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REVIEW 4 major objections 5 minor 38 references

DeepVIVONet: Using deep neural operators to optimize sensor locations with application to vortex-induced vibrations

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read DeepVIVONet reconstructs and forecasts the full cross-flow and in-line strain fields of a VIV-excited marine riser from only three observer sensors, and learns the sensor locations that minimize prediction error.

desk verdict A reasonable DeepONet application to VIV reconstruction and sensor placement, but the headline claim about beating POD rests on a single 0.3% MSE gap with no error bars. read the letter →

arxiv 2501.04105 v1 pith:V6WACEMO submitted 2025-01-07 cs.LG math.OCphysics.flu-dyn

Ruyin Wan , Ehsan Kharazmi , Michael S Triantafyllou , George Em Karniadakis This is my paper · ORCID
classification cs.LGmath.OCphysics.flu-dyn
keywords deepoperatornetworkvortex-inducedvibrationssensorplacementoptimizationtransferlearningmarinerisersparsemeasurementsproperorthogonaldecompositionstrainreconstruction
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 claims that the full vibration field of an offshore marine riser can be recovered from just three streamed strain measurements, using a neural operator it calls DeepVIVONet. The trained model both reconstructs the strain along the whole riser in the training window and forecasts it in a future window from the same three observer signals. The paper further claims that making the observer locations into learnable parameters and optimizing them alongside the network gives a sensor layout (sensors at 4, 67, and 92) whose prediction-window error is the lowest among the tested choices, including three manually selected POD-based placements. If right, this would mean offshore riser monitoring needs far fewer strain gauges than current practice, and sensor placement can be designed by the same model that does the monitoring.

What carries the argument

The load-bearing object is the DeepONet decomposition $G_\theta(u)(z^*) = \sum_{k=1}^P B_k(u) T_k(z^*) + B_0$, where the branch net $B_k$ consumes the $m$ observer strain values at a time step (or a look-back stack for forecasting) and the trunk net $T_k$ consumes the query location $(t_j, z^*)$. For sensor placement, observer locations are turned into learnable Gaussian distributions $(\mu_i, \sigma_i)$; at each training step $r$ realizations are sampled from each distribution, and the location parameters are optimized alternately with the network weights so the $\sigma_i$ shrink toward the informative positions. The POD baseline supplies three manually selected three-sensor combinations from the first three spatial modes, which the paper both matches and compares against.

What would settle it

Train DeepVIVONet on the test2430 shear case with m=2 observers instead of m=3, keep the same optimization procedure, and measure prediction-window MSE; if the error rises by more than an order of magnitude relative to the reported 1.290e-06, the 'three sensors suffice' claim is specific to that sensor count rather than a general low-dimensional property. A second check is to train on test2430 and test on test2500 (1.50 m/s vs 2.20 m/s) without transfer learning; the transfer claim predicts graceful degradation, while a collapse would bound the generalization to near-neighbor velocities.

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Extended reading notes

Core claim

On the paper's terms, the central discovery is that a DeepONet-style operator can learn a map from the m=3 observer strain histories to the entire strain field ε(z,t), and that this map is accurate enough that the prediction window (data never used in training) is matched to the level shown in the time-domain and FFT comparisons. The supporting quantitative comparison is Table 2, where the learned observer locations (4, 67, 92) give prediction-window MSE 1.290e-06, versus 3.745e-05 for the initial guesses and 9.838e-06, 1.294e-06, and 5.410e-06 for three POD-based choices. The learned locations are not uniformly better than every POD choice, but the paper argues POD selection is sensitive to manual choices while the learned locations are produced automatically. The paper also claims transfer learning: a network trained on shear-flow case test2430 (U=1.50 m/s) predicts the neighboring case test2420 (U=1.40 m/s) without retraining.

Load-bearing premise

The load-bearing premise is that three point strain measurements determine the entire riser strain field at that instant, meaning the VIV response is low-dimensional enough for a learned map from three observer values to all spatial locations to generalize across time windows and nearby flow speeds.

