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 and high-throughput PIML models for sophisticated applications which may require a large number of training points (e.g., involving complex and high-dimensional domains, non-linear operators or multi-physics), we detail a novel protocol based on $h$-analysis and data-parallel acceleration through the Horovod training framework. The protocol is backed by new convergence bounds for the generalization error and the train-test gap. We show that the acceleration is straightforward to implement, does not compromise training, and proves to be highly efficient and controllable, 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.

翻译：我们探索了物理信息机器学习（PIML）方案的数据并行加速，重点关注面向多图形处理单元（GPU）架构的物理信息神经网络（PINN）。为开发适用于复杂应用（如涉及高维域、非线性算子或多物理场，可能需要大量训练点）的尺度鲁棒且高吞吐量的PIML模型，我们详细提出了一种基于$h$-分析并通过Horovod训练框架实现数据并行加速的新型协议。该协议得到泛化误差与训练-测试差距的新收敛界限的支持。研究表明，该加速方法易于实现，不会影响训练，且具有高效率与可控性，为通用尺度鲁棒PIML铺平了道路。大量复杂度递增的数值实验展示了其稳健性与一致性，为实际仿真提供了广泛的可能性。