Investigation of Low and High-Speed Fluid Dynamics Problems Using Physics-Informed Neural Network

In this work, we have employed physics-informed neural networks (PINNs) to solve a few fluid dynamics problems at low and high speeds, with a focus on the latter. For high-speed fluid dynamics problems, we deal with the 1D compressible Euler equation, which is used to solve shock-tube problem, viz., Sod shock-tube, with weighted physics-informed neural networks (W-PINNs). This paper also demonstrates how domain extension (W-PINNs-DE) can improve the accuracy of the W-PINNs method. For high-speed flows, dispersion and dissipation errors are present near discontinuities. The W-PINNs-DE method is shown to mitigate this effect and is proven to have advantage over other approximations. Finally, we have solved the same high-speed problem with low-fidelity solution data to generate high-fidelity solutions. We have demonstrated that we can obtain accurate solutions using low-fidelity data in a few seconds of inference time. We have used relative L2 error for validation with exact or high-fidelity solutions.