Physics-informed neural network retrieval of spatially-resolved soot properties from multi-wavelength optical diagnostics

Improving models of soot formation is essential, which relies on accurate quantitative characterization of soot in standardized flames. Complete characterization requires the coupling of different diagnostic techniques. In the present work, spatially resolved soot properties are retrieved by jointly inverting line-of-sight attenuation (LOSA), spectral soot emission (SSE), and multi-angle light scattering (MALS) within a physics-informed neural network (PINN). The Rayleigh–Debye–Gans theory for fractal aggregates and Planck’s law are embedded, enabling the recovery of temperature, soot volume fraction, representative aggregate volume, composition fractions (amorphous, organic, graphitic) and optical index, under a single physics-constrained formulation. The framework is validated on synthetic datasets generated with the CoFlame code and perturbed with realistic noise. The method is then applied to spectrally resolved LOSA/SSE/MALS measurements in a laminar, axisymmetric ethylene coflow diffusion flame on a Gülder burner. For the first time, all measurands are determined simultaneously in agreement with combined multi-spectral data ranging from 405 to 750 nm. The coupling of LOSA, SSE, and MALS extends composition characterization to include amorphous carbon, which was not considered in previous advanced studies. A maturation trend from organic through amorphous to graphitic fractions is observed along streamlines. The proposed technique is shown to be innovative, and its calibration-free nature makes it very robust.