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.

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（PINNs）。为开发适用于复杂应用（例如涉及复杂高维域、非线性算子或多物理场）且需大量训练点的尺度鲁棒PIML模型，我们详细阐述了一种基于Horovod训练框架的协议。该协议以$h$分析为支撑，包含泛化误差的新收敛界。研究表明，该加速方法易于实现、不损害训练过程，且证明具有高效率，为通用尺度鲁棒PIML铺平了道路。通过复杂度递增的大规模数值实验，验证了其稳健性与一致性，为实际仿真提供了广泛可能。