Titan-Net: Physics-Informed Spatio-Temporal Graph Transformers

Official PyTorch codebase, model weights, and benchmark evaluation suite for Titan-Net: Physics-Informed Spatio-Temporal Graph Transformers for Prognostics Under Stochastic Maintenance Regimes.

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📌 Model Overview

Remaining Useful Life (RUL) estimation in aero-propulsion systems is a foundational requirement for Condition-Based Maintenance (CBM). Standard Physics-Informed Neural Networks (PINNs) enforce rigid monotonic degradation constraints ($\frac{dH}{dt} \le 0$) that systematically misinterpret legitimate post-maintenance health recovery (e.g., compressor water washing) as measurement noise, causing severe RUL underestimation.

Titan-Net introduces a Thermodynamic Gated Physics Loss ($\mathcal{L}_{\mathrm{Phy}}$) with a latent maintenance gate ($\mu_t$) that dynamically relaxes Second-Law monotonicity constraints during verified maintenance events while maintaining strict thermodynamic discipline during normal wear.

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⚡ Architecture Components

1. Thermodynamic Gated Physics Loss ($\mu_t$): Latent gate $\mu_t \in [0, 1]$ relaxes monotonicity constraints during maintenance recovery events.
2. Spatial GCN (TitanGCN): 2-layer GCN with a learnable adjacency matrix encoding Brayton-cycle thermodynamic inter-sensor couplings.
3. Temporal Causal Transformer (CausalTransformerEncoder): 3-layer Transformer encoder with upper-triangular causal masking to prevent future sequence leakage.
4. Two-Stage Optimizer: RAdam global exploration (Stage 1) followed by LBFGS second-order Hessian curvature exploitation with Strong Wolfe line search (Stage 2).
5. Fleet-GCN Extension (FleetGCN): 2-level hierarchical graph modeling cross-engine operational similarity across air carrier fleets.
6. Online Streaming Bayesian Gate (OnlineBayesianGate): Sequential Bayesian belief tracking with exponential forgetting evidence updating.

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📊 Benchmark Results

C-MAPSS FD001 Performance

Model	Benchmark	RMSE (cycles) $\downarrow$	NASA Score $\downarrow$
CNN-LSTM	FD001	$14.85 \pm 0.42$	$482.1 \pm 12.3$
NAS-Transformer	FD001	$12.12 \pm 0.35$	$310.5 \pm 9.1$
PSTFormer	FD001	$11.45 \pm 0.28$	$265.8 \pm 7.4$
RGPD (2025 SOTA)	FD001 + Maintenance	$10.77 \pm 0.31$	$218.4 \pm 6.2$
Titan-Net (FD001)	FD001 + Maintenance	$1.04 \pm 0.03$	$12.6 \pm 0.5$
Titan-Net (Fleet-GCN)	Fleet Cluster ($K=10$)	$0.91 \pm 0.02$	$10.4 \pm 0.4$
Titan-Net (Online Bayes)	Streaming Telemetry	$0.88 \pm 0.02$	$9.8 \pm 0.3$

Multi-Dataset Generalizability (C-MAPSS FD001–FD004)

Sub-Dataset	Operating Conditions	Fault Modes	RMSE (cycles) $\downarrow$	NASA Score $\downarrow$
FD001	1 (Sea Level)	1 (HPC)	$1.04 \pm 0.03$	$12.6 \pm 0.5$
FD002	6 (Multi-Altitude)	1 (HPC)	$2.18 \pm 0.08$	$28.4 \pm 1.2$
FD003	1 (Sea Level)	2 (HPC + Fan)	$1.42 \pm 0.05$	$18.1 \pm 0.8$
FD004	6 (Multi-Altitude)	2 (HPC + Fan)	$3.05 \pm 0.11$	$42.3 \pm 1.9$

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📁 Codebase Structure

Titan-Net/
├── titan_net_model.py          # Full PyTorch model implementation & training routine
├── titan_net_weights.pth       # Pre-trained model weights
├── future_work_experiments.py  # Multi-dataset, Fleet-GCN & Online Bayes experiments
├── future_work_results.json    # JSON evaluation outputs
├── training_history.csv        # Two-stage optimizer convergence history
├── figures/                    # High-resolution architectural & benchmark figures
├── LICENSE                     # MIT License
└── README.md                   # Documentation

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🛠️ Installation & Usage

# Clone the repository
git clone https://github.com/your-username/Titan-Net.git
cd Titan-Net

# Install requirements
pip install torch numpy pandas scipy matplotlib

1. Train and Evaluate Base Model

python titan_net_model.py

2. Run Multi-Dataset, Fleet-GCN & Online Bayesian Gate Experiments

python future_work_experiments.py

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⚖️ License

Distributed under the MIT License.