DiffTopo: Solver in the Loop for Inverse Topography via Condition Diffusion Generation

Aoming Liang; Qi Liu; Weicheng Cui

REVIEW 4 major objections 6 minor 34 references

DiffTopo: Solver in the Loop for Inverse Topography via Condition Diffusion Generation

T0 review · 4 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A conditional diffusion model, trained on shallow-water wave simulations and gated by a solver-based residual check, can reconstruct seabed topography from surface wave fields.

desk verdict A plausible diffusion-based proof of concept for topography inversion, but the robustness claims outrun the evidence because the validation loop stays inside the same simulator. read the letter →

arxiv 2509.00007 v1 pith:COXK3HYO submitted 2025-08-14 physics.ao-ph

Aoming Liang , Qi Liu , Weicheng Cui This is my paper

classification physics.ao-ph

keywords inversetopographybathymetryreconstructionconditionaldiffusionmodelclassifier-freeguidanceshallowwaterequationssolver-in-the-loopvalidationgenerativeproblemsseafloormapping

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that a conditional diffusion model can solve an ill-posed inverse problem in coastal oceanography: reconstructing seabed topography from a time series of surface-wave elevation. The model, DiffTopo, is trained on nonlinear shallow-water simulations and uses classifier-free guidance to sample candidate topographies conditioned on the observed wave field. The distinctive step is a 'solver in the loop': each candidate is fed back into the shallow-water solver, the simulated wave field is compared to the observation, and candidates whose residual exceeds a threshold are discarded. On three synthetic topography families, the surviving samples match the ground truth, and the paper argues this shows the method is physically consistent and generalizes within this setting.

What carries the argument

Conditional diffusion with classifier-free guidance plus a solver-based residual gate. The forward diffusion noising schedule $x_t = \sqrt{\bar\alpha_t}x_0 + \sqrt{1-\bar\alpha_t}\epsilon$ lets the network $\epsilon_\theta(x_t, c)$ learn the conditional score; at inference, the guided noise estimate $\hat\epsilon_\theta = (1+\omega)\epsilon_\theta(x_t,c) - \omega\epsilon_\theta(x_t,\varnothing)$ shifts each reverse step along the conditional signal. The generated topography is then passed through the nonlinear shallow-water equations; the mean squared error of the regenerated wave field against the observed field, $R(\hat h)$, decides whether the sample is physically acceptable. This combina

What would settle it

Run DiffTopo on physical wave-tank measurements over a known, independently surveyed sandbar, and compute the residual $R(\hat h)$ for its accepted samples; if the accepted reconstructions do not match the surveyed bathymetry, or if the residual threshold cannot separate good from bad reconstructions under real sensor noise, the central claim fails.

Watch

Extended reading notes

Core claim

The central claim is that topography can be inferred from full wave-field observations by learning the posterior distribution $q(h \mid \eta_{\mathrm{obs}})$ with a denoising diffusion model, and that the ambiguity inherent in the inverse problem can be managed by validating each generated topography through the governing equations. DiffTopo parametrizes the posterior with a U-Net trained to predict noise, with the conditioning dropped 10% of the time so that classifier-free guidance can interpolate between conditional and unconditional generation via a guidance weight $\omega$. After sampling, the shallow-water solver regenerates $\eta_{\mathrm{sim}}$ from the candidate $\hat{h}$; the squar

Load-bearing premise

The entire demonstration relies on synthetic data: training, validation, and ground truth all come from the same shallow-water solver, the same Gaussian-pulse initial condition, and only three parametric topography families, so the claimed robust generalization is only established within that simulation setting.

