A modified physics-informed neural network with positional encoding

Xinquan Huang, Tariq Ali Alkhalifah, Chao Song

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Scopus citations


Recently developed physics-informed neural network (PINN) for solving for the scattered wavefield in the Helmholtz equation showed large potential in seismic modeling because of its flexibility, low memory requirement, and no limitations on the shape of the solution space. However, the predicted solutions were somewhat smooth and the convergence of the training was slow. Thus, we propose a modified PINN using sinusoidal activation functions and positional encoding, aiming to accelerate the convergence and fit better. We transform the scalar input coordinate parameters using positional encoding into high-dimensional embedded vectors and train a fully-connected neural network to predict the real and imaginary parts of the scattered waveifeld. Numerical results show that, compared to the commonly used PINN, the proposed modified PINN using positional encoding exhibits notable superiority in terms of convergence and accuracy.
Original languageEnglish (US)
Title of host publicationFirst International Meeting for Applied Geoscience & Energy Expanded Abstracts
PublisherSociety of Exploration Geophysicists
Number of pages5
StatePublished - Sep 1 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-12-23
Acknowledgements: We thank KAUST for its support and the SWAG group for the collaborative environment. This work utilized the resources of the Supercomputing Laboratory at King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia, and we are grateful for that.


Dive into the research topics of 'A modified physics-informed neural network with positional encoding'. Together they form a unique fingerprint.

Cite this