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arxiv: 2410.08329 · v3 · submitted 2024-10-10 · 💻 cs.LG · eess.SP

Survey of Deep Learning and Physics-Based Approaches in Computational Wave Imaging

Youzuo Lin , Shihang Feng , James Theiler , Yinpeng Chen , Umberto Villa , Jing Rao , John Greenhall , Cristian Pantea
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Mark A. Anastasio Brendt Wohlberg
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Pith reviewed 2026-05-23 18:46 UTC · model grok-4.3

classification 💻 cs.LG eess.SP
keywords computational wave imagingdeep learningphysics-based methodsscientific machine learningseismic imagingultrasound tomographyinverse problemsnon-destructive testing
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The pith

A structured framework consolidates how deep learning enhances physics-based methods for computational wave imaging.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper surveys the development of deep neural networks and scientific machine learning techniques to enhance and integrate with traditional physics-based methods for solving computational wave imaging problems. These problems involve extracting hidden structures and physical properties from wave signals that pass through a volume, with uses in seismic exploration, acoustic imaging, non-destructive testing, and ultrasound tomography. The authors organize research across computational imaging, wave physics, and data science into a single structured framework. This matters to a sympathetic reader because physics-based methods offer high resolution and accuracy but suffer from computational intensity, ill-posedness, and nonconvexity, while the surveyed machine-learning approaches provide complementary strategies. The review identifies lessons, technical hurdles, and emerging trends from the literature.

Core claim

Contemporary scientific machine-learning techniques, and deep neural networks in particular, have been developed to enhance and integrate with traditional physics-based methods for solving CWI problems. We present a structured framework that consolidates existing research spanning multiple domains, including computational imaging, wave physics, and data science. This study concludes with important lessons learned from existing ML-based methods and identifies technical hurdles and emerging trends through a systematic analysis of the extensive literature on this topic.

What carries the argument

The structured framework that consolidates research on integrating deep learning with physics-based methods across computational imaging, wave physics, and data science domains.

Load-bearing premise

The surveyed literature from computational imaging, wave physics, and data science communities is sufficiently representative and the proposed structured framework accurately consolidates the integration strategies without major omissions.

What would settle it

Publication of a substantial body of new CWI papers whose integration approaches cannot be placed into the proposed structured framework categories.

Figures

Figures reproduced from arXiv: 2410.08329 by Brendt Wohlberg, Cristian Pantea, James Theiler, Jing Rao, John Greenhall, Mark A. Anastasio, Shihang Feng, Umberto Villa, Yinpeng Chen, Youzuo Lin.

Figure 1
Figure 1. Figure 1: An illustration of (a) CWI problems covered in this paper and [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A taxonomy of ML methods for CWI, based on two categorizations. Under supervision strategy, we distinguish fully supervised, semi-supervised, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Network architecture of InversionNet, a fully-supervised method [51]. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic illustration of semi-supervised learning strategies in CWI. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematic illustration of the network architecture of SiameseFWI [62], [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Schematic illustration of Fourier-DeepONet, a simulations/measurements-driven method [70]. Image courtesy of the authors of [70]. is implicitly represented via simulations and/or measure￾ments. • Physics-Aware. The method is built on a data-driven loss, but physics knowledge is introduced through explicit domain-aware regularization. • Parameterized Solution. The method is built on a physics-based loss as … view at source ↗
Figure 9
Figure 9. Figure 9: Schematic illustration of parameterization-based method [92]. Image [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: Schematic illustration of a physics-informed neural network [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Schematic illustration of the network architecture of PPP-CWI [95], a Plug-and-Play Priors framework for CWI that alternates between physics [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Illustration of the Kimberlina dataset and three modeling modules used to generate the simulated velocity maps. (a) CO [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Illustration of seismic full-waveform inversion with uncertainty quantification applying to noisy data. Ground Truth (Row 1); Results obtained [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Illustration of (a) ultrasonic imaging to identify high-contrast defects in multi-layered bonded structures and (b) Noninvasive acoustic temperature [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: (a) Geometry of the idealized 2D USCT imaging system in [9] with [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The overall trends of the ML methods developed in computational wave imaging. The figures are plotted based on a collection of over 200 papers. [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Illustrations of (a) a breakdown of all the collected papers in four groups of methods under supervision strategy for acoustic imaging, ultrasound [PITH_FULL_IMAGE:figures/full_fig_p024_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Adaptive Data Augmentation: Approximate solver [PITH_FULL_IMAGE:figures/full_fig_p024_17.png] view at source ↗
read the original abstract

Computational wave imaging (CWI) extracts hidden structure and physical properties of a volume of material by analyzing wave signals that traverse that volume. Applications include seismic exploration of the Earth's subsurface, acoustic imaging and non-destructive testing in material science, and ultrasound computed tomography in medicine. Current approaches for solving CWI problems can be divided into two categories: those rooted in traditional physics, and those based on deep learning. Physics-based methods stand out for their ability to provide high-resolution and quantitatively accurate estimates of acoustic properties within the medium. However, they can be computationally intensive and are susceptible to ill-posedness and nonconvexity typical of CWI problems. Machine learning-based computational methods have recently emerged, offering a different perspective to address these challenges. Diverse scientific communities have independently pursued the integration of deep learning in CWI. This review discusses how contemporary scientific machine-learning (ML) techniques, and deep neural networks in particular, have been developed to enhance and integrate with traditional physics-based methods for solving CWI problems. We present a structured framework that consolidates existing research spanning multiple domains, including computational imaging, wave physics, and data science. This study concludes with important lessons learned from existing ML-based methods and identifies technical hurdles and emerging trends through a systematic analysis of the extensive literature on this topic.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript is a literature survey on computational wave imaging (CWI) that reviews traditional physics-based methods alongside deep learning approaches. It claims that contemporary scientific machine-learning techniques, particularly deep neural networks, have been developed to enhance and integrate with physics-based methods for solving CWI problems in applications such as seismic exploration, acoustic imaging, and medical ultrasound. The paper presents a structured framework consolidating research across computational imaging, wave physics, and data science communities, and concludes by extracting lessons learned, technical hurdles, and emerging trends from the surveyed literature.

Significance. If the proposed framework accurately captures the range of integration strategies and the surveyed literature is representative, the work could serve as a useful interdisciplinary reference that clarifies how ML augments physics-based CWI solvers and identifies open challenges. The absence of any described literature-search methodology, however, prevents verification of completeness or categorization fidelity, limiting the potential impact to that of an informal overview rather than a definitive consolidation.

major comments (1)
  1. [Abstract] Abstract: The central claim that 'a structured framework consolidates existing research spanning multiple domains' is load-bearing for the paper's contribution, yet the abstract (and, by extension, the manuscript) provides no description of literature search protocol, inclusion/exclusion criteria, temporal scope, or database sources. Without these, it is impossible to assess whether key sub-areas (e.g., physics-informed neural operators for full-waveform inversion) are under-represented or mis-categorized, directly undermining the claimed consolidation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our survey manuscript. The point raised about literature search methodology is valid and we address it directly below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'a structured framework consolidates existing research spanning multiple domains' is load-bearing for the paper's contribution, yet the abstract (and, by extension, the manuscript) provides no description of literature search protocol, inclusion/exclusion criteria, temporal scope, or database sources. Without these, it is impossible to assess whether key sub-areas (e.g., physics-informed neural operators for full-waveform inversion) are under-represented or mis-categorized, directly undermining the claimed consolidation.

    Authors: We agree that explicitly documenting the literature search process would improve transparency and allow better assessment of coverage. In the revised version we will insert a new subsection (likely in Section 1 or a dedicated 'Survey Methodology' paragraph) that describes: the primary databases and repositories used (Google Scholar, arXiv, IEEE Xplore, Web of Science), the keyword combinations and Boolean queries employed, the temporal window (approximately 2015–2024 with selected earlier foundational works), inclusion/exclusion criteria (peer-reviewed journal/conference papers, relevance to wave-physics + deep-learning integration, exclusion of purely theoretical ML papers without imaging application), and the approximate number of papers screened versus retained. We will also note how we cross-checked coverage of specific sub-areas such as physics-informed neural operators applied to full-waveform inversion. This addition will support rather than alter the existing framework and categorization. revision: yes

Circularity Check

0 steps flagged

No circularity: literature survey with no derivations or predictions

full rationale

This document is a survey paper that reviews and categorizes existing work across computational imaging, wave physics, and data science. It presents a structured framework for consolidation but contains no equations, fitted parameters, predictions, or derivation chains. The abstract and conclusion discuss lessons from the literature and emerging trends without any self-referential reductions or load-bearing self-citations that would force the central claims by construction. The representativeness concern raised in the skeptic note is an issue of external completeness, not internal circularity of the type enumerated in the analysis criteria.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a survey the central claim rests on the assumption that the reviewed body of work is representative; no free parameters, mathematical axioms, or invented entities are introduced.

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discussion (0)

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