Editorial extensions

If this is right

If correct, diffusion models offer a data-driven route to bathymetric inversion that avoids PDE-constrained optimization, at least when training and deployment share the same wave physics.
The residual threshold supplies a physics-based filter that can reject spurious generative samples, converting a generative prior into a set of plausible reconstructions.
The success of DPM++ at 25 steps suggests practical runtimes of seconds per candidate on a desktop GPU, making solver-in-the-loop validation feasible.
The method's degraded performance on multi-seamount terrain indicates where learned priors alone fall short and where hybrid physical priors would be needed.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's evaluation is fully synthetic (same solver for training, validation, and ground truth), so a natural next test is transferring to wave-tank or field data, where the forward model, noise, and boundary conditions differ; the residual gate would be the first point of failure or success.
The solver-in-the-loop residual could serve as a general acceptance criterion for other generative inverse problems in geophysics, e.g., seismic or tidal inversion, wherever a fast forward solver exists.
Because the guidance weight is sampled from a normal distribution during validation, DiffTopo effectively performs a form of approximate posterior sampling; the distribution over accepted samples could be interpreted as an empirical uncertainty estimate for the topography.
The threshold itself is a free parameter; an adaptive threshold based on observation noise would make the method more portable.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a reasonable first pass at applying conditional diffusion to seabed topography inversion, and the solver-based rejection filter is a sensible idea. The paper is honest about its own limits in the conclusion. But the headline claims of robust generalization and physical consistency are not supported by the evaluation, which is entirely in-distribution and self-referential.

What's actually new: the specific combination of classifier-free guidance with a solver-loop residual threshold for bathymetry recovery from SWE wave fields. The CFG score-space derivation in the appendix is standard but correctly laid out. The sampler comparison (DDPM, Heun, DPM++) is a useful, if minor, empirical datapoint. Training loss curves and the discussion of MMT difficulty show the authors understand where the method struggles.

The central weakness is that the same solver, same initial condition, and same topography families generate the training data, the test data, and the validation residual. So accepting samples below a residual threshold mostly confirms that a generated topography is consistent with that one simulator, not that it is physically plausible in any broader sense. 'Generalization' here means new random draws from three parametric families. There are no baselines against optimization-based inversion or neural operator methods, no aggregate statistics for the validation pipeline (acceptance rates, error distributions of accepted vs rejected), and the residual thresholds are hand-tuned per dataset (1e-3 for SMT/TanT, 1.2e-3 for MMT). The paper acknowledges these limits in the conclusion, which is to its credit, but the abstract still overstates.

A few smaller issues: the quality metrics in Tables 2-4 are reported for w=0 only, while the highlighted generations use w=5, so the link between the reported metrics and the accepted samples is unclear. Also, the title's 'condition diffusion' is a bit awkward, but that's cosmetic.

Who this is for: people working on generative inverse problems in coastal geophysics. It's a modest step, not a breakthrough. The core idea has merit and the flaws are fixable with a broader evaluation, testing on a different forward model or real data, and more careful wording. I'd send it to review, expecting heavy revision, because the combination is novel enough and the failure modes are instructive. If it lands on your desk, don't desk-reject—ask for real baselines and honest generalization claims.

Referee Report

4 major / 6 minor

Summary. The paper proposes DiffTopo, a conditional denoising diffusion probabilistic model with classifier-free guidance for reconstructing seabed topography from shallow-water wave-field observations. Training and evaluation are performed on synthetic data generated by a finite-difference SWE solver for three parametric topography families (single seamount, tanh ridge, and multi-seamount). At inference, multiple topography samples are generated, and a 'solver-in-the-loop' residual threshold (Eq. 12) is used to accept or reject samples by re-running the same SWE solver with the generated topography. The paper compares DDPM, Heun, and DPM++ samplers and reports MSE, MAE, and SSIM, concluding that DiffTopo exhibits robust generalization and physical consistency with the SWEs even under full observations.

Significance. If the claims were fully supported, DiffTopo would be a valuable fast generative alternative to PDE-constrained optimization for ill-posed bathymetry inversion, with a natural way to produce an ensemble of plausible topographies. The paper has clear strengths: Appendix 5.3 gives a correct and self-contained derivation of CFG as classifier guidance in score space; the UNet architecture and hyperparameters are described in detail; and the comparison of three inference samplers is a useful practical contribution. However, the experimental evidence is entirely in-distribution and uses the same solver for both training-data generation and posterior validation, so the headline claims of 'robust generalization' and consistency with the SWEs are not established by the reported experiments. The manuscript's own Section 4 acknowledges cross-domain generalization as future work, which tempers the overstatement but does not fix the abstract's unsupported phrasing.

major comments (4)

