The bulk kinematics and thermodynamics of hot supernovae-driven galactic winds is critically dependent on both the amount of swept up cool clouds and non-spherical collimated flow geometry. However, accurately parameterizing these physics is difficult because their functional forms are often unknown, and because the coupled non-linear flow equations contain singularities. We show that deep neural networks embedded as individual terms in the governing coupled ordinary differential equations (ODEs) can robustly discover both of these physics, without any prior knowledge of the true function structure, as a supervised learning task. We optimize a loss function based on the Mach number, rather than the explicitly solved-for 3 conserved variables, and apply a penalty term towards near-diverging solutions. The same neural network architecture is used for learning both the hidden mass-loading and surface area expansion rates. This work further highlights the feasibility of neural ODEs as a promising discovery tool with mechanistic interpretability for non-linear inverse problems.

翻译：热超新星驱动的星系风体运动学与热力学关键依赖于所席卷的冷云数量及非球形准直流动几何结构。然而，精准参数化这些物理过程极具挑战性，因其函数形式未知，且耦合非线性流动方程存在奇点。研究表明，将深度神经网络作为控制耦合常微分方程（ODE）中的独立项嵌入，可在无先验函数结构知识的情况下，以监督学习方式稳健发现这两类物理机制。我们基于马赫数而非显式求解的三个守恒变量优化损失函数，并对趋近发散的解施加惩罚项。采用相同神经网络架构同时学习隐式质量加载率与表面积膨胀率。本工作进一步凸显了神经常微分方程作为非线性逆问题中具有机制可解释性的新型发现工具的可行性。