Escapil-Inchauspé Paul, Ruz Gonzalo A
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile.
Data Observatory Foundation, Santiago, Chile.
Sci Rep. 2023 Oct 16;13(1):17562. doi: 10.1038/s41598-023-44541-5.
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.
我们探索物理信息机器学习（PIML）方案的数据并行加速，重点关注适用于多种图形处理单元（GPU）架构的物理信息神经网络（PINN）。为了针对可能需要大量训练点的复杂应用（例如，涉及复杂高维域、非线性算子或多物理场的应用）开发具有尺度鲁棒性和高通量的PIML模型，我们详细介绍了一种基于h分析和通过Horovod训练框架进行数据并行加速的新协议。该协议有泛化误差和训练测试差距的新收敛界作为支撑。我们表明，这种加速易于实现，不影响训练，并且证明是高效且可控的，为通用的尺度鲁棒PIML铺平了道路。随着复杂度增加的大量数值实验说明了其鲁棒性和一致性，为实际模拟提供了广泛的可能性。