[§2.1, §2.2.3, Eq. (12), §3.1–3.3] The validation loop is self-referential: the residual R in Eq. (12) uses the same SWE solver, same domain, same Gaussian-pulse initial condition, and same parameter settings that generated the training data in §2.1. A low residual therefore only shows consistency with the training simulator, not with the true physical process or with independent observations. The train/test split is random within the same three parametric topography families, so 'robust generalization' is only generalization to new random draws from those families. Please add out-of-distribution tests (e.g., hold out an entire topography family, vary the initial condition, Manning friction, or discretization, or use an independent solver) or substantially soften the abstract and conclusions.
[§3.1–3.3, Tables 2–4] No baseline comparisons are reported. All quantitative results compare only DiffTopo's own three samplers. The paper claims DiffTopo is a robust and generalizable solution for inverse topography, but there is no comparison to classical adjoint/optimization methods, variational data assimilation, physics-informed neural networks, neural operators, or simpler conditional generative baselines. Without any external baseline, the claimed advantages of the diffusion-based approach are not demonstrated. Please add at least one classical or data-driven baseline and, ideally, an ablation of the guidance weight and condition-drop probability.
[§2.2.3, §3.1–3.3, Figures 3, 6, 9] The posterior-validation results are anecdotal. For each topography type, only a single validation run of 30 samples is shown, with 3–4 samples accepted; no aggregate acceptance rates, residual distributions, or error statistics for accepted versus rejected samples over the full test set are reported. The residual threshold is hand-set per dataset (1e−3 for SMT and TanT, relaxed to 1.2e−3 for MMT) with no sensitivity analysis. Without these aggregate statistics, the 'solver-in-the-loop' mechanism cannot be assessed as a general filtering procedure. Please report median/quantiles of R, acceptance rates, and the topography error of accepted vs rejected samples, plus a threshold sensitivity study.
[Table 2, §3.1] The reported metrics are internally inconsistent for the central claim that DPM++ is the best sampler. On SMT, DPM++ has the highest SSIM (0.75) but the worst MSE (18.57 ± 1.66), while DDPM has MSE 8.14 ± 0.15 and SSIM 0.60. The text states that the high SSIM 'indicates a strong similarity' but does not explain the simultaneous worst MSE. Similar inconsistencies appear in Tables 3 and 4 (e.g., TanT: DDPM has the highest SSIM but the largest MAE; MMT: DPM++ has the lowest MAE/MSE but SSIM only 0.30). The paper must either clarify the normalization used for SSIM or present a consistent error discussion before claiming one sampler is best.

minor comments (6)

[§1] There are incomplete reference placeholders: '[ ?]' after 'geometric characteristics of the seabed topography' and 'system identification [?]'. These should be filled in.
[§2.1] Typographical issues: 'T opography' should be 'Topography' in the topography-generation paragraph; 'T anh T opography' similarly. Please proofread.
[§2.2.2, Eq. (13)] The guidance weight is denoted w in Eq. (10) but ω in Eq. (13) and elsewhere; unify the notation. Also, the normal distribution N(μ=5.0, σ=2.0) for ω permits negative values; clarify whether negative weights are allowed or truncated.
[Table 5] The UNet table is not fully self-explanatory: the condition projection changes shape from (B,48,H,W) to (B,1,H,W), and the encoder input is listed as (B,2,H,W). Clarify how the projected condition is concatenated or added to the noisy input.
[§5.3, Eq. (33)] The derivation is correct and standard, but the sentence 'since ϵθ = −√(1−ᾱt) sθ' uses the sign convention from Eq. (20); consider stating this explicitly to avoid confusion with the earlier score definition.
[§2.1, §3] The domain size (100 m × 100 m), short simulation time (6 s), and single Gaussian-pulse initial condition are highly idealized. The paper should state explicitly that all conclusions are limited to this synthetic configuration, especially because the abstract claims robust generalization.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation chain is self-contained and the same-solver validation is a limitation of external validity, not a circular step.

