A Physics-Informed MobileNetV2 Framework for Thermal Infrared Gas Classification: Combining Thermodynamic Input Features and Loss-Level Physics Penalization

Technical Summary: A Physics-Informed MobileNetV2 Framework for Thermal Infrared Gas Classification

Problem Statement
Current deep-learning approaches for thermal-infrared (TIR) gas classification treat calibrated thermal images as standard RGB photographs, discarding the underlying thermodynamic laws that govern the data. Specifically, prior studies on the MultimodalGasData benchmark fail to utilize the fact that pixel values represent true, camera-calibrated temperatures governed by fixed physical laws. This oversight leads to two critical issues:

1. Physical Implausibility: Standard data augmentation techniques (e.g., vertical flipping) create physically impossible scenarios, such as heated gas plumes descending against gravity, which contradicts buoyancy-driven convection.
2. Lack of Interpretability: Models may achieve high accuracy by learning dataset-specific visual artifacts rather than genuine thermodynamic signals. Consequently, classifiers can assign high confidence to gas hazards in thermally flat, featureless regions where no physical justification exists, posing a risk for safety-critical deployments where generalization to changing ambient conditions is required.

Methodology
The authors propose a Physics-Informed Machine Learning (PIML) framework that integrates thermodynamic principles directly into both the input representation and the training objective. The methodology consists of four core components:

1. Physics-Informed Input Tensor Construction:
   Instead of the standard three-channel RGB representation, the authors construct a six-channel tensor for each image:

   • Temperature-Normalized RGB: Raw pixel intensities are rescaled to a normalized temperature range ($T_{norm} \in [0, 1]$) based on the camera's fixed physical range ($-40^\circ\text{C}$ to $330^\circ\text{C}$), preserving the physical relationship between intensity and temperature.
   • Thermal Gradient Maps: Horizontal ($G_x$) and vertical ($G_y$) gradient maps are computed using the Sobel operator on a denoised and contrast-enhanced image. These maps are derived from Fourier's law of heat conduction ($q = -k\nabla T$), encoding the spatial boundaries of heat flux between gas-disturbed and undisturbed thermal states.
   • Local Temperature-Anomaly Map: A map generated by subtracting the local neighborhood mean (15×15 pixels) from the pixel value, isolating localized thermal anomalies characteristic of gas activity while suppressing background trends.
   • Physically Consistent Augmentation: Augmentation is restricted to horizontal flipping and bounded brightness adjustments. Vertical flipping and large rotations are explicitly excluded to prevent the generation of thermodynamically impossible images (e.g., descending heat plumes).

2. Model Architecture:
   The framework utilizes a MobileNetV2 backbone, selected for its balance of accuracy and computational efficiency (approx. 14 MB). To accommodate the six-channel input, a custom input-projection block (two $1\times1$ convolutional layers) precedes the backbone, re-projecting the six channels into the three channels expected by the pretrained MobileNetV2 weights. The architecture includes a classification head with global average pooling, a dense layer, dropout, and a softmax output for four classes: No Gas, Perfume, Smoke, and Mixture.

3. Physics-Penalized Loss Function:
   The training objective combines standard categorical cross-entropy ($L_{CE}$) with a thermodynamic plausibility penalty ($L_{physics}$):
   $$L_{total} = L_{CE} + \lambda \cdot L_{physics}$$
   The penalty term is defined as the mean of the product of gas confidence and the exponential decay of gradient magnitude. This formulation penalizes the model when it predicts a gas hazard with high confidence in regions lacking the steep thermal gradients required by Fourier's law, effectively pruning physically implausible hypotheses during backpropagation.

4. Two-Phase Training Strategy:

   • Phase 1 (Feature Adaptation): The MobileNetV2 backbone is frozen; only the input-projection block and classification head are trained to adapt to the six-channel physics-informed input.
   • Phase 2 (Fine-Tuning): The top 30 layers of the backbone are unfrozen, and the model is trained end-to-end with a reduced learning rate and early stopping to prevent overfitting.

Key Contributions

1. Six-Channel Physics-Grounded Input: The first application of a six-channel tensor (temperature-normalized RGB, Sobel gradients, and anomaly maps) for this dataset, replacing the standard RGB approach.
2. Thermodynamic Loss Regularization: The introduction of a loss function that explicitly penalizes confident gas predictions in thermally flat regions, enforcing physical plausibility during optimization.
3. Physical-Plausibility Validation: The first use of occlusion-based saliency analysis on this dataset to verify that model attention aligns with thermodynamically meaningful regions (e.g., the base of rising plumes) rather than incidental visual artifacts.
4. Comprehensive Benchmarking: A full evaluation against prior state-of-the-art results on the MultimodalGasData benchmark, including detailed class-wise error analysis.

Results
The proposed model achieved the following performance metrics on the held-out test set (962 images):

• Overall Accuracy: 94.80% (Test) and 96.67% (Best Validation).
• Class Performance:
  • Mixture: F1-score of 99.58% with zero false positives across 722 non-Mixture test images.
  • Smoke: F1-score of 96.22%.
  • Perfume: F1-score of 93.20%.
  • No Gas: F1-score of 90.31%.
• Error Structure: The model eliminated all confusion between the Perfume and Smoke classes (a common failure mode in prior models) and confined residual errors to the boundary between No Gas and single-gas classes.
• Saliency Analysis: Occlusion maps confirmed that the model's attention was concentrated in thermodynamically expected regions: the base of rising smoke plumes, diffuse upper-region warmth for aerosols, and multi-region activation for mixtures.

Significance and Claims
The paper argues that while the proposed model trails a purely accuracy-optimized MobileNetV2 baseline (99.76% accuracy) by 4.96 percentage points, this gap represents a quantified, favorable trade-off between raw accuracy and physical grounding.

• Safety-Critical Reliability: The authors claim that for safety-critical deployment, the qualitative restructuring of errors is more significant than the aggregate accuracy gain. By eliminating false alarms for the highest-consequence "Mixture" class and removing confusion between distinct hazard types, the model prioritizes structural robustness over exploiting dataset-specific artifacts.
• Generalization Potential: The framework is argued to be more robust to shifts in ambient temperature, camera orientation, or background conditions because it relies on universal thermodynamic constants (Fourier's law) rather than spurious correlations.
• Interpretability: The study provides the first physical-plausibility validation for this benchmark, demonstrating that high benchmark accuracy does not guarantee that a model's reasoning is safe to trust without verification against physical laws.

The authors conclude that their approach offers a viable path toward interpretable, safety-aware gas detection systems, noting that future work could integrate these physics-informed thermal features with sensor-array data to approach or exceed multimodal fusion performance while retaining physical interpretability.