论文标题
从图像数据中发现具有伪柔性物理学知情的神经网络的相位场模型
Discovering Phase Field Models from Image Data with the Pseudo-spectral Physics Informed Neural Networks
论文作者
论文摘要
在本文中，我们介绍了一个新的深度学习框架，用于从现有图像数据中发现相位字段模型。新框架具有物理知情神经网络（PINN）的近似能力，以及伪 - 光谱方法的计算效率，我们将其命名为伪谱Pinn或Spinn。与基线PINN不同，伪谱Pinn具有多个优点。首先，它需要更少的培训数据。至少有两个具有均匀空间分辨率的快照是足够的。其次，它在计算上是有效的，因为伪谱法用于空间离散化。第三，与基线PINN相比，它需要较少的训练参数。因此，它大大简化了训练过程，并确保了更少的本地最小值或鞍点。我们通过几个数值示例说明了伪谱Pinn的有效性。新提出的伪谱Pinn相当笼统，可以很容易地应用于图像数据中的其他基于PDE的模型。
In this paper, we introduce a new deep learning framework for discovering the phase field models from existing image data. The new framework embraces the approximation power of physics informed neural networks (PINN), and the computational efficiency of the pseudo-spectral methods, which we named pseudo-spectral PINN or SPINN. Unlike the baseline PINN, the pseudo-spectral PINN has several advantages. First of all, it requires less training data. A minimum of two snapshots with uniform spatial resolution would be adequate. Secondly, it is computationally efficient, as the pseudo-spectral method is used for spatial discretization. Thirdly, it requires less trainable parameters compared with the baseline PINN. Thus, it significantly simplifies the training process and assures less local minima or saddle points. We illustrate the effectiveness of pseudo-spectral PINN through several numerical examples. The newly proposed pseudo-spectral PINN is rather general, and it can be readily applied to discover other PDE-based models from image data.