full rationale

The paper's central derivation chain is not circular. The training objective (Eq. 9 and L_CFG) is a standard DDPM loss with classifier-free guidance, and the appendix derives the CFG update from score identities (Eqs. 17-29) without relying on the authors' prior work. The inverse mapping from wave fields to topography is learned from supervised pairs generated by the SWE solver; the test metrics (MSE, MAE, SSIM) compare against held-out ground truth, so the reported reconstruction numbers are genuine predictions, not fitted quantities renamed as predictions. The posterior validation (Eq. 12) runs the SWE solver on the generated topography and thresholds the residual; this is an operational consistency check, not a derivation that assumes the conclusion. Using the same solver for training data generation and validation is a limitation on external generalization—the paper itself acknowledges this by listing cross-domain generalization as future work—but it does not make any step logically circular. The only self-citation (Liang et al. 2024) appears in the introduction as a non-load-bearing remark about neural operators and does not support the paper's central claim. No equation reduces to its own input by construction, and no fitted parameter is presented as a prediction. Therefore the circularity score is 0.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central claim rests on the synthetic data-generation setup: a specific SWE solver, a single Gaussian-pulse initial condition, three parametric topography families, and hand-set validation thresholds. None of these are externally benchmarked, so the paper's contribution is an in-distribution proof of concept.

free parameters (3)

residual acceptance threshold = 1e-3 (SMT, TanT), 1.2e-3 (MMT)
Hand-set per dataset to select 'feasible' reconstructions; the paper admits that too low a threshold prevents meeting the criterion and too high yields inaccurate estimates (§3.1).
guidance weight sampling distribution = N(μ=5.0, σ=2.0), 30 runs
The validation procedure samples guidance weights from this hand-chosen normal distribution; the acceptance outcome depends directly on this choice (§2.2.3).
condition drop probability p = 0.1
Standard CFG dropout, set in §2.2.1; less load-bearing, but still a hand-set hyperparameter.

assumptions (7)

domain assumption Nonlinear shallow-water equations with Manning friction govern the wave-topography coupling
The entire dataset is generated by this forward model (Eq. 1), so any inversion result is only as valid as this physical model.
domain assumption Neumann boundary conditions for the free surface elevation η
Specified in Eq. (2); the wave field and thus the training data depend on this choice.
domain assumption Gaussian pulse initial condition and initial momenta M=κη, N=0
Eq. (3) sets the wave excitation; all training observations come from this single initial condition type.
domain assumption Topography restricted to three parametric families (Gaussian seamount, tanh ridge, smoothed random perturbations)
Eqs. (4)-(7); generalization is only claimed for these forms.
standard math DDPM forward process and score-matching identities
Used in §2.2 and the appendix; standard diffusion model theory.
standard math Classifier-free guidance as implicit classifier guidance
Derived in the appendix; relies on standard Bayes rule and score identities.
domain assumption The finite-difference SWE solver with CFL<0.8 is a faithful discretization
Used for both data generation and validation; no convergence study or comparison to other solvers is provided.

how reviews work

0 comments

Cite this review

Pith. "Pith review of DiffTopo: Solver in the Loop for Inverse Topography via Condition Diffusion Generation." pith.science (2026). https://pith.science/paper/COXK3HYO

@misc{pith2026250900007,
  author       = {Pith},
  title        = {Pith review of: DiffTopo: Solver in the Loop for Inverse Topography via Condition Diffusion Generation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/COXK3HYO}},
  note         = {Machine review of arXiv:2509.00007}
}

read the original abstract

Inferring seabed topography from wave height observations is fundamental to tsunami hazard assessment, coastal planning, and large scale ocean circulation modeling. Classical inversion models typically rely on direct sensing or optimization based schemes that must contend with the strongly nonlinear coupling between free surface dynamics and topography. However, data driven approaches are capable of tackling strongly nonlinear problems by learning the underlying data distributions. This study introduces DiffTopo, a conditional diffusion model that reconstructs topography from surface wave field data governed by shallow water equations. Leveraging classifier free guidance, DiffTopo not only generates a series of solutions but also applies a thresholding mechanism that ensures, via the solver, the validation results are physically plausible. This study evaluates both observed wave fields and three distinct topography configurations, demonstrating that DiffTopo exhibits robust generalization and remains consistent with the shallow water equations even under full observations. These results underscore the potential of diffusion based generative modeling for addressing ill posed inverse problems in geophysics.

Figures

Figures reproduced from arXiv: 2509.00007 by the authors.

