论文标题
物理学告知RNN-DCT网络，以进行时间依赖的部分偏微分方程
Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations
论文作者
论文摘要
物理知识的神经网络允许模型受到一般非线性偏微分方程描述的物理定律的培训。但是，由于其建筑性质，传统体系结构难以解决更具挑战性的时间依赖性问题。在这项工作中，我们提出了一个新颖的物理知识框架，用于解决时间依赖时间的偏微分方程。仅使用管理微分方程以及问题初始和边界条件，我们生成了问题的时空动力学的潜在表示。我们的模型利用离散的余弦变换来编码空间频率和经常性神经网络来处理时间的演变。这种有效而灵活地产生了压缩表示形式，用于物理信息模型的其他条件。我们在Navier-Stokes方程的Taylor-Green Vortex解决方案上显示了实验结果。我们提出的模型相对于其他物理知识的基线模型，在泰勒绿色涡流上实现了最先进的性能。
Physics-informed neural networks allow models to be trained by physical laws described by general nonlinear partial differential equations. However, traditional architectures struggle to solve more challenging time-dependent problems due to their architectural nature. In this work, we present a novel physics-informed framework for solving time-dependent partial differential equations. Using only the governing differential equations and problem initial and boundary conditions, we generate a latent representation of the problem's spatio-temporal dynamics. Our model utilizes discrete cosine transforms to encode spatial frequencies and recurrent neural networks to process the time evolution. This efficiently and flexibly produces a compressed representation which is used for additional conditioning of physics-informed models. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations. Our proposed model achieves state-of-the-art performance on the Taylor-Green vortex relative to other physics-informed baseline models.
