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arxiv: 2606.23502 · v1 · pith:FFGNKKFJnew · submitted 2026-06-22 · 💻 cs.RO · cs.AI

DVL-DeepONet: A Physics-Guided Operator Learning for Resilient Underwater Navigation

Arup Kumar Sahoo , Itzik Klein This is my paper

Pith reviewed 2026-06-26 08:30 UTC · model grok-4.3

classification 💻 cs.RO cs.AI
keywords AUV navigationDVLDeepONetphysics-guided learningvelocity estimationunderwater roboticsoperator learningsensor fusion
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The pith

A physics-guided neural operator estimates AUV velocity from incomplete or noisy DVL beam data by enforcing measurement consistency.

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

The paper tries to establish that a deep neural operator framework can map sequences of inertial and DVL sensor readings to vehicle velocity while a consistency constraint keeps the output aligned with the physical relationship between individual beam velocities and the overall velocity vector. This would matter because real missions frequently lose or corrupt DVL beams due to obstacles, reflections, or disturbances, and some low-cost platforms lack inertial sensors, both of which degrade standard navigation. The framework includes variants for noise-resilient coupled sensing, DVL-only operation, and beam recovery. On roughly 10 km of real AUV field data the models outperform model-based and other learning baselines. A reader would care if the approach truly delivers reliable velocity estimates under the degraded conditions typical of underwater work.

Core claim

By learning a nonlinear operator that maps temporal inertial and DVL observations directly to vehicle velocity while enforcing a DVL measurement physics consistency constraint, the DVL-DeepONet framework enables robust velocity estimation under multiple degraded sensing scenarios including noise, missing beams, and DVL-only operation, as shown by its validation on approximately 10,000 meters of real-world AUV experiments where it outperforms baselines.

What carries the argument

DVL-DeepONet, a physics-guided deep neural operator that maps temporal inertial/DVL observations to vehicle velocity while enforcing a DVL measurement physics consistency constraint.

If this is right

  • Velocity estimates remain usable when DVL beams are lost to marine obstacles or seabed reflections.
  • Navigation functions on low-cost platforms that carry only DVL sensors without inertial units.
  • Missing individual beam measurements can be recovered while the recovered values still satisfy the physical beam-to-velocity relationship.
  • Overall navigation error drops relative to both model-based fusion and other learning methods across the tested real-world paths.

Where Pith is reading between the lines

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

  • The same operator-plus-constraint pattern could be tried on other partial-measurement velocity problems in mobile robotics.
  • Adding vehicle dynamics constraints alongside the DVL constraint might further reduce sensitivity to the exact training paths.
  • Cross-testing on AUVs with different beam geometries or sensor noise characteristics would reveal how much the learned operator depends on the original hardware.

Load-bearing premise

Enforcing the DVL physics consistency constraint during training on the 10 km dataset will produce models that generalize to unseen marine conditions rather than memorizing dataset-specific patterns.

What would settle it

Apply the trained models to a fresh AUV dataset collected in a different location or under substantially different environmental disturbances and check whether velocity estimation error stays 40 percent lower than the same baselines.

Figures

Figures reproduced from arXiv: 2606.23502 by Arup Kumar Sahoo, Itzik Klein.

Figure 1
Figure 1. Figure 1: Geometry of the four-beam Janus DVL mounted on the AUV and the associated body-fixed coordinate system. 𝐲 𝑝 𝑘 = 𝐌𝑘 ( 𝐇𝐯𝑑 𝑏,𝑘 + 𝐧𝑘 ) . (8) The number of available beams is 𝑁𝑏,𝑘 = ∑ 4 𝑖=1 𝑚𝑖,𝑘. (9) When 𝑁𝑏,𝑘 ≥ 3 a reduced LS solution may still be computed. However, when 𝑁𝑏,𝑘 < 3, the velocity estimation problem becomes underdetermined, as rank(𝐇 𝑝 𝑘 ) < 3. (10) Here 𝐇 𝑝 𝑘 ∈ ℝ 𝑁𝑏,𝑘×3 denotes the reduced beam … view at source ↗
Figure 2
Figure 2. Figure 2: Schematic illustration of the proposed DVL-DeepONet architecture. 3.3. DVL-Only Learning DVL-DeepONet-II addresses scenarios where IMU measurements are unavailable or unreliable. In this case, the branch input contains only DVL beam observations. For a temporal window of length 𝑊 , the branch input is constructed as 𝐁𝑘 = [ 𝐲𝑘−𝑊 +1, 𝐲𝑘−𝑊 +2, …, 𝐲𝑘 ] ∈ ℝ 𝑊 ×4 . (36) The learned operator becomes  (𝐼𝐼) 𝜃 ∶ (𝐁… view at source ↗
Figure 3
Figure 3. Figure 3: Top-view of the 13 AUV trajectories used in this study. trajectories provide a comprehensive evaluation of the proposed DVL-DeepONet framework under varying operating conditions. For cross-validation purposes, we partition the dataset into three distinct splits. In the first, the training set comprises T1, T6–T13, and the validation set comprises T2 and T3. The remain￾ing two trajectories, T4 and T5, are r… view at source ↗
Figure 4
Figure 4. Figure 4: Velocity reconstruction error profiles of Trajectories 4 and 5 using DVL-DeepONet-I. mean velocity error remains relatively consistent throughout the mission, oscillating around 0.08– 0.12 m/s. Trajectory 5 exhibits slightly larger error fluctuations, as the mean error increases to approximately 0.15–0.17 m/s. However, none of the trajectories exhibits a sustained growth in error over mission progress. Thi… view at source ↗
Figure 5
Figure 5. Figure 5: Ablation study of the influence of temporal window size 𝑊 on the VRMSE of DVL-DeepONet in the noise-resilient estimation scenario. each fold, nine trajectories are used for training, two trajectories for validation, and two for testing, corresponding to an approximate 70%-15%-15% train-validation-test split [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: GT trajectories used as unseen test missions in the three-fold cross-validation study. 5. Conclusion Existing DVL-based velocity estimation meth￾ods either rely on model-based LS estimators or employ purely data-driven models. Moreover, the model-based algorithms become unreliable under beam outages and rank-deficient measure￾ment configurations, and data-driven models are black-box in nature and do not ex… view at source ↗
read the original abstract

