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.

该论文提出了一种分布式数据范围方法，通过严格限制信息范围来预测局部属性，从而解决了深度学习架构在传输现象模拟中的不兼容问题，实验证明该方法显著加速了训练收敛并提高了大规模工程模拟的模型泛化能力。

数据范围确定：高效学习通用传输偏微分方程的演化

Data Scoping: Effectively Learning the Evolution of Generic Transport  PDEs

We have developed a new data-driven paradigm for the rapid inference,
modeling and simulation of the physics of transport phenomena by deep learning.
Using conditional generative adversarial networks (cGAN), we train models for
the direct generation of solutions to steady state heat conduction and
incompressible fluid flow purely on observation without knowledge of the
underlying governing equations. Rather than using iterative numerical methods
to approximate the solution of the constitutive equations, cGANs learn to
directly generate the solutions to these phenomena, given arbitrary boundary
conditions and domain, with high test accuracy (MAE$<$1\%) and state-of-the-art
computational performance. The cGAN framework can be used to learn causal
models directly from experimental observations where the underlying physical
model is complex or unknown.

使用条件生成对抗网络（cGAN）的数据驱动模式，无需对基础控制方程有先验知识，直接生成稳态导热和不可压缩流的解，具有高测试精度（MAE＜1％）和最先进的计算性能，并可用于从实验观测中直接学习因果模型。