{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T00:45:09Z","timestamp":1776386709837,"version":"3.51.2"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T00:00:00Z","timestamp":1676764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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\u00d7 faster on a 64 \u00d7 64 computational grid and ~15\u00d7 faster on a 128 \u00d7 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 \u00d7 10\u22123 in Shepp\u2013Logan, 1.5 \u00d7 10\u22122 in synthetic vasculature, 1.1 \u00d7 10\u22122 in tumor and 1.9 \u00d7 10\u22122 in Mason-M phantoms on a 64 \u00d7 64 computational grid and a root mean squared of 6.9 \u00b1 5.5 \u00d7 10\u22123 in the AWA2 dataset on a 128 \u00d7 128 computational grid.<\/jats:p>","DOI":"10.3390\/a16020124","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T01:36:37Z","timestamp":1676856997000},"page":"124","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Fourier Neural Operator Network for Fast Photoacoustic Wave Simulations"],"prefix":"10.3390","volume":"16","author":[{"given":"Steven","family":"Guan","sequence":"first","affiliation":[{"name":"Bioengineering Department, George Mason University, Fairfax, VA 22030, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9677-7655","authenticated-orcid":false,"given":"Ko-Tsung","family":"Hsu","sequence":"additional","affiliation":[{"name":"Bioengineering Department, George Mason University, Fairfax, VA 22030, USA"}]},{"given":"Parag V.","family":"Chitnis","sequence":"additional","affiliation":[{"name":"Bioengineering Department, George Mason University, Fairfax, VA 22030, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2528\/PIER14032303","article-title":"Photoacoustic tomography: Principles and advances","volume":"147","author":"Xia","year":"2014","journal-title":"Electromagn. 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