论文标题
用物理信息的神经网络计算时间相关的dirac方程
Computation of the Time-Dependent Dirac Equation with Physics-Informed Neural Networks
论文作者
论文摘要
我们建议使用物理知识的神经网络（PINNS）计算时间依赖性的DIRAC方程，这是一种科学机器学习的新工具，避免使用差异操作员的近似衍生物。 PINNS搜索解决方案以参数化（深）神经网络的形式，其衍生物（在时空中）通过自动分化执行。计算成本源于需要使用随机梯度方法解决高维优化问题，并用大量点训练网络。具体而言，我们得出了基于PINNS的算法，并在不同物理框架中应用于DIRAC方程时，介绍了这些算法的一些关键基本属性。
We propose to compute the time-dependent Dirac equation using physics-informed neural networks (PINNs), a new powerful tool in scientific machine learning avoiding the use of approximate derivatives of differential operators. PINNs search solutions in the form of parameterized (deep) neural networks, whose derivatives (in time and space) are performed by automatic differentiation. The computational cost comes from the need to solve high-dimensional optimization problems using stochastic gradient methods and train the network with a large number of points. Specifically, we derive PINNs-based algorithms and present some key fundamental properties of these algorithms when applied to the Dirac equations in different physical frameworks.
