TY - JOUR

T1 - Physics-informed neural networks for inverse problems in supersonic flows

AU - Jagtap, Ameya D.

AU - Mao, Zhiping

AU - Adams, Nikolaus

AU - Karniadakis, George Em

N1 - Publisher Copyright:
© 2022 Elsevier Inc.

PY - 2022/10/1

Y1 - 2022/10/1

N2 - 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 the 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 to deploy 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.

AB - 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 the 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 to deploy 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.

KW - Entropy conditions

KW - Extended physics-informed neural networks

KW - Inverse problems

KW - Supersonic compressible flows

UR - http://www.scopus.com/inward/record.url?scp=85133464482&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2022.111402

DO - 10.1016/j.jcp.2022.111402

M3 - Article

AN - SCOPUS:85133464482

SN - 0021-9991

VL - 466

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 111402

ER -