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  4. Vol 10, Issue 1, 2025

An Adaptive Physics-Informed Neural Network by Sampling Alternately from Time and Space for Solving Spatiotemporal PDE

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DOI: 10.23977/jnca.2025.100110 | Downloads: 4 | Views: 414

Author(s)

Hanya Wen 1, Jin Su 1,2

Affiliation(s)

1 School of Science, Xi'an Polytechnic University, Xi'an, Shaanxi, 710048, China
2 Key Laboratory of Functional Textile Material and Product, Ministry of Education, Xi'an Polytechnic University, Xi'an, 710048, Shaanxi, China; Xi'an International Science and Technology Cooperation Base for Big Data Analysis and Algorithms, Xi'an, Shaanxi, 710048, China

Corresponding Author

Jin Su

ABSTRACT

In the past several years, Physics-Informed Neural Network (PINN) for solving partial differential equations (PDE) has an advance development, however, under the traditional sampling method, it is difficult for the network to accurately capture the changes of the solution in complex areas. For this reason, we propose a spatio-temporal collaborative sampling strategy of PINN for solving PDE, to optimize the layout of omni-directional sampling points. In our method, the time interval is first subdivided into multiple sub-intervals, and local optimization sampling is performed for each sub-interval. The entire procedures of sampling will be pulled out alternatively in two stages in each sub-interval: first, in the aspect of spatial adaptive sampling, we adopt a dynamic resampling strategy based on the dynamical training error of neural network, which can sensitively identify the changing region of the solution and automatically increase the sampling density in the region with dramatic changes to capture more details; Secondly, time dimension sampling was performed similarly. Numerical tests on the Schrödinger and heat-conduction PDE show over 40% faster convergence and a reduction in relative L2 compared to traditional PINN. This work presents a new approach for efficiently solving complex PDE with PINN.

KEYWORDS

Physical Information Neural Network; Sampling Alternately from Time and Space; Adaptive Sampling

CITE THIS PAPER

Hanya Wen, Jin Su, An Adaptive Physics-Informed Neural Network by Sampling Alternately from Time and Space for Solving Spatiotemporal PDE. Journal of Network Computing and Applications (2025) Vol. 10: 81-95. DOI: http://dx.doi.org/10.23977/jnca.2025.100110.

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