We explore the data-parallel acceleration of physics-informed machine learning (PIML) schemes, with a focus on physics-informed neural networks (PINNs) for multiple graphics processing units (GPUs) architectures. In order to develop scale-robust PIML models for sophisticated applications (e.g., involving complex and high-dimensional domains, non-linear operators or multi-physics), which may require a large number of training points, we detail a protocol based on the Horovod training framework. This protocol is backed by $h$-analysis, including a new convergence bound for the generalization error. We show that the acceleration is straightforward to implement, does not compromise training, and proves to be highly efficient, paving the way towards generic scale-robust PIML. Extensive numerical experiments with increasing complexity illustrate its robustness and consistency, offering a wide range of possibilities for real-world simulations.

本文探讨了物理知识驱动的机器学习（PIML）方案的数据并行加速，重点是针对多个图形处理单元（GPU）架构的物理知识驱动的神经网络（PINNs）。通过使用基于Horovod的训练框架详细说明了开发规模鲁棒的 PHP 模型的协议，包括对广义误差的新收敛界限的$h$分析，我们将加速做法应用于规模鲁棒的 PIML 模型，并且通过大量实验验证了其鲁棒性和一致性，为实现各种真实世界模拟提供了广泛的可能性。

h分析和数据并行的物理信息神经网络