Physics-informed neural networks for inverse problems in supersonic flows

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...

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Vydáno v:Journal of computational physics Ročník 466; s. 111402
Hlavní autoři: Jagtap, Ameya D., Mao, Zhiping, Adams, Nikolaus, Karniadakis, George Em
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge Elsevier Science Ltd 01.10.2022
Témata:
Aerospace engineering
Aerospace vehicles
Compressible flow
Computational physics
Density gradients
Elastic waves
Euler-Lagrange equation
Inverse problems
Neural networks
Schlieren photography
Shock waves
Supersonic flow
ISSN:0021-9991, 1090-2716
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Shrnutí: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.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2022.111402