Editorial extensions

If this is right

  • A three-sensor strain array on a riser can replace denser instrumentation for reconstruction and short-horizon forecasting of both cross-flow and in-line strain.
  • Sensor placement can be included in neural-operator training, making the placement problem differentiable rather than a separate heuristic.
  • A model trained at one maximum flow speed transfers to a neighboring speed without full retraining, reducing calibration cost when operating conditions drift.
  • The trained network acts as a fast surrogate, so monitoring can run in near-real time instead of relying on CFD or dense instrumentation.
  • POD-based placement remains a useful initialization but its manual mode-selection step causes large variation in error; the learned locations automate that selection.

Reading between the lines

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

  • Editorial inference: the same differentiable-location optimization could be applied to other sparse-sensing problems, such as temperature or pressure field reconstruction in structures, provided the underlying field is comparably low-dimensional.
  • Editorial inference: because the POD analysis in Section 4.2 shows 96.91% of variance in three modes for one shear case, the method's success likely tracks that low-dimensionality; a natural test is to run the same pipeline on a multi-frequency VIV case with richer modal content and check whether three observers still suffice.
  • Editorial inference: the paper's comparison does not include robustness of the learned locations to sensor failure; a testable extension is to retrain with one observer randomly dropped at test time and measure error degradation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript proposes DeepVIVONet, a DeepONet-based surrogate that maps time histories from m=3 observer strain sensors on a marine riser to the full CF/IL strain field, and uses the trained network in an outer-loop optimization to learn sensor locations. Experiments use NDP VIV field data for three shear-flow cases (U=0.50, 1.50, and 2.20 m/s) for reconstruction and forecasting, one transfer-learning case (U=1.5 to U=1.4 m/s), and a sensor-placement comparison against three manually selected POD-based location sets. The paper claims that DeepVIVONet provides accurate reconstruction and forecasting and that its learned sensor locations are more precise and cost-effective than POD-based placements.

Significance. If the claims held, the paper would offer a practical sparse-sensing framework for riser monitoring and a data-driven alternative to POD-based sensor placement. The use of real experimental NDP data, the direct comparison to POD, and the clear description of the DeepONet input/output structure are strengths. However, the central quantitative evidence is thin: the reconstruction/forecasting and transfer-learning claims are supported mainly by qualitative plots, and the sensor-placement superiority claim rests on a 0.3% MSE difference with no statistical characterization. The contribution is primarily empirical, and the conclusions need stronger quantitative support before they can be relied upon.

major comments (4)
  1. [Section 4.4, Table 2] The claim that DeepVIVONet's learned observer locations are "more precise and cost-effective" than POD-based placement rests on a single MSE pair: learned locations (4,67,92) give 1.290e-06, while the best POD placement (29,43,81) gives 1.294e-06, a difference of about 0.3%. No seeds, error bars, or statistical comparison are reported, and the POD placements are chosen manually from Figure 12 rather than by an automated criterion. The observed gap is smaller than the run-to-run variation expected after 500,000 stochastic training iterations, so the practical superiority claim is not established by the evidence presented.
  2. [Section 3.1, Figures 5-8] The reconstruction and forecasting results for the CF cases and the IL case are reported only as qualitative time-series and FFT plots; no quantitative error metric (MSE, relative L2, or similar) is given for the test window, and no confidence intervals are provided. This makes it impossible to assess the abstract's claims of "accurately reconstructing" and "accurate predictions" across the tested velocity regimes. The only quantitative numbers in the paper appear in Table 2 for the sensor-placement study.
  3. [Section 3.2] The transfer-learning demonstration uses a single near-neighbor case (U=1.5 m/s to U=1.4 m/s) and reports no quantitative metric or comparison with a model trained directly on the target case, so the abstract's claim of generalization to other flow conditions via transfer learning is not supported. At minimum, the authors should report the prediction-window error for the transferred model and compare it with a model trained directly on the target case.
  4. [Section 4.1] The sensor-placement optimization is performed on a "reconstructed dataset" discretized at 500 equidistant points, but the construction of this dense field is never described. If it relies on interpolation or on the same surrogate family as DeepVIVONet, the MSE values in Table 2 may not reflect performance on the original 23-sensor field data. The construction should be specified, and the final evaluation should be reported on the original sensor locations as well.
minor comments (5)
  1. [Section 4.2] The definition of the matrix E is inconsistent: the text says "with 100 spatial elements, and 100 time samples," but the displayed matrix has 250 rows and the preceding sentence mentions 250 time samples. Please clarify the number of time samples used in the POD analysis.
  2. [Section 4.4] The sentence "The observer locations optimized by DeepVIVONet consistently delivered superior results" is misleading given that POD placement (29,43,81) achieves an MSE of 1.294e-06, nearly identical to the learned placement's 1.290e-06; a more precise wording would acknowledge that the two are statistically indistinguishable on the reported evidence.
  3. [Section 4.1] The text says "we use our DeepVIVONet model as a surrogate" and describes sampling r realizations from the location distributions, but the number r and the method for obtaining strain values at non-instrumented sampled locations are not specified. Please state r and explain how the strain at those sampled points is obtained from the discrete sensor data.
  4. [Section 3.1] The choice m=3 is not justified beyond the POD variance argument; no experiments with other sensor counts are shown, so it is unclear how sensitive the method is to the number of observers. A brief sensitivity study or at least a discussion of the choice would strengthen the paper.
  5. [Throughout] There are several typographical and grammatical errors, e.g., "explaind" in Section 4, "the the motion" in the Introduction, and "We find that that" in the Abstract. A careful proofreading pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: held-out prediction windows and an independently computed POD baseline make the main reconstruction, forecasting, and sensor-placement comparisons genuine generalization tests.

