Flame response inference from pressure-only data via physics-informed neural networks

This study presents a physics-informed neural network framework to reconstruct spatio-temporal acoustic pressure fields and hidden quantities—namely, velocity and heat-release-rate fluctuations—in axial combustors using only sparse pressure measurements. By embedding the linearized Euler equations into the training process, the network simultaneously enforces physical consistency and fits limited experimental data, enabling identification of the flame response. The methodology is validated across progressively more complex configurations, from canonical one-dimensional problems to quasi-one-dimensional ducts with geometric discontinuities, using high-fidelity computational fluid dynamics datasets. A two-stage training strategy, incorporating tailored activation functions and physics-based constraints, enhances robustness in flame response prediction. The framework accurately reconstructs acoustic fields, infers heat-release fluctuations, and captures flame dynamics across relevant frequency ranges. These results demonstrate the potential of physics-informed neural networks to bridge the gap between limited measurements and comprehensive thermoacoustic characterization.