Transport phenomena (e.g., fluid flows) are governed by time-dependent partial differential equations (PDEs) describing mass, momentum, and energy conservation, and are ubiquitous in many engineering applications. However, deep learning architectures are fundamentally incompatible with the simulation of these PDEs. This paper clearly articulates and then solves this incompatibility. The local-dependency of generic transport PDEs implies that it only involves local information to predict the physical properties at a location in the next time step. However, the deep learning architecture will inevitably increase the scope of information to make such predictions as the number of layers increases, which can cause sluggish convergence and compromise generalizability. This paper aims to solve this problem by proposing a distributed data scoping method with linear time complexity to strictly limit the scope of information to predict the local properties. The numerical experiments over multiple physics show that our data scoping method significantly accelerates training convergence and improves the generalizability of benchmark models on large-scale engineering simulations. Specifically, over the geometries not included in the training data for heat transferring simulation, it can increase the accuracy of Convolutional Neural Networks (CNNs) by 21.7 \% and that of Fourier Neural Operators (FNOs) by 38.5 \% on average.

翻译：输运现象（例如流体流动）受描述质量、动量和能量守恒的含时偏微分方程控制，在众多工程应用中普遍存在。然而，深度学习架构从根本上与这些偏微分方程的模拟不兼容。本文明确阐述并解决了这一不兼容问题。通用输运偏微分方程的局部依赖性意味着，在预测下一时间步某位置的物理性质时，仅需利用局部信息。然而，随着层数增加，深度学习架构不可避免地会扩大用于此类预测的信息作用域，这可能导致收敛缓慢并损害泛化能力。本文旨在通过提出一种具有线性时间复杂度的分布式数据作用域方法来解决该问题，该方法严格限制预测局部性质所需的信息作用域。多物理场的数值实验表明，我们的数据作用域方法显著加速了训练收敛，并提升了基准模型在大规模工程模拟中的泛化能力。具体而言，对于未包含在热传递模拟训练数据中的几何结构，该方法平均可将卷积神经网络的准确率提高21.7%，将傅里叶神经算子的准确率提高38.5%。