Full Waveform Inversion with a Learned Preconditioner
Abstract
Full-waveform inversion (FWI) is a powerful approach for reconstructing subsurface velocity models, but its practical performance is limited by ill-conditioning, sensitivity to the update direction, and the high cost of curvature-based methods. In this project, we investigate whether a neural operator trained on reverse-time-migration (RTM) images can provide a useful learned preconditioner for FWI. We compare projected FWI against neural-preconditioned FWI using either a standard Fourier neural operator (FNO) or a Jacobian-informed FNO (JI-FNO). The neural preconditioner applies the normal operator of the learned RTM map to modify the true Devito FWI gradient. Our experiments show that the JI-FNO preconditioner achieves the lowest model error while maintaining data-residual decay comparable to baseline projected FWI. In contrast, the standard FNO preconditioner is unstable and gives worse model recovery, despite using the same neural-preconditioning framework. We also identify a failure mode of a nonlinear neural Gauss Newton-type inner solve: directly matching the neural RTM output to the FWI gradient creates an objective-space mismatch and does not yield a reliable descent direction. These results suggest that forward RTM-image prediction alone is insufficient for learned preconditioning; accurate learned derivatives and objective-consistent use of the neural operator are critical for producing useful inversion updates.
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BibTeX
@misc{park2026full,
title = {{Full Waveform Inversion with a Learned Preconditioner}},
author = {Jeongjin Park},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15331},
eprint = {2610.15331},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15331},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Full Waveform Inversion with a Learned Preconditioner
AU - Jeongjin Park
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15331
UR - https://arxiv.org/abs/2610.15331
AB - Full-waveform inversion (FWI) is a powerful approach for reconstructing subsurface velocity models, but its practical performance is limited by ill-conditioning, sensitivity to the update direction, and the high cost of curvature-based methods. In this project, we investigate whether a neural operator trained on reverse-time-migration (RTM) images can provide a useful learned preconditioner for FWI. We compare projected FWI against neural-preconditioned FWI using either a standard Fourier neural operator (FNO) or a Jacobian-informed FNO (JI-FNO). The neural preconditioner applies the normal operator of the learned RTM map to modify the true Devito FWI gradient. Our experiments show that the JI-FNO preconditioner achieves the lowest model error while maintaining data-residual decay comparable to baseline projected FWI. In contrast, the standard FNO preconditioner is unstable and gives worse model recovery, despite using the same neural-preconditioning framework. We also identify a failure mode of a nonlinear neural Gauss Newton-type inner solve: directly matching the neural RTM output to the FWI gradient creates an objective-space mismatch and does not yield a reliable descent direction. These results suggest that forward RTM-image prediction alone is insufficient for learned preconditioning; accurate learned derivatives and objective-consistent use of the neural operator are critical for producing useful inversion updates.
ER -