Physics-Constrained Denoising Autoencoders for Data-Scarce Wildfire UAV Sensing

TL;DR

Wildfire monitoring relies on low-cost UAV sensors whose outputs suffer baseline drift, cross-sensitivity, and lag, and labeled data are scarce (approximately $8\times10^{3}$ samples at 1 Hz). To address this, the authors propose PC$^2$DAE, a physics-informed denoising autoencoder with a shared Temporal Convolutional Network encoder, environmental conditioning, and three sensor-family decoder heads (Black Carbon, Gas, CO$_2$), plus learnable temporal smoothing and a softplus-based positivity constraint. In data-scarce regimes, two variants—PC$^2$DAE-Lean (~21k params) and PC$^2$DAE-Wide (~204k params)—achieve zero physics violations while delivering state-of-the-art denoising, with Lean outperforming Wide (67.3% smoothness, 90.7% HF reduction). Evaluation on 7,894 synchronized 1 Hz samples from prescribed burns demonstrates practical viability for edge-ready, onboardable denoising with potential for real-time wildfire sensing and more reliable pollutant estimates.

Abstract

Wildfire monitoring requires high-resolution atmospheric measurements, yet low-cost sensors on Unmanned Aerial Vehicles (UAVs) exhibit baseline drift, cross-sensitivity, and response lag that corrupt concentration estimates. Traditional deep learning denoising approaches demand large datasets impractical to obtain from limited UAV flight campaigns. We present PC$^2$DAE, a physics-informed denoising autoencoder that addresses data scarcity by embedding physical constraints directly into the network architecture. Non-negative concentration estimates are enforced via softplus activations and physically plausible temporal smoothing, ensuring outputs are physically admissible by construction rather than relying on loss function penalties. The architecture employs hierarchical decoder heads for Black Carbon, Gas, and CO$_2$ sensor families, with two variants: PC$^2$DAE-Lean (21k parameters) for edge deployment and PC$^2$DAE-Wide (204k parameters) for offline processing. We evaluate on 7,894 synchronized 1 Hz samples collected from UAV flights during prescribed burns in Saskatchewan, Canada (approximately 2.2 hours of flight data), two orders of magnitude below typical deep learning requirements. PC$^2$DAE-Lean achieves 67.3\% smoothness improvement and 90.7\% high-frequency noise reduction with zero physics violations. Five baselines (LSTM-AE, U-Net, Transformer, CBDAE, DeSpaWN) produce 15--23\% negative outputs. The lean variant outperforms wide (+5.6\% smoothness), suggesting reduced capacity with strong inductive bias prevents overfitting in data-scarce regimes. Training completes in under 65 seconds on consumer hardware.

Figures (5)

• Figure 1: The Black Kite sensor suite mounted on an Aurelia X6 Pro V2 hexacopter. The payload integrates 15 sensors across five families (Black Carbon, Gas, PM, CO$_2$, Environmental) sampling at 1 Hz, producing synchronized multi-channel time series for post-processing. This platform provides the data used to develop and evaluate our denoising architecture.
• Figure 2: Data flow architecture showing multi-sensor integration and preprocessing. All streams are synchronized to 1 Hz for post-flight denoising via PC$^2$DAE, which currently operates offboard but is designed for future onboard deployment.
• Figure 3: PC$^2$DAE architecture for physics-constrained sensor denoising. The shared TCN encoder comprises three dilated 1D convolutional blocks with exponentially increasing dilation factors $(1,2,4)$ yielding $\sim$57-sample receptive field matched to sensor response dynamics. The symmetric decoder feeds into family-specific physics-constrained heads (BC: 4 channels, Gas: 9 channels, CO$_2$: 2 channels), each enhanced with channel attention and learnable temporal smoothing modules. Environmental conditioning ($T$, RH, $P$) modulates decoder outputs to compensate for temperature-dependent drift and humidity cross-sensitivity. The architecture currently executes offboard but is designed for onboard deployment on UAV-class edge hardware.
• Figure 4: Signal reconstruction comparison for Black Carbon and Gas sensor families. (a) Black Carbon UV channel: Raw input (gray shaded) exhibits characteristic high-frequency noise. PC$^2$DAE-Lean (teal) achieves 65.1% smoothness improvement and 95.3% HF noise reduction while maintaining strict positivity. LSTM-AE (orange dashed) achieves lower smoothness (19.7%) and produces 41.3% physics violations (negative outputs). Inset shows detail of noise suppression. (b) Gas sensor CO channel: PC$^2$DAE-Lean achieves 74.7% smoothness and 93.0% HF reduction with zero violations, substantially outperforming PC$^2$DAE-Wide (61.2%, 71.7%). Unconstrained baselines produce 20--29% negative outputs due to cross-sensitivity artifacts.
• Figure 5: Multi-dimensional comparison across six evaluation axes: Smoothness, HF Reduction, Physics compliance (100 $-$ % violations), Parameter Efficiency (inverse of parameter count), Training Speed, and Inference Speed. PC$^2$DAE-Lean (dark teal) achieves 100% physics compliance while maximizing denoising performance with 21k parameters, 62.7s training time, and 2.2ms inference per window. PC$^2$DAE-Wide (light teal) also achieves perfect physics compliance. All unconstrained baselines fail on physics compliance (77--85%), producing physically impossible negative concentrations.