Fourier Neural Operator Network for Fast Photoacoustic Wave Simulations

Abstract

Simulation tools for photoacoustic wave propagation have played a key role in advancing photoacoustic imaging by providing quantitative and qualitative insights into parameters affecting image quality. Classical methods for numerically solving the photoacoustic wave equation rely on a fine discretization of space and can become computationally expensive for large computational grids. In this work, we applied Fourier Neural Operator (FNO) networks as a fast data-driven deep learning method for solving the 2D photoacoustic wave equation in a homogeneous medium. Comparisons between the FNO network and pseudo-spectral time domain approach were made for the forward and adjoint simulations. Results demonstrate that the FNO network generated comparable simulations with small errors and was orders of magnitude faster than the pseudo-spectral time domain methods (~26× faster on a 64 × 64 computational grid and ~15× faster on a 128 × 128 computational grid). Moreover, the FNO network was generalizable to the unseen out-of-domain test set with a root-mean-square error of 9.5 × 10−3 in Shepp–Logan, 1.5 × 10−2 in synthetic vasculature, 1.1 × 10−2 in tumor and 1.9 × 10−2 in Mason-M phantoms on a 64 × 64 computational grid and a root mean squared of 6.9 ± 5.5 × 10−3 in the AWA2 dataset on a 128 × 128 computational grid.

Towards accelerating particle‐resolved direct numerical simulation with neural operators

“…Particularly, the Fourier neural operators (FNOs) [14,16] learn mappings between infinite-dimensional function spaces. A brief description of FNOs is provided in Appendix A. FNOs have become a popular alternative to the conventional neural networks for a wide range of physical applications like climate modeling [22], multiphase flows in porous media [12,26], and wave propagation [9]. This popularity is due to their low computational cost, relatively small errors, and the support of features like zero-shot super-resolution for turbulent flows, which are limited in other machine learning methods.…”

Efficient Photoacoustic Image Synthesis with Deep Learning

“…The usage of FNO networks was motivated by the solution of partial differential equations in Fourier space. The FNO architecture has already been applied in the estimation of photoacoustic wave propagation [ 31 ] and other physical phenomena such as fluid dynamics [ 23 ]. In contrast to convolutional neural networks, which capture local features such as edges and shapes in their kernels and only learn the global context by pooling or down-sampling, the Fourier layers can learn global sinusoidal features.…”

A Deep Learning Method for Dynamic Process Modeling of Real Landslides Based on Fourier Neural Operator

“…Moreover, FNO showcases super‐resolution prowess, permitting training on low‐resolution data while delivering high‐resolution results devoid of accuracy loss (Lu et al., 2021). The FNO‐based neural network paradigm has found successful applications across diverse domains, yielding outstanding performance (Guan et al., 2023; Rosofsky et al., 2023; Wen et al., 2022; You et al., 2022). Nevertheless, to date, there exists a conspicuous paucity of endeavors employing FNO‐based methodologies to address real‐world dynamic processes (especially landslide dynamics).…”