Time-dependent Dirac Equation with Physics-Informed Neural Networks: Computation and Properties
Time-dependent Dirac Equation with Physics-Informed Neural Networks: Computation and Properties
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DOI：
10.1016/j.cpc.2022.108474
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发表时间：
2022-08
期刊：
影响因子：
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通讯作者：
E. Lorin;Xu Yang
中科院分区：
文献类型：
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作者：
E. Lorin;Xu Yang
在本文中，我们感兴趣的是使用物理信息神经网络（PINNs）计算时间相关的狄拉克方程，PINNs是科学机器学习中一种新的强大工具，避免使用微分算子的近似导数。PINN以参数化（深度）神经网络的形式搜索解决方案，其导数（在时间和空间上）通过自动微分来执行。计算成本来自于在训练网络时使用随机梯度方法来解决高维优化问题的需要，该网络具有标准PDE求解器的离散化点的大量点类似物。具体来说，我们推导出一种基于PINNS的算法，并给出了应用于不同物理框架中的狄拉克方程时的一些关键基本性质。
In this paper, we are interested in the computation of 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 in the training the network with a large number of points analogues of the discretization points for standard PDE solvers. Specifically, we derive a PINNs-based algorithm and present some key fundamental properties when applied to the Dirac equations in different physical frameworks.