Mosaic Flow is a novel domain decomposition method designed to scale
physics-informed neural PDE solvers to large domains. Its unique approach
leverages pre-trained networks on small domains to solve partial differential
equations on large domains purely through inference, resulting in high
reusability. This paper presents an end-to-end parallelization of Mosaic Flow,
combining data parallel training and domain parallelism for inference on
large-scale problems. By optimizing the network architecture and data parallel
training, we significantly reduce the training time for learning the Laplacian
operator to minutes on 32 GPUs. Moreover, our distributed domain decomposition
algorithm enables scalable inferences for solving the Laplace equation on
domains 4096 times larger than the training domain, demonstrating strong
scaling while maintaining accuracy on 32 GPUs. The reusability of Mosaic Flow,
combined with the improved performance achieved through the distributed-memory
algorithms, makes it a promising tool for modeling complex physical phenomena
and accelerating scientific discovery.

Mosaic Flow 是一种新颖的域分解方法，通过推理利用在小域上预训练的网络，在大域上纯粹进行偏微分方程求解，实现高度的可重用性。本文介绍了 Mosaic Flow 的端到端并行化，将数据并行训练和域并行化相结合，用于大规模问题的推理。通过优化网络架构和数据并行训练，我们将学习拉普拉斯算子的训练时间显著缩短为 32 个 GPU 上的几分钟。此外，我们的分布式域分解算法使得在 32 个 GPU 上能够在域尺度大于训练域 4096 倍的情况下解决拉普拉斯方程，展示了较强的扩展性同时保持精度。Mosaic Flow 的可重用性结合分布式内存算法所实现的性能改进，使其成为建模复杂物理现象和加速科学发现的有前景工具。