Enhanced Physics-Informed Neural Networks with Optimized Sensor Placement via Multi-Criteria Adaptive Sampling

Chenhong Zhou, Jie Chen*, Zaifeng Yang, Alexander Matyasko, Ching Eng Png

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

Abstract

Physics-informed neural networks (PINNs) have emerged as promising and powerful tools for solving partial differential equations (PDEs). To enforce PINNs that yield accurate solutions to PDEs, a set of scattered spatiotemporal points, known as collocation points, are typically sampled within the computational domain. The choices of collocation points significantly impact the performance of PINNs. However, existing sampling methods primarily rely on the PDE residual, which is insufficient for solutions with steep gradients. To enhance the accuracy of PINNs, we propose a novel multi-criteria adaptive sampling (MCAS) approach to optimally select appropriate collocation points. The MCAS approach integrates three sampling criteria: PDE’s residual, the gradient of residual, and the gradient of solutions, enabling us to capture the PDE violations and the sharpness of solutions. Experimental results demonstrate that the proposed MCAS approach is not only applicable for collocation points but also for optimizing sensor placement, consistently outperforming the residual-based sampling methods.
Original languageEnglish
Title of host publicationProceedings - 2024 International Joint Conference on Neural Networks (IJCNN)
PublisherIEEE
Pages1-8
Number of pages8
ISBN (Electronic)9798350359312
ISBN (Print)9798350359329
DOIs
Publication statusPublished - 9 Sept 2024
Event2024 International Joint Conference on Neural Networks, IJCNN 2024 - Yokohama, Japan
Duration: 30 Jun 20245 Jul 2024
https://2024.ieeewcci.org/ (Conference website)
https://ieeexplore.ieee.org/xpl/conhome/10649807/proceeding (Conference proceeding)

Publication series

NameProceedings - International Joint Conference on Neural Networks (IJCNN)
ISSN (Print)2161-4393
ISSN (Electronic)2161-4407

Conference

Conference2024 International Joint Conference on Neural Networks, IJCNN 2024
Country/TerritoryJapan
CityYokohama
Period30/06/245/07/24
Internet address

User-Defined Keywords

  • Multi-criteria adaptive sampling
  • Optimized sensor placement
  • Partial differential equations
  • Physics-informed neural networks
  • Residual-based sampling

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