Autonomous Underwater Vehicles (AUVs) rely heavily on the fusion of inertial sensors and Doppler velocity logs (DVLs) for navigation. In standard autonomous navigation systems, the DVL measures four beam velocities, thereby enabling the estimation of the AUV velocity vector. However, during real-world missions, the DVL may receive noisy or incomplete beam measurements due to marine obstacles, seabed reflections, or environmental disturbances. Furthermore, some low-cost underwater platforms operate without inertial sensors to reduce system complexity and cost. In such cases, reliable estimation of the AUV velocity vector in real-world missing beam scenarios becomes challenging, leading to degraded navigation solutions. To circumvent these challenges and enable resilient underwater navigation, we propose DVL-DeepONet, a physics-guided deep neural operator framework along with three variants. The proposed models are designed to estimate DVL-based velocity information under multiple operational scenarios, including (i) noise-resilient estimation in coupled inertial/DVL measurements, (ii) DVL-only learning, and (iii) beam measurement recovery. By learning a nonlinear operator that maps temporal inertial/DVL observations directly to vehicle velocity while enforcing DVL measurement physics through a consistency constraint, the proposed approach enables robust velocity estimation even under degraded sensing conditions. The proposed framework is validated using real-world AUV experiments, comprising a cumulative path length of approximately 10,000 m. Experimental results demonstrate that the proposed DVL-DeepONet architectures outperform baseline model-based approaches and learning-based algorithms by 40%.

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

2 major / 1 minor

Summary. The manuscript proposes DVL-DeepONet, a physics-guided deep neural operator framework (with three variants) for estimating AUV velocity from inertial/DVL data under noisy, incomplete, or DVL-only conditions. It enforces DVL measurement physics via a consistency constraint during training and reports validation on real-world AUV experiments totaling ~10 km path length, claiming 40% outperformance over model-based and learning-based baselines.

Significance. If the physics consistency constraint demonstrably improves generalization beyond the training distribution, the approach could advance resilient navigation for low-cost AUVs. The real-world 10 km dataset provides a concrete testbed, which is a strength. However, the absence of equations, error bars, dataset splits, ablations, or held-out mission results in the provided text prevents assessment of whether gains arise from the operator learning or from dataset-specific fitting.

major comments (2)
  1. [Abstract] Abstract: the central claim of '40% outperformance' over baselines is load-bearing for the resilient-navigation contribution, yet no quantitative metrics (e.g., RMSE, drift rates), error bars, train/test splits, or ablation results are supplied; without these the claim cannot be evaluated.
  2. [Abstract] Abstract (and implied methods): the physics consistency constraint is invoked to enable generalization to unseen marine conditions, but no equations, loss formulation, or evidence of held-out missions/different seabeds/OOD disturbances are shown; the 10 km cumulative path on a single distribution does not test the generalization required for the resilience claim.
minor comments (1)
  1. [Abstract] The abstract mentions 'three variants' but does not name or differentiate them; a brief enumeration would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address each major comment below and indicate where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim of '40% outperformance' over baselines is load-bearing for the resilient-navigation contribution, yet no quantitative metrics (e.g., RMSE, drift rates), error bars, train/test splits, or ablation results are supplied; without these the claim cannot be evaluated.

    Authors: The 40% outperformance figure is computed from the velocity estimation errors (primarily RMSE) across the full set of real AUV experiments described in the results section. We agree that the abstract would be clearer if it included supporting quantitative details. We will revise the abstract to report the key RMSE values for the proposed variants versus baselines, note the use of cross-validation splits on the 10 km paths, and indicate that error statistics are aggregated over multiple runs. revision: yes

  2. Referee: [Abstract] Abstract (and implied methods): the physics consistency constraint is invoked to enable generalization to unseen marine conditions, but no equations, loss formulation, or evidence of held-out missions/different seabeds/OOD disturbances are shown; the 10 km cumulative path on a single distribution does not test the generalization required for the resilience claim.

    Authors: The equations and loss formulation for the physics consistency constraint appear in the methods section. The 10 km dataset comprises multiple real missions that include noisy beams, partial beam loss, and varying seabed interactions. We will revise the abstract to reference the constraint explicitly and will add a short paragraph in the experiments section clarifying the train/test partitioning and an ablation isolating the contribution of the physics term. The current data do not include entirely separate missions from different seabeds; any such additional OOD evaluation would require new field trials. revision: partial

Circularity Check

0 steps flagged

No circularity in derivation chain; physics constraint and empirical validation remain independent

full rationale

The provided abstract and description contain no equations, self-citations, or load-bearing steps that reduce predictions or operators to fitted inputs by construction. The framework is described as learning a nonlinear operator with an added consistency constraint and is validated on real-world 10 km AUV data, with outperformance presented as an empirical result rather than a definitional renaming or self-referential fit. No uniqueness theorems, ansatzes smuggled via prior work, or fitted parameters renamed as predictions appear. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities can be extracted. The physics consistency constraint is referenced but not formalized.

pith-pipeline@v0.9.1-grok · 5806 in / 970 out tokens · 20430 ms · 2026-06-26T08:30:13.404904+00:00 · methodology

discussion (0)

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Reference graph

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