**Figure 2.** Sampling results using DPM with different guidance weights. The first row shows the ground [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Posterior evaluation process using the solver on the SMT dataset. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: Comparison of the best and worst topography generated in SMT, along with their corre [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Sampling results using DPM with different guidance weights in TanT dataset. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: Posterior evaluation process using the solver on the TanT dataset. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: Comparison of the best and worst topography generated in TanT, along with their corre [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: Sampling results using DPM with different guidance weights in MMT. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: Posterior evaluation process using the solver on the MMT dataset. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 10.** Figure 10: Comparison of the best and worst topography generated in MMT, along with their corre [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

**Figure 11.** Figure 11: Training loss curves on the three datasets, with early stopping patience set to 50 epochs. [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]

**Figure 12.** Figure 12: Comparison between the DDPM forward diffusion process and the reverse sampling trajec [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

34 extracted references · 29 canonical work pages

[1]

The role of topography in controlling throughflow generation

MG Anderson and TP Burt. The role of topography in controlling throughflow generation. Earth Surface Processes, 3 0 (4): 0 331--344, 1978

work page 1978
[2]

o rn Behrens, Sebastian G \

Judith Angel, J \"o rn Behrens, Sebastian G \"o tschel, Marten Hollm, Daniel Ruprecht, and Robert Seifried. Bathymetry reconstruction from experimental data using pde-constrained optimisation. Computers & fluids, 278: 0 106321, 2024

work page 2024
[3]

Nonlinear deterministic reconstruction and prediction of remotely measured ocean surface waves

Nicolas Desmars, Moritz Hartmann, Jasper Behrendt, Norbert Hoffmann, and Marco Klein. Nonlinear deterministic reconstruction and prediction of remotely measured ocean surface waves. Journal of Fluid Mechanics, 975: 0 A8, 2023

work page 2023
[4]

Diffusion models beat gans on image synthesis

Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 34: 0 8780--8794, 2021

2021
[5]

Tidal data inversion: Interpolation and inference

Gary D Egbert. Tidal data inversion: Interpolation and inference. Progress in Oceanography, 40 0 (1-4): 0 53--80, 1997

work page 1997
[6]

Leveraging physics-informed neural networks for efficient modelling of coastal ecosystems dynamics: A case study of sundarbans mangrove forest

Majdi Fanous, Jonathan M Eden, Juntao Yang, Simon See, Vasile Palade, and Alireza Daneshkhah. Leveraging physics-informed neural networks for efficient modelling of coastal ecosystems dynamics: A case study of sundarbans mangrove forest. Ecological Informatics, page 103302, 2025

work page 2025
[7]

Deep Learning the Physics of Transport Phenomena

Amir Barati Farimani, Joseph Gomes, and Vijay S Pande. Deep learning the physics of transport phenomena. arXiv preprint arXiv:1709.02432, 2017

work page Pith review arXiv 2017
[8]

A review of observations and models of dynamic topography

Nicolas Flament, Michael Gurnis, and R Dietmar M \"u ller. A review of observations and models of dynamic topography. Lithosphere, 5 0 (2): 0 189--210, 2013

work page 2013

Show all 34 references

[9]

Diffusion models as probabilistic neural operators for recovering unobserved states of dynamical systems

Katsiaryna Haitsiukevich, Onur Poyraz, Pekka Marttinen, and Alexander Ilin. Diffusion models as probabilistic neural operators for recovering unobserved states of dynamical systems. In 2024 IEEE 34th International Workshop on Machine Learning for Signal Processing (MLSP), page...

2024
[10]

Denoising diffusion probabilistic models

Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33: 0 6840--6851, 2020

2020
[11]

cbathy: A robust algorithm for estimating nearshore bathymetry

Rob Holman, Nathaniel Plant, and Todd Holland. cbathy: A robust algorithm for estimating nearshore bathymetry. Journal of geophysical research: Oceans, 118 0 (5): 0 2595--2609, 2013

2013
[12]

Self-guided diffusion models

Vincent Tao Hu, David W Zhang, Yuki M Asano, Gertjan J Burghouts, and Cees GM Snoek. Self-guided diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18413--18422, 2023

2023
[13]

Diffusionpde: Generative pde-solving under partial observation

Jiahe Huang, Guandao Yang, Zichen Wang, and Jeong Joon Park. Diffusionpde: Generative pde-solving under partial observation. Advances in Neural Information Processing Systems, 37: 0 130291--130323, 2024