full rationale

The derivation chain is not circular. The reconstruction and forecasting results (Section 3) are evaluated on temporally held-out prediction windows defined in Table 1 and shown in Figures 5-8, so the trained network is not being tested on its own training labels. The transfer-learning experiment (Section 3.2) predicts a different flow case (test2420) from a network trained on test2430, which is an external generalization check. The sensor-location optimization (Sections 4.1-4.3) fits the observer locations and network parameters on the training setup, and then Table 2 reports MSE in the prediction window; although the optimization objective and the evaluation metric are both MSE, the evaluation window is temporally distinct, so the comparison is a genuine generalization test rather than a fitted parameter renamed as a prediction. The POD baseline is implemented independently in Section 4.2, with modes computed from the data and the first three modes accounting for 96.91% of the variance; the cited reference [38] is used only as methodological motivation, not as a load-bearing uniqueness claim. Self-citations to DeepONet [31] reference a published architecture whose representation guarantee rests on an external theorem [33]; they are not used to forbid alternatives. The main caveats—unspecified origin of the 'reconstructed dataset' at 500 points in Section 4.1, lack of error bars around Table 2, and the small gap to the best POD placement—are correctness or statistical concerns, not circularity. No step in the claimed derivation is equivalent to its inputs by construction.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard operator approximation theory, a low-dimensionality assumption for the strain field, and a near-neighbor transfer assumption. The fitted parameters are mainly the sensor location distributions and architecture choices; no code or data are provided to audit them.

free parameters (5)
  • Observer sensor location means μ_i (m=3) = 4, 67, 92 (discretized spatial indices in test2430)
    Optimized by the proposed outer-loop to minimize training reconstruction loss; these values are the paper's main output (Table 2).
  • Observer location standard deviations σ_i = Not reported numerically; described as converging to minimal values
    Part of the learned location distribution; exact converged values are not given, so the optimization result is only partly specified.
  • DeepONet architecture (layers/neurons) = 6 hidden layers, 50 neurons for branch and trunk nets
    Chosen without ablation or justification; network capacity directly affects the surrogate quality and hence the sensor placement comparison.
  • Data normalization factor = 0.2 * max(ε(z,t))
    Ad hoc scaling applied to all strain data; effect on results is not analyzed.
  • Forecasting look-back window lb = Not reported
    Defines the branch input for forecasting in Section 2.4; without its value the forecasting experiment cannot be reproduced.
assumptions (5)
  • standard math Neural networks and DeepONet can approximate the operator mapping observer signals to full-field strain.
    Invoked via universal approximation theorems [32,33] and DeepONet [31]; standard background for the method, not proved here.
  • domain assumption VIV strain dynamics follow the linear beam-string equation (2.2).
    Used to motivate the riser model in Section 2.3, though the DeepVIVONet training loss is purely data-driven and does not enforce Eq. (2.2).
  • domain assumption Three instantaneous point measurements determine the full spatiotemporal strain field (low-rank or spatial-coherence assumption).
    Load-bearing for using m=3 observers; supported only indirectly by POD analysis (first 3 modes about 96.91% variance for test2430) and not checked for other cases or sensor counts.
  • domain assumption Frozen network parameters trained at U=1.5 m/s transfer to U=1.4 m/s without adaptation.
    Transfer learning experiment in Section 3.2 assumes the nearby velocity case lies in the same learned regime; no retraining or fine-tuning is performed and no quantitative error is reported.
  • domain assumption Pinned boundary conditions; two imaginary zero sensors at riser ends.
    Added in Section 3 to enforce boundary behavior; relies on the NDP test setup description [34].

