Data-Free PINNs for Compressible Flows: Mitigating Spectral Bias and Gradient Pathologies via Mach-Guided Scaling and Hybrid Convolutions
This paper presents a fully data-free Physics-Informed Neural Network (PINN) capable of solving compressible inviscid flows (ranging from supersonic to hypersonic, up to Ma=15, where Ma is the Mach number) around a circular cylinder. To overcome the spatial blindness of standard Multi-Layer Perceptrons, a structured hybrid architecture combining radial 1D convolutions with anisotropic azimuthal 2D convolutions is proposed to embed directional inductive biases. For stable optimization across disparate flow regimes, a regime-dependent, Mach-number-guided dynamic residual scaling strategy is introduced. Crucially, this approach scales down residuals to mitigate extreme gradient stiffness in ...
| Authors | Ryosuke Yano |
|---|---|
| Primary category | physics.flu-dyn |
| Published | 1 March 2026 |
| Last updated at source | 1 March 2026 |
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