cluster-09-exergy-field-pinn

Cluster 9 Exergy Field PINN

A Physics-Informed Neural Network predicting entropy generation, exergy destruction, and cycle efficiency for a heat engine running between any hot and cold reservoir temperature. Trained as part of the 9-cluster Scientific AI Cluster Orchestration Framework — the final cluster in the series — which pairs this network with exact symbolic ("Symetria") Carnot and Curzon-Ahlborn efficiency limits and two safety checks under LangGraph supervision.

Architecture

Entropy generation must be non-negative by the Second Law of Thermodynamics — a hard physical constraint, not an approximation — so that output is built using a Softplus function, which can only ever produce zero or positive numbers by construction. Since exergy destruction relates to entropy generation by an exact identity (Gouy-Stodola: exergy destroyed = T₀ × entropy generated), it's computed directly from the entropy-generation output rather than predicted as an independent, redundant third quantity.

Quickstart

import torch
from huggingface_hub import hf_hub_download
from modeling import ExergyFieldPINN

ckpt_path = hf_hub_download("dave1368/cluster-09-exergy-field-pinn", "exergy_field_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 = ExergyFieldPINN()
model.load_state_dict(checkpoint["model_state_dict"])  # checkpoint also carries training-time loss history, see training_metrics.json
model.eval()

# coords: (x, y, normalized_temp, hot_reservoir_K, cold_reservoir_K)
# normalized_temp ranges over [0, eta_carnot), the "Carnot deficit budget"
coords = torch.tensor([[0.5, 0.5, 0.1, 873.15, 298.15]])
s_gen, exergy_dest, efficiency = model(coords)[0].tolist()
print(f"s_gen={s_gen:.6f}  exergy_dest={exergy_dest:.4f}  efficiency={efficiency:.4f}")

Training data

Exact thermodynamic identities — no synthetic correlation needed. Labels come from the Clausius inequality combined with basic energy balance (η = η_Carnot − Tc·s_gen) and the Gouy-Stodola theorem (exergy destroyed = T₀ × entropy generated), not from measured or correlation-fit data:

• 60,000 training points, 10,000 validation points
• Domain: Th ∈ [100, 1500] °C, Tc ∈ [−50, 100] °C (with Th > Tc enforced)
• Final train loss: 7.30e-05 · Final val loss: 7.29e-05 (MSE, normalized target scale)

Validated against classical sources (post-deployment finding)

Cross-checked against Carnot (1824), Clausius (1865), Gouy (1889) & Stodola (1905), and Curzon & Ahlborn (1975) — the papers cited in this cluster's Master Specification. Full data tables in the Space README.

Limitations

• The Second Law safety check can't distinguish a good model from a bad one — it's a structural guarantee (see above), not a training-quality measure.
• The Carnot-limit check only catches predicted efficiency being too high; a model producing nonsensically negative efficiency would still pass it. In practice, this trained network's efficiency predictions stay well-behaved (see the validation table above), so this hasn't caused an actual wrong result — but the check alone isn't a complete sanity test.
• Models the general thermodynamic identities of a heat engine, not a specific engine cycle (Rankine, Brayton, etc.) — the spatial field being sampled represents an abstract operating-point sweep, not a real engine's physical geometry.

Related

• Space (interactive demo)