A physics-informed neural network for non-linear laser absorption tomography

Hyperspectral absorption tomography has emerged as a promising technique for combustion diagnostics due to its rich spectral measurements. However, the non-linear and ill-posed nature of the inverse problem makes obtaining accurate results challenging. This paper proposes a novel application of a physics-informed neural network to address the non-linear inverse problem in hyperspectral absorption spectroscopy. This method utilizes physical laws and measurement data to guide the neural network in finding the optimal solution, without requiring training data. To demonstrate its capabilities, the physics-informed neural network is employed to retrieve temperature and CO${}_2$ mole fraction fields in axisymmetric laminar diffusion flames via $4.3\mu m$ TDLAS (tunable diode laser absorption spectroscopy). The developed neural network is applied to resolve the spatial distributions from the spectral dimensions, requiring fewer spatial measurements for directly retrieving temperature and CO${}_2$ mole fraction profiles. We investigate the minimum radial projections needed for accurate retrievals and evaluate the model’s robustness to random noise through the inversion of a simulated flame. The developed model is further applied to reconstruct the temperature and CO${}_2$ mole fraction fields for an experimentally measured flame. Our results demonstrate that the proposed model maintains high retrieval accuracy even with limited, noisy data. This work highlights the potential of the physics-informed neural network for robust solutions to non-linear laser absorption tomography problems in scientific and engineering applications.