论文标题
双曲线系统的热力学一致的物理信息神经网络
Thermodynamically consistent physics-informed neural networks for hyperbolic systems
论文作者
论文摘要
物理知识的神经网络体系结构已成为开发灵活的PDE求解器的强大工具，该工具易于吸收数据，但面临与PDE离散化有关的挑战，这些挑战是基于它们的基础。相反，通过调整最小二乘时空控制量方案，我们避免了与施加边界条件和保护的问题，同时减少解决方案的规律性要求。此外，与经典有限体积方法的连接允许将偏差应用于熵解决方案，总变化降低了属性。对于反问题，我们可能会施加进一步的热力学偏见，从而使我们能够将冲击流体动力学模型拟合到稀有气体和金属的分子模拟中。由此产生的数据驱动状态方程可能会纳入传统的冲击流体动力学代码中。
Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a least squares space-time control volume scheme, we circumvent issues particularly related to imposition of boundary conditions and conservation while reducing solution regularity requirements. Additionally, connections to classical finite volume methods allows application of biases toward entropy solutions and total variation diminishing properties. For inverse problems, we may impose further thermodynamic biases, allowing us to fit shock hydrodynamics models to molecular simulation of rarefied gases and metals. The resulting data-driven equations of state may be incorporated into traditional shock hydrodynamics codes.
