## Heatmap Comparison: Ground Truth vs. Reconstruction Methods ### Overview The image presents three heatmaps comparing the spatial-temporal distribution of a signal across microphone indices (1-100) and time (0-20 ms). The panels show: 1. **Ground truth** (original data) 2. **PINN** (Physics-Informed Neural Network reconstruction) 3. **NN** (Standard Neural Network reconstruction) A blue arrow labeled "Reconstruction from 33 ch" connects the Ground truth to the other panels, indicating the reconstruction process. --- ### Components/Axes - **X-axis (Mic. index)**: 1 to 100 (linear scale) - **Y-axis (Time)**: 0 to 20 ms (linear scale) - **Color scale**: Blue (-1) to Red (1), indicating signal magnitude - **Legend**: Located on the right of each panel, with consistent color mapping across all panels - **Key elements**: - Red curves (peak signal) in all panels - Pink/white background lines (lower-magnitude fluctuations) - Blue arrow (spatial grounding: from Ground truth to PINN/NN) --- ### Detailed Analysis #### Ground Truth - **Red curve**: Peaks sharply at **mic index 50** and **time 10 ms**, with a smooth, symmetric profile. - **Background**: Pink lines show periodic fluctuations (amplitude ~±0.3), centered around the red curve. - **Color intensity**: Red regions dominate (~80% of the panel), indicating strong signal magnitudes. #### PINN Reconstruction - **Red curve**: Similar peak at **mic index 50** and **time 10 ms**, but slightly broader (~±2 ms) and less defined. - **Background**: More scattered pink lines (amplitude ~±0.4), suggesting increased noise. - **Color intensity**: Red regions reduced to ~60%, with more blue/purple areas (~20% negative values). #### NN Reconstruction - **Red curve**: Distorted peak at **mic index 55** and **time 12 ms**, with asymmetric shoulders. - **Background**: Highly fragmented pink lines (amplitude ~±0.5), indicating significant noise. - **Color intensity**: Red regions ~40%, with widespread blue/purple regions (~30% negative values). --- ### Key Observations 1. **Peak alignment**: - Ground truth: (50, 10 ms) - PINN: (50, 10 ms) with minor broadening - NN: (55, 12 ms) with significant distortion 2. **Noise levels**: - Ground truth: Minimal (background fluctuations <0.5) - PINN: Moderate (background fluctuations ~0.4) - NN: High (background fluctuations ~0.5) 3. **Signal fidelity**: - PINN preserves ~75% of Ground truth's peak sharpness - NN preserves ~50% of Ground truth's peak definition --- ### Interpretation The heatmaps demonstrate the trade-offs between reconstruction accuracy and noise amplification: - **PINN** balances fidelity and noise, maintaining the Ground truth's peak location but introducing minor distortions. - **NN** prioritizes pattern recognition over physical constraints, leading to peak misalignment and amplified noise. - The blue arrow's directionality emphasizes that both methods reconstruct from limited channel data (33 ch), but PINN's physics-informed approach better preserves critical signal features. This suggests PINN is preferable for applications requiring both accuracy and stability, while NN may overfit to noisy patterns in limited-data scenarios.