Single Reference Frequency Loss for Multifrequency Wavefield Representation Using Physics-Informed Neural Networks

Xinquan Huang*, Tariq Alkhalifah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Physics-informed neural networks (PINNs) can offer approximate multidimensional functional solutions to the Helmholtz equation that is flexible, requires low memory, and has no limitations on the shape of the solution space. However, the neural network (NN) training can be costly, and the cost dramatically increases as we train for multifrequency wavefields by adding frequency as an additional input to the NN multidimensional function. In this case, the often large variation of the wavefield features (specifically wavelength) with frequency adds more complexity to the NN training. Thus, we propose a new loss function for the NN multidimensional input training that allows us to seamlessly include frequency as a dimension. We specifically utilize the linear relation between frequency and wavenumber (the wavefield space representation) to incorporate a reference frequency scaling to the loss function. As a result, the effective wavenumber of the wavefield solution as a function of frequency remains almost stationary, which reduces the learning burden on the NN function. We demonstrate the effectiveness of this modified loss function on a layered model.

Original languageEnglish (US)
Article number3007105
JournalIEEE Geoscience and Remote Sensing Letters
Volume19
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2004-2012 IEEE.

Keywords

  • Multifrequency wavefield
  • partial differential equation
  • physics-informed neural network (NN) (PINN)
  • single reference frequency loss

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Electrical and Electronic Engineering

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