AI-Enhanced Automatic Design of Efficient Underwater Gliders

Daniela Rus; John Romanishin; Niklas Hagemann; Peter Yichen Chen; Pingchuan Ma; Wei Wang; Wojciech Matusik

REVIEW 4 major objections 5 minor 34 references

AI-Enhanced Automatic Design of Efficient Underwater Gliders

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read An automated pipeline that co-optimizes hull shape and control with a neural fluid surrogate is claimed to yield underwater gliders whose measured lift-to-drag ratio beats conventional torpedo designs.

desk verdict Clever co-design pipeline with real hardware, but the headline efficiency claim compares a pool measurement against a different vehicle's CFD number, so the outperformance is not yet controlled. read the letter →

arxiv 2505.00222 v1 pith:OM7ZEFDB submitted 2025-04-30 cs.RO cs.AIcs.GRcs.LGphysics.comp-ph

Peter Yichen Chen , Pingchuan Ma , Niklas Hagemann , John Romanishin , Wei Wang , Daniela Rus , Wojciech Matusik This is my paper · ORCID

classification cs.ROcs.AIcs.GRcs.LGphysics.comp-ph

keywords underwatergliderlift-to-dragrationeuralfluidsurrogatedeformationcageco-optimizationofshapeandcontrolcomputationaldesignhydrodynamicoptimization

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

The paper sets out to replace manual trial-and-error hull design for underwater gliders with an automated, end-to-end computational pipeline. It argues that the reason existing gliders look alike is not manufacturing but the lack of design tools that can explore non-trivial shapes and evaluate their fluid performance cheaply. The proposed workflow represents a hull by a low-dimensional deformation cage, predicts its lift and drag with a neural network trained on computational fluid dynamics data, and co-optimizes the shape and the angle of attack to maximize the lift-to-drag ratio $\eta = c_l/c_d$. The authors report that two fabricated designs from this pipeline reach measured effective efficiencies of $\eta = 2.5$ and $\eta = 2.4$, compared with $\eta = 0.3$ for a standard torpedo-shaped glider, so the practical upshot would be a path to more energy-efficient ocean sampling vehicles.

What carries the argument

The load-bearing mechanism is the pairing of a three-dimensional deformation cage with a four-layer MLP (multilayer perceptron) fluid surrogate. The deformation cage takes offsets of cage handles as input and produces a deformed mesh of an initial ellipsoid; the paper curates 20 base shapes and interpolated morphs so that every geometry in the dataset shares the same low-dimensional parameterization. The neural surrogate maps cage parameters plus angle of attack to drag and lift coefficients, replacing a CFD solve with a fast differentiable evaluation. A covariance matrix adaptation evolution strategy (CMA-ES) then maximizes $\eta = c_l/c_d$ within the convex hull of the training shapes, and the selected optimum is exported directly to CAD for three-dimensional printing. The argument's force comes from moving the expensive fluid solve into training-data generation, leaving the design loop itself cheap enough to iterate over many shapes and angles.

What would settle it

Measure the lift-to-drag ratio of the fabricated four-wing design at its 30-degree operating angle in the same wind tunnel used for the 9-degree design; if the measured $\eta$ does not exceed the torpedo baseline's $\eta = 0.3$ by the margin the surrogate predicts, the surrogate's generalization to unseen shapes is not established.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is that a differentiable neural fluid surrogate, coupled with a compact geometry parameterization, is enough to navigate a design space of hull shapes that would be impractical to search with full computational fluid dynamics at every iteration. The authors demonstrate this by optimizing the lift-to-drag ratio $\eta$, which their appendix shows is the sole shape-dependent factor in buoyancy-engine work per distance, across angles of attack from $-30^\circ$ to $+30^\circ$. The optimizer returns a family of non-torpedo hulls, two of which were fabricated as exchangeable shells on a common internal hardware assembly. Wind-tunnel measurements on the 9-degree design agree with the surrogate to an average 4.5% error, and pool tests give effective lift-to-drag ratios of $\eta = 2.5$ for the two-wing and $\eta = 2.4$ for the four-wing glider, both said to outperform the torpedo baseline at $\eta = 0.3$.

Load-bearing premise

The load-bearing premise is that the neural fluid model trained on simulated data for 20 curated hull shapes and their interpolated variants also predicts the performance of the newly optimized shapes; if that generalization fails, the claimed efficiency advantage over conventional torpedo designs does not follow.

