Physics-informed neural networks for reacting flows: Species reconstruction with finite rate chemistry from sparse and noisy velocity measurements

We present Reactive Flow Physics-informed neural networks (RF-PINNs), an extension of PINNs tailored for reactive flow problems involving finite-rate chemistry. The idea is to use only partially available and possibly noisy information of the flow field (we use velocity data without loss of generality) to infer all other missing quantities. We demonstrate that our method accurately reconstructs velocities, pressure, temperature, density, species mass fractions, reaction rates, and heat release. To our knowledge, this is the first application of PINNs to reactive flows incorporating finite-rate chemistry mechanisms, featuring 9 species and 21 reactions for hydrogen, and 21 species and 84 reactions for methane, alongside a mixture-averaged diffusion model. The central novelty of this study lies in the reconstruction of the reactive flow fields from sparse velocity measurements with incomplete boundary conditions. Velocities and temperature are reconstructed with a relative error below 1%. This was achieved through two key novelties to the RF-PINN framework. First, we introduce a specialized output layer that embeds physical constraints into the architecture by bounding the species mass fractions while ensuring their summation to unity. Second, we develop the Elemental Mass Flow Loss, a novel physics-informed loss function that enforces global conservation of elemental mass flow across the domain, eliminating the need for inlet boundary conditions. This loss enables the reconstruction of inlet profiles with high fidelity, demonstrating its potential to derive boundary conditions from sparse experimental data. RF-PINNs offer a powerful tool for combustion diagnostics by reconstructing flow fields and boundary conditions from sparse inputs, such as PIV velocity data, especially in scenarios with limited experimental access. While we demonstrate RF-PINNs on stationary hydrogen and methane flames, our methodology is readily extendable to other chemical kinetics mechanisms, fuels and operating conditions.