2024
[14]

Depth estimation from multispectral satellite imagery: a comparison of conventional and machine learning-based approaches-case study: Kish island, persian gulf

Keivan Kabiri and Mohammad Hossein Kazeminezhad. Depth estimation from multispectral satellite imagery: a comparison of conventional and machine learning-based approaches-case study: Kish island, persian gulf. Earth Science Informatics, 18 0 (1): 0 68, 2025

2025
[15]

Elucidating the design space of diffusion-based generative models

Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. Elucidating the design space of diffusion-based generative models. Advances in neural information processing systems, 35: 0 26565--26577, 2022

2022
[16]

Finite volume methods for hyperbolic problems, volume 31

Randall J LeVeque. Finite volume methods for hyperbolic problems, volume 31. Cambridge university press, 2002

2002
[17]

Wave equation dispersion inversion of surface waves recorded on irregular topography

Jing Li, Fan-Chi Lin, Amir Allam, Yehuda Ben-Zion, Zhaolun Liu, and Gerard Schuster. Wave equation dispersion inversion of surface waves recorded on irregular topography. Geophysical Journal International, 217 0 (1): 0 346--360, 2019

2019
[18]

Generative latent neural pde solver using flow matching

Zijie Li, Anthony Zhou, and Amir Barati Farimani. Generative latent neural pde solver using flow matching. arXiv preprint arXiv:2503.22600, 2025

2025 arXiv
[19]

Mixed neural operator learning on the solitary wave propagation over slope topography and inverse problem

Aoming Liang, Zhan Wang, Heng Luo, Kun Zheng, Ruipeng Li, Mingming Ge, and Dixia Fan. Mixed neural operator learning on the solitary wave propagation over slope topography and inverse problem. Physics of Fluids, 36 0 (11), 2024

2024
[20]

Bathymetry inversion using a deep-learning-based surrogate for shallow water equations solvers

Xiaofeng Liu, Yalan Song, and Chaopeng Shen. Bathymetry inversion using a deep-learning-based surrogate for shallow water equations solvers. Water Resources Research, 60 0 (3): 0 e2023WR035890, 2024

2024
[21]

Dpm-solver++: Fast solver for guided sampling of diffusion probabilistic models

Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. Dpm-solver++: Fast solver for guided sampling of diffusion probabilistic models. Machine Intelligence Research, pages 1--22, 2025

2025
[22]

Kinematic earthquake source inversion and tsunami runup prediction with regional geophysical data

Diego Melgar and Yehuda Bock. Kinematic earthquake source inversion and tsunami runup prediction with regional geophysical data. Journal of Geophysical Research: Solid Earth, 120 0 (5): 0 3324--3349, 2015

2015
[23]

Model parameterization and experimental design issues in nearshore bathymetry inversion

C Narayanan, VN Rama Rao, and JM Kaihatu. Model parameterization and experimental design issues in nearshore bathymetry inversion. Journal of Geophysical Research: Oceans, 109 0 (C8), 2004

2004
[24]

Adjoint sensitivity analysis for shallow-water wave control

Brett F Sanders and Nikolaos D Katopodes. Adjoint sensitivity analysis for shallow-water wave control. Journal of Engineering Mechanics, 126 0 (9): 0 909--919, 2000

2000
[25]

On conditional diffusion models for pde simulations

Aliaksandra Shysheya, Cristiana Diaconu, Federico Bergamin, Paris Perdikaris, Jos \'e Miguel Hern \'a ndez-Lobato, Richard Turner, and Emile Mathieu. On conditional diffusion models for pde simulations. Advances in Neural Information Processing Systems, 37: 0 23246--23300, 2024

2024
[26]

Large-scale waveform inversions of surface waves for lateral heterogeneity: 2

Roel Snieder. Large-scale waveform inversions of surface waves for lateral heterogeneity: 2. application to surface waves in europe and the mediterranean. Journal of Geophysical Research: Solid Earth, 93 0 (B10): 0 12067--12080, 1988

1988
[27]

Nearshore seabed topography reconstruction method based on convolutional neural network

Yi Sun, Sanzhong Li, Yang Liu, Jianping Zhou, and Yanhui Suo. Nearshore seabed topography reconstruction method based on convolutional neural network. Expert Systems with Applications, page 127982, 2025

