Spatiotemporal prediction plays an important role in solving natural problems
and processing video frames, especially in weather forecasting and human action
recognition. Recent advances attempt to incorporate prior physical knowledge
into the deep learning framework to estimate the unknown governing partial
differential equations (PDEs), which have shown promising results in
spatiotemporal prediction tasks. However, previous approaches only restrict
neural network architectures or loss functions to acquire physical or PDE
features, which decreases the representative capacity of a neural network.
Meanwhile, the updating process of the physical state cannot be effectively
estimated. To solve the above mentioned problems, this paper proposes a
physical-guided neural network, which utilizes the frequency-enhanced Fourier
module and moment loss to strengthen the model's ability to estimate the
spatiotemporal dynamics. Furthermore, we propose an adaptive second-order
Runge-Kutta method with physical constraints to model the physical states more
precisely. We evaluate our model on both spatiotemporal and video prediction
tasks. The experimental results show that our model outperforms
state-of-the-art methods and performs best in several datasets, with a much
smaller parameter count.

该研究论文提出了一种物理引导的神经网络，利用频率增强的傅里叶模块和矩损失来增强模型估计时空动态的能力，并提出了具有物理约束的自适应二阶龙格 - 库塔方法，以更准确地建模物理状态。实验结果表明，该模型在时空预测和视频预测任务中表现出色，在多个数据集上具有最佳性能，而参数数量却更少。