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REVIEW 3 major objections 5 minor 2 cited by

Optimization and Generation in Aerodynamics Inverse Design

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Aerodynamic inverse design reduces to a single tilted distribution that couples shape-preserving optimization with guided generation.

desk verdict The optimization side is solid and the SKL loss is a real contribution, but SA-MC as written omits the sigma_t^2/alpha_t scale from its own Eq. 20, so the headline generation numbers come from an unstated variant. read the letter →

arxiv 2602.03582 v3 pith:EN3G6ON2 submitted 2026-02-03 cs.LG

Huaguan Chen , Ning Lin , Luxi Chen , Jiacheng Cen , Rui Zhang , Wenbing Huang , Chongxuan Li , Hao Sun This is my paper
classification cs.LG
keywords aerodynamicinversedesignflowmatchingguidedgenerationdragreductionshapepreservationcovarianceestimationsecantupdatedivergence-basedtraining
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 tries to establish that aerodynamic inverse design—cutting drag while keeping a car or aircraft visually recognizable—can be captured by one probability distribution: the learned shape distribution reweighted by aerodynamic cost. Optimization then becomes finding the most probable point of that distribution, and generation becomes sampling from it. To make this work, the authors introduce a divergence-based loss for training cost predictors, a density-gradient optimizer that keeps shapes plausible, and a low-cost covariance estimator for guided generation. Their central empirical claim, checked with high-fidelity CFD and wind-tunnel tests, is that this approach reduces vehicle drag by 5.8% relative to the initial design, cuts the best aircraft drag-to-lift objective by 28.8%, and, for view-based generation, improves vehicle drag by 3.0% and the aircraft objective by 68.6% relative to direct generation—while preserving visual features. If true, the framework provides a practical, low-cost route to early-stage design exploration without repeated expensive simulations.

What carries the argument

The central object is the tilted design distribution q_λ(x) ∝ p(x) exp(−λJ(x)), which unifies optimization and generation. The computational workhorse is the secant-pair recursion of Theorem 2.3: B_{k+1} = u_k(V_k^T B_k V_k + ρ_k y_k y_k^T) + w_k I, which approximates the Jacobian ∇_x v_t of the flow-matching velocity field using trajectory differences (s_k, r_k). This low-rank compact representation B = γI + UΓU^T permits a semi-numerical matrix square root, giving an affordable estimate of the conditional covariance for guidance. The symmetric-KL minibatch loss for the λ-conditioned cost predictor is the other key piece; it replaces plain mean-squared-error training to emphasize the region

What would settle it

Run SA-MC on a low-dimensional problem where the exact Jacobian ∇_x v_t and the true conditional covariance can be computed analytically, and compare the guided samples with those produced by the exact covariance. A second check is to compare SA-MC with and without the σ_t^2/α_t scale factor explicitly applied, since the paper's Eq. 20 defines the covariance that way but the pseudocode leaves the computed scale unused.

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Extended reading notes

Core claim

The paper's central claim is that inverse design has two canonical solutions—a point solution and a distributional solution—and that both arise from the same tilted target q_λ(x) ∝ p(x) exp(−λJ(x)), where p is the learned distribution of plausible shapes and J is the aerodynamic cost. With p as the prior, the MAP estimate of this tilted distribution is the optimal design (optimization), and sampling from it is guided generation. The paper then shows that existing training-free guidance estimators differ precisely in how they approximate the conditional covariance, and that a correct Gaussian approximation requires the Jacobian of the velocity field. It introduces SA-MC, which estimates this

Load-bearing premise

The load-bearing premise is that the secant-pair recursion over ODE trajectory differences yields a good positive-definite approximation of the velocity-field Jacobian (and hence of the conditional covariance), and that the algorithm uses the correct covariance scale; if this approximation or the σ_t^2/α_t scaling is off, the guidance targets a distribution different from the one claimed.

