h-Analysis and data-parallel physics-informed neural networks.

Area of Science:

• Computational Science and Engineering
• Machine Learning
• Numerical Analysis

Background:

• Physics-informed machine learning (PIML) and physics-informed neural networks (PINNs) are powerful tools for scientific simulations.
• Scaling PIML models to handle complex, high-dimensional problems with large datasets is computationally challenging.
• Existing methods may struggle with efficiency and robustness for sophisticated real-world applications.

Purpose of the Study:

• To develop a scale-robust and high-throughput protocol for data-parallel acceleration of PIML schemes.
• To investigate the implementation and efficiency of physics-informed neural networks (PINNs) on multiple graphics processing units (GPUs).
• To provide new theoretical convergence bounds for generalization error and train-test gap in accelerated PIML.

Main Methods:

• A novel protocol combining h-analysis with data-parallel acceleration using the Horovod training framework.
• Implementation of the protocol on multiple GPU architectures.
• Derivation of new convergence bounds for generalization error and train-test gap.

Main Results:

• The proposed data-parallel acceleration protocol is straightforward to implement and does not compromise training accuracy.
• The method demonstrates high efficiency and controllability, enabling scale-robust PIML.
• Extensive numerical experiments confirm the robustness and consistency of the approach across increasing complexity.

Conclusions:

• Data-parallel acceleration offers a viable and efficient path towards generic, scale-robust PIML.
• The Horovod framework facilitates straightforward implementation on multi-GPU systems.
• This work opens new possibilities for advanced real-world simulations using PIML.