Physics-informed neural network for dynamic demodulation of Fabry-Perot sensors under ultra-sparse sampling

We propose a physics-informed neural network (PINN) for dynamic cavity-length demodulation of fiber Fabry-Perot (F-P) sensors operating under ultra-sparse eight-channel arrayed-waveguide-grating (AWG) sampling. The F-P interference equation is embedded as a differentiable operator within the loss function, anchoring network optimization to the analytically correct fringe pattern at discrete wavelength channels spaced 0.8 nm apart. To mitigate the phase ambiguity inherent to sub-Nyquist spectral sampling, this physical operator is coupled with a total-variation (TV) regularization term, forming a regularized physics-informed training objective that suppresses non-physical fringe-order jumps between consecutive time steps. The network is trained in a fully self-supervised manner using only one second of single-condition raw data, and thereafter provides stable cavity-length tracking across vibration frequencies (5-40 Hz), displacement amplitudes (500-1300 µm), and two initial cavity-length settings within the same interrogation platform. Validation at a 10 kHz acquisition rate yields linear demodulation with R²>0.96 for all tested conditions, indicating that embedding physical priors into the optimization objective can mitigate the resolution limits imposed by sparse AWG hardware.