论文标题
神经网络：解决星际介质的化学反应
Neural networks: solving the chemistry of the interstellar medium
论文作者
论文摘要
非平衡化学是研究星际培养基（ISM）的关键过程，特别是分子云的形成，因此是恒星的形成。但是，从计算上讲，这是在天体物理模拟中包括的最困难的任务之一，因为通常具有较高的反应数量（> 40），短进化时间表（大约比ISM动力学时间少10美元^4 $倍）以及相关的普通微分方程系统（ODES）的特征性非线性和刚度（ODES）。在此概念验证的工作中，我们表明物理知情的神经网络（PINN）是用于僵硬的热化学系统的传统ode时间积分器的可行替代方案，即达到分子氢的形成（9种和46种反应）。 Testing different chemical networks in a wide range of densities ($-2< \log n/{\rm cm}^{-3}< 3$) and temperatures ($1 < \log T/{\rm K}< 5$), we find that a basic architecture can give a comfortable convergence only for simplified chemical systems: to properly capture the sudden chemical and thermal variations a Deep Galerkin Method is needed.一旦受过训练（$ \ sim 10^3 $ gpuhr），Pinn很好地再现了解决方案的强非线性性质（错误$ \ lyssim 10 \％$），并且可以将相对于传统Ode solvers的速度提高到$ \ sim 200 $。此外，对于不同的初始$ n $和$ t $，后者的完成时间约为$ \ sim 30 \％$，而Pinn方法的变化可忽略不计。速度和负载平衡的潜在改善都表明，PINN驱动的模拟是解决天体物理和宇宙学问题中复杂化学计算的一种非常可口的方法。
Non-equilibrium chemistry is a key process in the study of the InterStellar Medium (ISM), in particular the formation of molecular clouds and thus stars. However, computationally it is among the most difficult tasks to include in astrophysical simulations, because of the typically high (>40) number of reactions, the short evolutionary timescales (about $10^4$ times less than the ISM dynamical time) and the characteristic non-linearity and stiffness of the associated Ordinary Differential Equations system (ODEs). In this proof of concept work, we show that Physics Informed Neural Networks (PINN) are a viable alternative to traditional ODE time integrators for stiff thermo-chemical systems, i.e. up to molecular hydrogen formation (9 species and 46 reactions). Testing different chemical networks in a wide range of densities ($-2< \log n/{\rm cm}^{-3}< 3$) and temperatures ($1 < \log T/{\rm K}< 5$), we find that a basic architecture can give a comfortable convergence only for simplified chemical systems: to properly capture the sudden chemical and thermal variations a Deep Galerkin Method is needed. Once trained ($\sim 10^3$ GPUhr), the PINN well reproduces the strong non-linear nature of the solutions (errors $\lesssim 10\%$) and can give speed-ups up to a factor of $\sim 200$ with respect to traditional ODE solvers. Further, the latter have completion times that vary by about $\sim 30\%$ for different initial $n$ and $T$, while the PINN method gives negligible variations. Both the speed-up and the potential improvement in load balancing imply that PINN-powered simulations are a very palatable way to solve complex chemical calculation in astrophysical and cosmological problems.
