h-Analysis and data-parallel physics-informed neural networks
Abstract 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 sophistic...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2023-10-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-44541-5 |
| _version_ | 1797559912133296128 |
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| author | Paul Escapil-Inchauspé Gonzalo A. Ruz |
| author_facet | Paul Escapil-Inchauspé Gonzalo A. Ruz |
| author_sort | Paul Escapil-Inchauspé |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-03-10T17:51:55Z |
| format | Article |
| id | doaj.art-7f1853786b704486b52a1cbe9de8dea8 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-10T17:51:55Z |
| publishDate | 2023-10-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-7f1853786b704486b52a1cbe9de8dea82023-11-20T09:20:00ZengNature PortfolioScientific Reports2045-23222023-10-0113111910.1038/s41598-023-44541-5h-Analysis and data-parallel physics-informed neural networksPaul Escapil-Inchauspé0Gonzalo A. Ruz1Facultad de Ingeniería y Ciencias, Universidad Adolfo IbáñezFacultad de Ingeniería y Ciencias, Universidad Adolfo IbáñezAbstract 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.https://doi.org/10.1038/s41598-023-44541-5 |
| spellingShingle | Paul Escapil-Inchauspé Gonzalo A. Ruz h-Analysis and data-parallel physics-informed neural networks Scientific Reports |
| title | h-Analysis and data-parallel physics-informed neural networks |
| title_full | h-Analysis and data-parallel physics-informed neural networks |
| title_fullStr | h-Analysis and data-parallel physics-informed neural networks |
| title_full_unstemmed | h-Analysis and data-parallel physics-informed neural networks |
| title_short | h-Analysis and data-parallel physics-informed neural networks |
| title_sort | h analysis and data parallel physics informed neural networks |
| url | https://doi.org/10.1038/s41598-023-44541-5 |
| work_keys_str_mv | AT paulescapilinchauspe hanalysisanddataparallelphysicsinformedneuralnetworks AT gonzaloaruz hanalysisanddataparallelphysicsinformedneuralnetworks |