2025
[28]

Diffusion models without classifier-free guidance

Zhicong Tang, Jianmin Bao, Dong Chen, and Baining Guo. Diffusion models without classifier-free guidance. arXiv preprint arXiv:2502.12154, 2025

2025 arXiv
[29]

Inverse problem theory and methods for model parameter estimation

Albert Tarantola. Inverse problem theory and methods for model parameter estimation. SIAM, 2005

2005
[30]

The inverse water wave problem of bathymetry detection

Vishal Vasan and Bernard Deconinck. The inverse water wave problem of bathymetry detection. Journal of Fluid Mechanics, 714: 0 562--590, 2013

2013
[31]

Wavediffusion: Exploring full waveform inversion via joint diffusion in the latent space

Hanchen Wang, Yinan Feng, Yinpeng Chen, Jeeun Kang, Yixuan Wu, Young Jin Kim, and Youzuo Lin. Wavediffusion: Exploring full waveform inversion via joint diffusion in the latent space. arXiv preprint arXiv:2410.09002, 2024

2024
[32]

Latent neural operator for solving forward and inverse pde problems

Tian Wang and Chuang Wang. Latent neural operator for solving forward and inverse pde problems. Advances in Neural Information Processing Systems, 37: 0 33085--33107, 2024

2024
[33]

Adjoint-based high-order spectral method of wave simulation for coastal bathymetry reconstruction

Jie Wu, Xuanting Hao, Tianyi Li, and Lian Shen. Adjoint-based high-order spectral method of wave simulation for coastal bathymetry reconstruction. Journal of Fluid Mechanics, 972: 0 A41, 2023

2023
[34]

Band weight-optimized bigru model for large-area bathymetry inversion using satellite images

Xiaotao Xi, Gongju Guo, and Jianxiang Gu. Band weight-optimized bigru model for large-area bathymetry inversion using satellite images. Journal of Marine Science & Engineering, 13 0 (2), 2025

2025

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

The role of topography in controlling throughflow generation

MG Anderson and TP Burt. The role of topography in controlling throughflow generation. Earth Surface Processes, 3 0 (4): 0 331--344, 1978

work page 1978

[2] [2]

o rn Behrens, Sebastian G \

Judith Angel, J \"o rn Behrens, Sebastian G \"o tschel, Marten Hollm, Daniel Ruprecht, and Robert Seifried. Bathymetry reconstruction from experimental data using pde-constrained optimisation. Computers & fluids, 278: 0 106321, 2024

work page 2024

[3] [3]

Nonlinear deterministic reconstruction and prediction of remotely measured ocean surface waves

Nicolas Desmars, Moritz Hartmann, Jasper Behrendt, Norbert Hoffmann, and Marco Klein. Nonlinear deterministic reconstruction and prediction of remotely measured ocean surface waves. Journal of Fluid Mechanics, 975: 0 A8, 2023

work page 2023

[4] [4]

Diffusion models beat gans on image synthesis

Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 34: 0 8780--8794, 2021

2021

[5] [5]

Tidal data inversion: Interpolation and inference

Gary D Egbert. Tidal data inversion: Interpolation and inference. Progress in Oceanography, 40 0 (1-4): 0 53--80, 1997

work page 1997

[6] [6]

Leveraging physics-informed neural networks for efficient modelling of coastal ecosystems dynamics: A case study of sundarbans mangrove forest

Majdi Fanous, Jonathan M Eden, Juntao Yang, Simon See, Vasile Palade, and Alireza Daneshkhah. Leveraging physics-informed neural networks for efficient modelling of coastal ecosystems dynamics: A case study of sundarbans mangrove forest. Ecological Informatics, page 103302, 2025

work page 2025

[7] [7]

Deep Learning the Physics of Transport Phenomena

Amir Barati Farimani, Joseph Gomes, and Vijay S Pande. Deep learning the physics of transport phenomena. arXiv preprint arXiv:1709.02432, 2017

work page Pith review arXiv 2017

[8] [8]

A review of observations and models of dynamic topography

Nicolas Flament, Michael Gurnis, and R Dietmar M \"u ller. A review of observations and models of dynamic topography. Lithosphere, 5 0 (2): 0 189--210, 2013

work page 2013