Deep Learning Surrogates for Gas Dynamics: A Physics-Informed Pedagogical Approach

TL;DR

This work presents a physics-informed deep learning framework that creates high-fidelity surrogates for five canonical 1D gas-dynamics problems—Rayleigh flow, Fanno flow, oblique shocks, normal shocks in convergent-divergent nozzles, and unsteady shock tubes—addressing the nonlinear, implicit relationships that challenge traditional methods. By tailoring architectures to each regime (e.g., branch-splitting for Rayleigh, log-space targets and physics-informed features for Fanno, anchors for oblique shocks, and hybrid AI-analytical solvers for shocks and Riemann problems), the authors achieve real-time, differentiable mappings that preserve thermodynamic consistency and allow instant exploration of design spaces. Key contributions include domain decomposition to resolve non-injective mappings, anchors to enforce physical limits, and hybrid solvers that combine neural inference with exact gas-dynamics reconstruction. The approach promises impactful applications in education and engineering design, enabling rapid inverse calculations and intuitive visualization of complex flow phenomena, while laying a foundation for extending these methods to higher dimensions and reacting flows.

Abstract

Compressible flow problems are characterized by highly nonlinear, implicit, and often transcendental governing equations. In undergraduate gas dynamics education, solving these equations traditionally relies on iterative numerical methods or extensive look-up tables, which can obscure the physical intuition of the solution space. This paper introduces a comprehensive framework using Deep Learning to generate high-fidelity surrogate models for five canonical problems: Rayleigh flow, Fanno flow, oblique shocks, convergent-divergent nozzles, and unsteady shock tubes. We detail the specific neural network architectures and physics-informed feature engineering strategies required for each problem, such as using logarithmic inputs for Fanno friction parameters or geometric anchors for oblique shocks. The resulting models achieve high accuracy and enable instantaneous visualization of complex design spaces, such as thermodynamic T s diagrams and unsteady x t wave interactions. This approach demonstrates how modern data-driven techniques can be integrated into the physics curriculum to enhance conceptual understanding.

Figures (14)

• Figure 1: Detailed comparison of Rayleigh flow properties. The neural network captures the specific nonlinear behavior of each property ratio, including the velocity increase and density decrease associated with heat addition in subsonic flow.
• Figure 2: Relative error analysis for Rayleigh flow predictions. The error distribution is centered around zero with minimal variance, confirming the robustness of the ML model across the entire Mach regime.
• Figure 3: Solution to the inverse Rayleigh problem. The grey line represents the analytical solution. The red dashed line shows the subsonic ML prediction, and the blue dashed line shows the supersonic ML prediction, demonstrating the model's ability to handle the multi-valued nature of the function.
• Figure 4: The Rayleigh line on a T-s diagram generated by the neural network. The model correctly identifies the point of maximum entropy ($M=1$), consistent with the Second Law of Thermodynamics. The arrow indicates the direction of heat addition driving the flow towards the sonic state.
• Figure 5: Comparison of analytical vs. neural network predictions for Fanno flow property ratios. The model accurately captures the divergent behavior of pressure and density at low Mach numbers and the extremum at M=1.