arxiv: 2604.14189 · v1 · submitted 2026-04-01 · ⚛️ physics.gen-ph · physics.comp-ph

Recognition: no theorem link

SWEEP (Seismic Wave Equation Exploration Platform): A Unified Solver Framework for Differentiable Wave Physics

Shaowen Wang , Tariq Alkhalifah

Authors on Pith no claims yet

Pith reviewed 2026-05-13 22:28 UTC · model grok-4.3

classification ⚛️ physics.gen-ph physics.comp-ph

keywords seismic wave equationfull-waveform inversionautomatic differentiationwave propagation modelingseismic inversiondifferentiable physicsanisotropic media

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The pith

SWEEP provides one extensible library for solving acoustic, elastic, anisotropic and attenuative seismic waves with automatic differentiation built in for inversion.

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

The paper presents SWEEP as a single software framework that implements multiple wave-propagation engines side by side. Automatic differentiation is included so that gradients required for optimization are obtained directly from the solvers. This setup targets full-waveform inversion, least-squares reverse-time migration and similar gradient-based tasks. The architecture is designed to accept custom loss functions, neural networks and multi-GPU execution through a plug-and-play interface.

Core claim

SWEEP is a unified and extensible wave-equation solver library that supports acoustic, elastic, attenuative, VTI, TTI and Born-approximation engines together with automatic differentiation. The library thereby allows direct implementation of full-waveform inversion, least-squares reverse-time migration and other gradient-based seismic inverse methods inside the same code base.

What carries the argument

The SWEEP unified solver architecture with automatic differentiation that keeps wave-physics models interchangeable while preserving gradient flow.

If this is right

Full-waveform inversion and least-squares reverse-time migration can be coded directly from the provided wave engines without separate adjoint derivations.
Different wave approximations (acoustic to TTI) can be swapped inside the same inversion workflow.
Custom loss functions and neural-network modules can be inserted at the optimization level without rewriting the wave propagators.
Multi-GPU scaling becomes available for the supported wave types through the library's built-in support.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Developers could test new hybrid physics-plus-machine-learning inversion schemes by swapping only the loss or network layer rather than the entire solver stack.
The same differentiable-wave core might be repurposed for related inverse problems in other wave-dominated fields once the seismic-specific engines are abstracted.
If the automatic-differentiation overhead remains low, end-to-end differentiable pipelines that jointly optimize velocity models and network parameters become feasible at field scales.

Load-bearing premise

The plug-and-play design and automatic-differentiation layer can combine custom losses, neural networks and multi-GPU runs without hidden performance penalties that would block practical large-scale use.

What would settle it

A timing or accuracy test in which replacing a hand-written gradient or loss function with the corresponding SWEEP module produces either substantially slower execution or visibly different inversion results would falsify the claim of seamless integration.

Figures

Figures reproduced from arXiv: 2604.14189 by Shaowen Wang, Tariq Alkhalifah.

**Figure 2.** Figure 2: Wavefields of the pseudoelastic wave equations. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Wavefields of the VTI acoustic wave equation with different anisotropic parameters. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Wavefields of the TTI acoustic wave equation with different anisotropic parameters. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: Wavefields of the first order and second acoustic wave equation. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: Wavefields of the VTI acoustic wave equation (left: [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 7.** Figure 7: Wavefields of the VTI acoustic wave equation with different anisotropic parameters. [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 8.** Figure 8: Wavefields of the TTI acoustic wave equation with different anisotropic parameters. [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

**Figure 9.** Figure 9: Attenuation and dispersion in acoustic wave equations. [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗

**Figure 10.** Figure 10: Wavefields of P (first row), vx (second row) and vz (thrid row) at different time steps. where τxx, τzz, and τxz are the stress components, ρ is the density, and fx and fz are the source terms in the x and z directions, respectively. The equations that contains laplace operator ∂ 2 ∂x2 + ∂ 2 ∂z2 can be solved by pseudo spectral method, which is v † x = F −1 (− F(vx) k 2 x + k 2 z ), v † z = F −1 (− F(vz) … view at source ↗

**Figure 11.** Figure 11: Wavefields of the pseudo elastic wave equation. [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗

read the original abstract

SWEEP (Seismic Wave Equation Exploration Platform) is a unified and extensible wave equation solver library designed for wavefield modeling and inversion. It supports a wide range of wave propagation engines, including acoustic, elastic, attenuative, VTI, TTI, and their Born approximations, among others. With a built-in support for automatic differentiation, the framework enables seamless implementation of full-waveform inversion (FWI), least-squares reverse time migration (LSRTM), and other gradient-based optimization methods. It also features a plug-and-play architecture, allowing easy integration and flexible combination of custom loss functions, multi-GPU computation, neural networks, and more. This makes Sweep a powerful and customizable platform for tackling advanced seismic inverse problems.

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.

Desk Editor's Note private letter to a colleague

SWEEP packages several established seismic solvers into one autodiff-enabled library, which is useful engineering but adds little new physics or verified performance.

read the letter

The core point is that this paper introduces SWEEP as a single framework that supports acoustic, elastic, attenuative, VTI, TTI, and Born-approximation engines all with automatic differentiation turned on. That setup is meant to make full-waveform inversion and least-squares migration easier by letting users drop in custom losses or neural nets without rewriting the wave propagator each time. The individual solvers are not new, but the claim is that the unified interface and plug-and-play design remove a lot of the usual code-switching friction in computational geophysics. If the integration actually works as described, the library could save time for groups that currently maintain separate codes for different wave types. The paper does a reasonable job laying out the architecture and the intended use cases for gradient-based methods. The soft spots are the lack of any reported benchmarks, timing numbers, or error comparisons against existing tools. Without those, it is hard to know whether the autodiff overhead stays acceptable on large models or whether the multi-GPU path introduces hidden synchronization costs. The abstract also does not show concrete examples of a full inversion run, so the practical payoff remains untested in the text. This work is aimed at researchers who already do seismic inversion and want a more flexible code base rather than a new theoretical result. A reader who needs to prototype gradient methods quickly would find it worth a look once the code and tests are available. I would send it to peer review so referees can check the implementation details and ask for the missing performance data.

Referee Report

2 major / 0 minor

Summary. The manuscript introduces SWEEP, a unified and extensible solver library for seismic wave propagation that supports acoustic, elastic, attenuative, VTI, TTI, and Born-approximation engines. It claims built-in automatic differentiation enables direct use in gradient-based methods such as full-waveform inversion (FWI) and least-squares reverse time migration (LSRTM), together with a plug-and-play architecture for custom loss functions, multi-GPU execution, and neural-network integration.

Significance. If the claimed seamless AD integration and extensibility hold without hidden performance costs, SWEEP could become a useful platform for the seismic imaging community by reducing the engineering overhead of implementing differentiable wave-physics workflows and facilitating hybrid physics-ML inversions. The absence of any verification data, however, prevents assessment of whether these advantages are realized in practice.

major comments (2)

[Abstract] Abstract: the central claim that the framework provides 'seamless implementation' of FWI/LSRTM and 'plug-and-play' support for multi-GPU and neural-network components is not accompanied by any description of the underlying discretization, the AD backend (e.g., PyTorch/JAX), or how custom operators are registered, rendering the extensibility assertions unverifiable.
[Abstract] No section supplies numerical benchmarks, convergence tests, or comparisons against established codes (e.g., Devito, SPECFEM), which are required to substantiate the performance and accuracy claims for the listed wave engines.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and for highlighting areas where the manuscript requires greater technical specificity and verification. We address each major comment below and indicate the changes planned for the revised version.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the framework provides 'seamless implementation' of FWI/LSRTM and 'plug-and-play' support for multi-GPU and neural-network components is not accompanied by any description of the underlying discretization, the AD backend (e.g., PyTorch/JAX), or how custom operators are registered, rendering the extensibility assertions unverifiable.

Authors: We agree that the abstract and main text are insufficiently detailed on implementation. In the revision we will add a dedicated 'Implementation' section that specifies the finite-difference discretizations (staggered-grid schemes with orders 2–8 depending on the engine), identifies PyTorch as the automatic-differentiation backend, and explains operator registration via custom torch.autograd.Function classes together with the plug-in mechanism for loss functions and neural-network modules. These additions will make the extensibility claims directly verifiable. revision: yes
Referee: [Abstract] No section supplies numerical benchmarks, convergence tests, or comparisons against established codes (e.g., Devito, SPECFEM), which are required to substantiate the performance and accuracy claims for the listed wave engines.

Authors: We acknowledge the absence of verification results in the submitted manuscript. The revision will include a new 'Numerical Verification' section containing (i) grid-convergence studies reporting L2 error norms for the acoustic and elastic engines, (ii) accuracy checks against analytic solutions for homogeneous media, and (iii) runtime and memory benchmarks versus Devito on identical 2-D test cases. Comprehensive side-by-side comparisons with SPECFEM for all supported physics (including attenuative and anisotropic cases) exceed the scope of the present work and will be noted as a limitation; we will instead provide the available Devito comparisons and discuss relative engineering overhead. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents SWEEP as a software framework and library for wave equation solvers with built-in AD support across multiple physics engines. No derivation chain, parameter fitting, or predictive claims are made that reduce to inputs by construction. The abstract and description focus on architecture, extensibility, and integration features without invoking uniqueness theorems, self-citations as load-bearing premises, or renaming empirical results. This is a standard tool-description paper whose central claims are design statements rather than derived results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that standard wave-equation physics models can be correctly implemented and differentiated within a single extensible code base; no free parameters or invented entities are introduced.

axioms (1)

domain assumption Standard acoustic, elastic, attenuative, VTI, and TTI wave equations are accurately discretized and solved by the framework.
The description relies on established seismic wave physics without providing independent verification.

pith-pipeline@v0.9.0 · 5424 in / 1223 out tokens · 49925 ms · 2026-05-13T22:28:30.820025+00:00 · methodology

discussion (0)

Reference graph

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