Editorial extensions

If this is right

A glider's travel distance per unit of buoyancy-engine work is set by $\eta$, so if the reported $\eta = 2.5$ transfers to real missions, each ballast cycle carries the glider several times farther than the $\eta = 0.3$ torpedo shape for the same energy.
Because the pipeline exports fabrication-ready CAD, the design-to-prototype loop can be closed much faster than manual trial and error, and the same internal hardware can be re-shelled for different missions.
Wind-tunnel agreement within 4.5% suggests the surrogate can stand in for CFD throughout the optimization loop, which is what makes the co-design of shape and angle of attack tractable.
The co-optimization perspective implies that a hull optimized for one operating angle may be suboptimal at another, so choosing the angle of attack is part of the design problem rather than a post-hoc controller setting.

Reading between the lines

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

Inference: the same cage-plus-surrogate recipe should transfer to other lift-driven vehicles, such as aerial gliders or underwater helicopters, whenever the objective can be written as a ratio of aerodynamic coefficients; the paper's contribution is the workflow, not a claim limited to gliders.
Inference: the reported sim-to-real gap for the two-wing design ($\eta = 7$ in simulation versus $2.5$ measured) suggests that adding a shear-stress or surface-roughness penalty to the surrogate could recover most of the lost efficiency, and that the shape optimizer may already be near the practical optimum for smooth hulls.
Inference: because the search is restricted to the convex hull of 20 curated shapes and the paper notes the cage handles thin shapes poorly, the claimed optimum is relative to a curated design space; a representation allowing thin or toroidal geometries could plausibly shift the optimum further.
Inference: a testable extension is to optimize a single hull for a distribution of angles of attack or for robustness to currents, rather than emitting a separate optimal shape per angle, which would make the designs more useful in unsteady ocean environments.

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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

Chen et al. build an automated pipeline: cage-based shape parameterization over 20 curated base shapes, a shared neural surrogate for lift-to-drag across angles of attack, then CMA-ES co-optimization of shape and control. The wind tunnel check of the 9-degree design (average 4.5% error in lift-to-drag) and the modular hardware with two fabricated shells are real evidence. The appendix derivation linking glider work-per-distance to cd/cl is clean. This is a coherent, well-engineered paper, and the integrated result is genuinely new relative to the cited literature, which mostly tunes low-dimensional hulls or optimizes shape and control separately.

The soft spots are all around the central efficiency claim. Section III-D compares η=2.5 measured in the pool for the two-wing glider against η=0.3 from Ref. [19], which is a CFD study of a different torpedo-shaped glider. That is not a matched baseline. No pool data are given for a 'traditional' shell on the same modular hardware, even though Figure 5 shows one. The pool measurements have no run counts or uncertainty. And Section IV honestly reports the sim-to-real gap: simulation said η=7, the pool said 2.5. The authors attribute it to surface details and manufacturing holes; that is plausible, but it means the surrogate's predictions for optimized shapes are accurate in the wind tunnel at model scale and much less accurate for the actual flooded, detailed vehicle. So the claim that the designed gliders 'significantly outperform' the previous standard design is not yet supported to the level the text states. It is a plausible claim; the paper simply lacks the controlled experiment needed to establish it.

Two smaller notes. The design space is the convex hull of 20 manually curated shapes, so 'optimal' is relative to that hull, and the paper does not discuss how restrictive that is despite the cage's expressiveness. No code or data are released, so reproducibility is limited, though the wind tunnel table helps.

Who is this for? Anyone working on computational robot co-design or underwater glider hull optimization. It deserves a serious referee. The main fix is not new theory; it is a matched baseline: run the same modular vehicle with the traditional shell and one of the optimized shells in the same pool protocol, report repeats and spread, and frame the comparison around that. With that addition the central claim becomes credible. I would treat the paper as a conditional accept if I were the editor.

Referee Report

4 major / 5 minor

Summary. The paper presents an end-to-end automated framework for designing underwater glider hull shapes. The method combines a deformation-cage shape parameterization, a neural-network surrogate for lift and drag coefficients trained on OpenFOAM simulation data, and CMA-ES optimization to maximize the lift-to-drag ratio η across different angles of attack. The authors validate the surrogate in a wind tunnel for one optimized shape at four angles of attack, report a dynamics simulation, fabricate two optimized hull shells (a two-wing design for 9° and a four-wing design for 30°) around a modular internal hardware assembly, and conduct swimming-pool gliding tests. The pool tests yield inferred lift-to-drag ratios of η=2.5 and η=2.4 for the two designs, which the authors compare to a literature CFD value of η=0.3 for a torpedo-shaped glider, claiming significant outperformance. The paper also includes an appendix derivation showing that glider energy efficiency per distance is inversely proportional to cd/cl, hence proportional to η.