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Cite this review

Pith. "Pith review of DeepVIVONet: Using deep neural operators to optimize sensor locations with application to vortex-induced vibrations." pith.science (2026). https://pith.science/paper/V6WACEMO

@misc{pith2026250104105,
  author       = {Pith},
  title        = {Pith review of: DeepVIVONet: Using deep neural operators to optimize sensor locations with application to vortex-induced vibrations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V6WACEMO}},
  note         = {Machine review of arXiv:2501.04105}
}
read the original abstract

We introduce DeepVIVONet, a new framework for optimal dynamic reconstruction and forecasting of the vortex-induced vibrations (VIV) of a marine riser, using field data. We demonstrate the effectiveness of DeepVIVONet in accurately reconstructing the motion of an off--shore marine riser by using sparse spatio-temporal measurements. We also show the generalization of our model in extrapolating to other flow conditions via transfer learning, underscoring its potential to streamline operational efficiency and enhance predictive accuracy. The trained DeepVIVONet serves as a fast and accurate surrogate model for the marine riser, which we use in an outer--loop optimization algorithm to obtain the optimal locations for placing the sensors. Furthermore, we employ an existing sensor placement method based on proper orthogonal decomposition (POD) to compare with our data-driven approach. We find that that while POD offers a good approach for initial sensor placement, DeepVIVONet's adaptive capabilities yield more precise and cost-effective configurations.

Figures

Figures reproduced from arXiv: 2501.04105 by the authors.

Figure 1
Figure 1. DeepONet architecture. This unique architecture is comprised of two primary networks, namely, Trunk Network (TN) and Branch [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. DeepVIVONet in VIV problem: DeepVIVONet is based on DeepONet for the VIV problem. This framework reconstructs the dynamics [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Detailed structure of input and output data for the DeepVIVONet framework. Left: the background shows the actual space–time data. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: NDP data set: CF strain for shear flow case “test2430”. The vertical axis z is the distance from the bottom of the riser in meter. The [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: DeepVIVONet: Prediction of CF strain for shear flow case “test2430”. Left panel: the location of all sensors (dashed line), observers [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: DeepVIVONet: Prediction of CF strain for shear flow case “test2330”. Left panel: the location of all sensors (dashed line), observers [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: DeepVIVONet: Prediction of CF strain for shear flow case “test2500”. Left panel: the location of all sensors (dashed line), observers [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: DeepVIVONet: Prediction of IL strain for shear flow case “test2430”. Left panel: the location of all sensors (dashed line), observers [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: DeepVIVONet: Prediction of CF strain for shear flow case “test2420” using the trained network on case “test2430”. Left panel: the [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: Observer location optimization. Here, r realizations are sampled from each observer location distribution, with strains at these points [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: Eigenvalues of the first 5 dominant eigenmodes and their percentage contribution to the total energy. (a) Eigenvalues of the first 5 [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: First 3 dominant POD modes with observer locations indicated. The locations are random initial guesses from DeepVIVONet, learned [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 13
Figure 13. Figure 13: DeepVIVONet observer location variation during iterations. Every 100 iterations are saved here as 1 iteration. [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]
Figure 14
Figure 14. Figure 14: DeepVIVONet predictions at a certain reconstructed location using observer locations at initial guesses and at learned observer locations. [PITH_FULL_IMAGE:figures/full_fig_p012_14.png]
Figure 15
Figure 15. Figure 15: Reconstructed RMS for prediction window using data from 3 observers. Left: Prediction using randomly selected initial guesses of 3 [PITH_FULL_IMAGE:figures/full_fig_p013_15.png]

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Reference graph

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