Many problems in physical sciences are characterized by the prediction of space-time sequences. Such problems range from weather prediction to the analysis of disease propagation and video prediction. Modern techniques for the solution of these problems typically combine Convolution Neural Networks (CNN) architecture with a time prediction mechanism. However, oftentimes, such approaches underperform in the long-range propagation of information and lack explainability. In this work, we introduce a physically inspired architecture for the solution of such problems. Namely, we propose to augment CNNs with advection by designing a novel semi-Lagrangian push operator. We show that the proposed operator allows for the non-local transformation of information compared with standard convolutional kernels. We then complement it with Reaction and Diffusion neural components to form a network that mimics the Reaction-Advection-Diffusion equation, in high dimensions. We demonstrate the effectiveness of our network on a number of spatio-temporal datasets that show their merit.

翻译：物理科学中的许多问题都涉及时空序列的预测，例如天气预报、疾病传播分析和视频预测等。解决这些问题的现代技术通常将卷积神经网络（CNN）架构与时间预测机制相结合。然而，这类方法在信息的长程传播方面往往表现不佳，且缺乏可解释性。本研究提出了一种受物理学启发的架构来解决此类问题。具体而言，我们通过设计一种新颖的半拉格朗日推送算子，将对流机制引入CNN进行增强。研究表明，与标准卷积核相比，该算子能够实现信息的非局部变换。我们进一步将其与反应和扩散神经组件相结合，构建了一个在高维空间中模拟反应-对流-扩散方程的网络。通过在多个时空数据集上的实验，我们验证了该网络的有效性及其优势。