Significance. If the framework's claims are supported, the work would be a valuable contribution to computational robot design: it demonstrates a differentiable, surrogate-based pipeline from a reduced-order shape representation to physical fabrication, and the wind-tunnel validation of the surrogate is a concrete strength. The modular hardware system with exchangeable shells is also a practical contribution. However, the headline claim of superior efficiency over a prior design is not yet rigorously established, the reported surrogate accuracy is presented in a misleading way, and the optimality claims are restricted to a curated design space that is not clearly described in the abstract. The strongest contribution is the demonstration of a fully automated design loop, not the specific efficiency comparison.

major comments (4)

[Section III-D and Section IV] The comparison of pool-measured η=2.5 (two-wing) and η=2.4 (four-wing) to the literature CFD value η=0.3 from Ref. [19] is not a controlled comparison. The baseline is a different torpedo-shaped glider evaluated with a different method (CFD) and no matched experimental protocol involving the same hardware, pool, and test conditions. The paper's own Section IV reports a simulation-to-reality gap of approximately threefold for the two-wing glider (simulated η=7 vs measured η=2.5), so the measured value is not the optimized objective value. Without a same-protocol baseline, for example the 'traditional' shell [31] shown in Fig. 5a tested in the same pool with the same internal hardware, the claim that the designs 'significantly outperform' the previous standard design is not supported.
[Section III-A and Table I] The reported 'average of 4.5% error' in the wind-tunnel validation is computed as the mean signed error (+0.34) divided by the maximum simulated η (7.53), rather than as a conventional relative or mean-absolute-percentage error. This normalization makes the error appear much smaller than it is in the low-angle-of-attack regime. At 0° AoA, the error is +0.87 against a measured wind-tunnel value of 1.10, corresponding to a relative error of roughly 79%. Thus the validation statement overstates the surrogate's accuracy, and this misreporting is load-bearing because the wind-tunnel experiment is the primary evidence that the surrogate can replace CFD in the optimization loop.
[Sections II-D, III-A, and III-D] The surrogate is validated in the wind tunnel for only one fabricated shape, the 9° optimal hull, while the framework claims to discover optimal shapes across a range of angles of attack, including the 30° four-wing design. No independent hydrodynamic validation is provided for the four-wing design or for any other optimized shape, and the simulated performance of the four-wing design is not reported. The generalization of the surrogate to the broader optimized design space is therefore not established, which weakens the claim that the framework 'discovers a wide range of optimal, non-trivial glider designs'.
[Section II-E and Abstract/Introduction] The optimization is explicitly constrained to the convex hull of the 20 manually curated base shapes ('we constrain this search to fall inside the convex hull defined by the base shapes'), so the 'optimal' designs are optimal only within that curated subspace. The abstract and introduction do not state this restriction, and the introduction even says prior designs 'have not yet approached what could be considered the globally optimal configuration', implying a global search. The assumption that this convex hull contains the relevant high-efficiency designs is neither justified nor tested. The optimality claims should be framed as relative to the chosen design space.

minor comments (5)

[Section II-A] The text states 'the work required to pump water is directly proportional to η', but the appendix derivation shows the work per distance is proportional to cd/cl, i.e., inversely proportional to η. The conclusion to maximize η is correct, but the wording is backwards.
[Section III-D] The pool-test results report horizontal and vertical speeds and inferred η values without uncertainty quantification, number of runs, or details of the test protocol (e.g., pool depth, glide distance, starting conditions). Adding this information would strengthen the quantitative claims.
[Table I] The caption and the 'Overall' row do not define how the '+4.50%' error is computed. Clarify whether the reported error is the mean signed error, mean absolute error, or a normalized quantity.
[Section II-D] The OpenFOAM setup is described only as echoing 'characteristic values found in sea waters'; the Reynolds number, mesh resolution, turbulence model, and boundary conditions are not specified, which limits reproducibility of the surrogate training data.
[Section III-B] The dynamics simulation is presented as validation of the surrogate in a dynamic setting, but no quantitative comparison between simulated and measured trajectories or glide velocities is reported. Consider rephrasing this as a qualitative demonstration or adding quantitative comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the optimization objective is grounded in external OpenFOAM CFD training data and checked against wind-tunnel and pool experiments; the few overlapping-author citations are background or prior-tool references, not load-bearing justifications.

