Physics-informed neural networks for inverse problems in supersonic flows

Abstract

Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren photography as well as data at the inflow and part of wall boundaries. These inverse problems are notoriously difficult and traditional methods may not be adequate to solve such ill-posed inverse problems. To this end, we employ the physics-informed neural networks (PINNs) and its extended version, extended PINNs (XPINNs), where domain decomposition allows deploying locally powerful neural networks in each subdomain, which can provide additional expressivity in subdomains, where a complex solution is expected. Apart from the governing compressible Euler equations, we also enforce the entropy conditions in order to obtain viscosity solutions. Moreover, we enforce positivity conditions on density and pressure. We consider inverse problems involving two-dimensional expansion waves, two-dimensional oblique and bow shock waves. We compare solutions obtained by PINNs and XPINNs and invoke some theoretical results that can be used to decide on the generalization errors of the two methods.

arXiv comment19 pages, 20 figures

References in corpus (10)

• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
• hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition
• Physics-informed neural networks for inverse problems in nano-optics and metamaterials
• Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
• Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks
• Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks
• PINNeik: Eikonal solution using physics-informed neural networks
• A physics-informed neural network for quantifying the microstructure properties of polycrystalline Nickel using ultrasound data
• Constraint-Aware Neural Networks for Riemann Problems
• DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators