[P, rho, u, v]])

Training data

Exact Rankine-Hugoniot normal-shock solution — no synthetic correlation needed. A stationary shock at x=0.5, planar (independent of y, z); upstream state is ISA-standard-day ambient, downstream state via the exact jump ratios:

• 60,000 training points, 10,000 validation points
• Domain: x ∈ [0, 1] (spatially oversampled near x=0.5, the shock), y, z ∈ [0, 1], M1 ∈ [1, 10]
• Final train loss: 0.00237 · Final val loss: 0.00388 (MSE, 3000 epochs, cosine LR decay)

Design notes and a known limitation

The shock is a true physical discontinuity in x (not a synthetic approximation), but unlike Cluster 3's multi-valued potential, a step function has no topological obstruction to a smooth network approximating it well — it just needs adequate local sampling density near the discontinuity, which the training data provides by design.

For upstream Mach numbers roughly in [1.10, 1.60], the network's own predicted pressure/temperature jump implies a spurious entropy decrease — a genuine approximation gap, not a bug in the audit or the orchestrator. The true entropy jump scales as (M1²−1)³, vanishing cubically as M1→1, while the network's absolute error stays roughly constant across the full Mach range — so near M1≈1, a small, otherwise-unremarkable prediction error can be larger than the true (tiny) margin it's being compared against. This is a capacity/formulation limit (the downstream audit combines two independently-evaluated points into a ratio, which can't resolve a cubically-vanishing margin), not a fixable training issue. See the Space README for the full data.

Validated against classical sources (post-deployment finding)

Cross-checked against Rankine (1870), Hugoniot (1887), and Mach (1887) — the papers cited in this cluster's Master Specification. Full data tables in the Space README.

Check	Result
Symetria exact ratios vs. published table (Anderson, Modern Compressible Flow)	Exact match at every tested M1
Second Law + downstream-subsonic (M2<1), exact solution	Holds at every tested M1
Network's predicted jump vs. exact, M1 outside [1.10, 1.60]	Passes Second Law audit at every tested point
Network's predicted jump vs. exact, M1 inside [1.10, 1.60]	Fails — genuine approximation gap, see above
Mach angle μ=arcsin(1/M1) (Mach, 1887)	Computed independently as context; not modeled by this network

Limitations

• Models a stationary 1D normal shock only — no oblique shocks or the Mach cone geometry Mach's own photographs captured.
• A bounded weak-shock Mach range (≈1.10–1.60) fails its own Second Law audit due to a real, unresolved approximation gap (see above). The orchestrator's retry mechanism cannot recover a different result for these inputs, since neither the network nor its check points are randomized between attempts.

Related

• Space (interactive demo)