full rationale

The paper's claimed derivation chain is not circular. The lift-to-drag objective eta = cl/cd is defined from standard aerodynamic coefficients, and its relation to buoyancy-engine work is derived from a force-balance argument in the appendix; it does not presuppose the optimized result. The neural surrogate is trained on OpenFOAM ground truth for 20 curated shapes and interpolated morphs at five angles of attack, and the optimized hulls are then evaluated with a held-out CFD validation and a wind-tunnel test (average 4.5% error), so the surrogate's output is an independent prediction rather than a fitted target. The pool tests measure actual gliding performance, and the comparison with Ref. [19]'s eta = 0.3 is an external literature benchmark. Although that comparison is not perfectly matched (pool-measured versus CFD-only, with a documented sim-to-real gap), that concerns experimental control, not circularity. The deformation-cage representation cites the authors' prior work [20], and Ref. [34] is mentioned only as future inspiration, but neither citation carries the argument by itself: the optimization and validation stand on the OpenFOAM-trained surrogate and physical experiments. The convex-hull constraint on the search space is a stated limitation rather than a circular step. Thus no step reduces by construction to its own input; any weaknesses are correctness or experimental-design concerns rather than circularity.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central result rests on a trained surrogate, a hand-curated shape basis, CFD ground truth, and a steady-state efficiency derivation; none of these are independently verified beyond the limited wind-tunnel and pool tests.

free parameters (3)

Neural surrogate weights and biases (4-layer MLP with batch norm, tanh) = Not reported
Trained on OpenFOAM data; the optimizer's predicted cl and cd come from these fitted parameters, and the paper reports no held-out test error.
Angle-of-attack training samples = -30, -15, 0, 15, 30 degrees
The surrogate is trained at five discrete angles; optimization at intermediate AoAs relies on interpolation, so the sampling scheme is a hand-chosen modeling choice.
OpenFOAM solver hyperparameters (mesh resolution, turbulence model, boundary conditions) = Not stated
The CFD labels that supervise the neural network depend on these unstated settings; they are not enumerated in Section II-D.

assumptions (6)

domain assumption Glider energy consumption is dominated by the buoyancy engine and work per distance is proportional to cd/cl.
Used in Section I and the Appendix to equate maximizing lift-to-drag ratio with maximizing efficiency; ignores other losses and assumes constant engine efficiency.
domain assumption OpenFOAM CFD results are accurate ground truth for lift and drag in the relevant sea-water regime.
Training labels for the neural surrogate come from OpenFOAM with unspecified mesh and turbulence settings (Section II-D).
domain assumption The neural surrogate generalizes from 20 curated base shapes and morphs to optimized shapes at continuous angles of attack.
The optimizer explores cage parameters inside the training convex hull (Section II-E), but only five AoAs were sampled for training.
ad hoc to paper The convex hull of 20 manually curated base shapes contains the relevant high-efficiency glider design space.
The search is intentionally restricted to this hull (Section II-E), so the 'optimal' shape is optimal only within this hand-selected family.
domain assumption Wind-tunnel measurements at matched Reynolds number transfer to the underwater gliding regime.
Section III-A validates one 3D-printed shape in air; the paper assumes this confirms the surrogate in water.
standard math The glider is in steady equilibrium during gliding, so lift and drag are perpendicular and the force-balance vector diagram in the Appendix applies.
The efficiency derivation in the Appendix assumes steady gliding with no transient or added-mass effects.

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Cite this review

Pith. "Pith review of AI-Enhanced Automatic Design of Efficient Underwater Gliders." pith.science (2026). https://pith.science/paper/OM7ZEFDB

@misc{pith2026250500222,
  author       = {Pith},
  title        = {Pith review of: AI-Enhanced Automatic Design of Efficient Underwater Gliders},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OM7ZEFDB}},
  note         = {Machine review of arXiv:2505.00222}
}

read the original abstract

The development of novel autonomous underwater gliders has been hindered by limited shape diversity, primarily due to the reliance on traditional design tools that depend heavily on manual trial and error. Building an automated design framework is challenging due to the complexities of representing glider shapes and the high computational costs associated with modeling complex solid-fluid interactions. In this work, we introduce an AI-enhanced automated computational framework designed to overcome these limitations by enabling the creation of underwater robots with non-trivial hull shapes. Our approach involves an algorithm that co-optimizes both shape and control signals, utilizing a reduced-order geometry representation and a differentiable neural-network-based fluid surrogate model. This end-to-end design workflow facilitates rapid iteration and evaluation of hydrodynamic performance, leading to the discovery of optimal and complex hull shapes across various control settings. We validate our method through wind tunnel experiments and swimming pool gliding tests, demonstrating that our computationally designed gliders surpass manually designed counterparts in terms of energy efficiency. By addressing challenges in efficient shape representation and neural fluid surrogate models, our work paves the way for the development of highly efficient underwater gliders, with implications for long-range ocean exploration and environmental monitoring.

Figures

Figures reproduced from arXiv: 2505.00222 by the authors.

**Figure 1.** Efficient underwater gliders. (a) and (b) Efficient underwater glider designs differ based on the angle of attack, and our algorithm discovers a span of them. We illustrate 4 representative optimal designs for different angles of attack (AoA) and their corresponding efficiency versus AoA curve. (c) Two glider designs were chosen for fabrication and tested as modular outer shells for an internal hardware assembly. (d… view at source ↗

**Figure 2.** Computational design framework. Our co-design framework computes both optimal shape and control for the underwater glider. Shape and control serve as input to our efficient neural fluid model, which efficiently computes the hydrodynamic parameters of the glider. Leveraging these parameters, our framework accurately simulates the performances of these gliders. We then leverage an optimization framework that computati… view at source ↗

**Figure 3.** We include several representative marine animals [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 3.** Figure 3: Efficient computational fluid dynamics. A key component of our design framework is a neural network-based fluid surrogate model. (Top) Dataset: We begin with a set of base shapes, which are represented using a cage representation. This approach allows for efficient int…

**Figure 4.** Figure 4: Dynamics Simulation. Our dynamics modeling tools accurately simulate the glider’s transition from static modes to downward gliding modes. III. RESULTS We demonstrate the effectiveness of our computational design framework by automatically designing and fabricating unde…

**Figure 5.** Figure 5: Hardware overview. (a) The internal hardware tube-assembly in a ’traditional’ setup with basic wings attached, (b) our optimized two-wing design and (c) our optimized four-wing designs during pool testing. (d) An overview of the internal hardware assembly, including bu…

**Figure 6.** Figure 6: Force balancing of a buoyancy-engine-driven glider. Here, fd is the drag force, fl is the lift force, and cd and cl are the drag and lift coefficients, respectively. fb represents the total body force, which is the difference between the buoyancy force and the gravitat…

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Computational discovery of microstructured compos- ites with optimal stiffness-toughness trade-offs,

B. Li, B. Deng, W. Shou, T.-H. Oh, Y . Hu, Y . Luo, L. Shi, and W. Matusik, “Computational discovery of microstructured compos- ites with optimal stiffness-toughness trade-offs,” Science Advances , vol. 10, no. 5, p. eadk4284, 2024

2024

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [19]

Computational fluid dynamics study of the hydrodynamic characteristics of a torpedo-shaped underwater glider,

T.-L. Le and D.-T. Hong, “Computational fluid dynamics study of the hydrodynamic characteristics of a torpedo-shaped underwater glider,” Fluids, vol. 6, no. 7, p. 252, 2021

work page 2021

[2] [31]

Williams

A. Williams. (2017) OSUG: Open-source underwa- ter glider. [Online]. Available: https://hackaday.io/project/ 20458-osug-open-source-underwater-glider

work page 2017

[3] [1]

Underwater glider system study,

S. A. Jenkins, D. E. Humphreys, J. Sherman, J. Osse, C. Jones, N. Leonard, J. Graver, R. Bachmayer, T. Clem, P. Carroll et al. , “Underwater glider system study,” 2003

work page 2003

[4] [2]

Underwater glider motion control,

N. Mahmoudian and C. Woolsey, “Underwater glider motion control,” in 2008 47th IEEE Conference on Decision and Control. IEEE, 2008, pp. 552–557

work page 2008

[5] [3]

Analysis of an autonomous underwater glider,

A. Bender, D. M. Steinberg, A. L. Friedman, and S. B. Williams, “Analysis of an autonomous underwater glider,” in Proceedings of the Australasian conference on robotics and automation , 2008, pp. 1–10

work page 2008

[6] [4]

Glider technology for ocean observations: A review,

D. Meyer, “Glider technology for ocean observations: A review,” Ocean Science Discussions , vol. 2016, pp. 1–26, 2016

work page 2016

[7] [5]

A year at the forefront of gliding locomotion,

P. C. Khandelwal, M. A. Zakaria, and J. J. Socha, “A year at the forefront of gliding locomotion,” Biology Open , vol. 12, no. 8, p. bio059973, 2023

work page 2023

[8] [6]

Efficient automatic design of robots,

D. Matthews, A. Spielberg, D. Rus, S. Kriegman, and J. Bongard, “Efficient automatic design of robots,” Proceedings of the National Academy of Sciences , vol. 120, no. 41, p. e2305180120, 2023

2023