Editorial extensions

If this is right

  • Optimization in a learned latent space with a density-gradient term keeps refined shapes plausible while lowering drag—5.8% for vehicles and 28.8% for the aircraft drag-to-lift objective in the paper's measurements.
  • View-based guided generation from the same input view produces lower-cost candidates than unguided generation—3.0% better vehicle drag and 68.6% better aircraft drag-to-lift in the paper's comparisons.
  • The covariance-matching analysis shows why existing shortcut guidance can be biased: some methods ignore the covariance dependence and others assume a fixed covariance, whereas SA-MC estimates it online.
  • The SKL-trained cost predictor better preserves global low-cost basins than an MSE-trained predictor, reducing systematic drift during guided generation.
  • The same guidance procedure transfers to offline reinforcement learning planning, where it improves average normalized scores relative to unguided planning in the paper's benchmarks.

Reading between the lines

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

  • If the tilted-distribution framing holds, the same optimization-plus-guidance recipe could transfer to other physics objectives, such as thermal or structural inverse design, by swapping the cost term; the paper demonstrates aerodynamics and offline RL but not those settings.
  • A controlled robustness test would be to measure guided-generation gains on out-of-distribution inputs with per-input guidance-scale selection; the paper itself notes fluctuations in that regime, so a practical prescription might involve tuning λ per input or early stopping.
  • The secant-based covariance estimator is derived from the generation trajectory itself, which suggests the same machinery could support uncertainty-aware sampling in other flow-matching inverse problems, not just aerodynamics.
  • Because the paper finds that SKL training preserves global low-cost basins better than MSE, a natural next step is to check whether that advantage persists with noisy or biased cost labels, as would occur with real wind-tunnel measurements.
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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

3 major / 5 minor

Summary. The manuscript proposes a unified probabilistic treatment of aerodynamic inverse design, linking point-solution optimization to distributional guided generation. It introduces a symmetric-KL training loss for cost predictors, a density-gradient optimization method using a flow-matching score prior, and a new algorithm, SA-MC, for estimating the conditional covariance in SIM-style guidance via secant updates along the ODE trajectory. Experiments include a 2D controlled study, 3D vehicle and aircraft optimization/generation with OpenFOAM evaluations, wind-tunnel smoke tests, and offline RL benchmarks. The headline claims are that visual-feature-preserving optimization reduces vehicle drag by 5.8% and aircraft Cd/Cl by 28.8%, and that guided generation reduces vehicle drag by 3.0% and aircraft Cd/Cl by 68.6% relative to unguided generation, while maintaining visual consistency.

Significance. If the central claims held, the paper would offer a practical and theoretically grounded route to shape-preserving aerodynamic inverse design, unifying existing guidance estimators and providing an efficient high-dimensional covariance approximation. The theoretical organization (Theorems 2.1–2.5) and the SKL training objective are valuable contributions in their own right, and the inclusion of OpenFOAM and wind-tunnel validation is a strength. However, the main generation claim is undermined by an apparent mismatch between the derived covariance scaling and the implemented algorithm. The reported gains are also selected over a guidance-scale sweep, which inflates the headline percentages. With correction, the framework may be useful, but the current empirical evidence does not support the paper's central claims.

major comments (3)
  1. [Sec. 2.5, Algorithms 5–6] Equation (20) requires the perturbation covariance to be Sigma_t = (sigma_t^2/alpha_t) * grad_{x_t} E[x_1|x_t]. Theorem 2.3 approximates the gradient by B_k, but Theorem 2.5 and Algorithm 5 factorize B_k, not Sigma_t, as L L^T. Algorithm 6 line 6 sets xi^(i) = L epsilon^(i) without multiplying by sqrt(sigma_t^2/alpha_t), even though line 4 computes sigma(t) and leaves it unused. For the typical schedule alpha_t=t, sigma_t=1-t, the missing factor varies by orders of magnitude across t. Consequently, the sampled perturbations have covariance B_k rather than (sigma_t^2/alpha_t) B_k, changing both the scale and the selection of samples and therefore the guidance direction. The generation results in Secs. 4.3–4.4 and the abstract are not produced by the algorithm as derived; they reflect an unstated perturbation scheme.
  2. [Sec. 4.4, Fig. 5c] The headline 68.6% aircraft Cd/Cl improvement is obtained by selecting the best lambda in {1,10,100} for each method ('To mirror practice, we select the best lambda...'). This is a best-of-three selection on the evaluation set, not a fixed-scale comparison. No standard errors or confidence intervals are reported for the selected value, and Fig. 4c shows that SA-MC can underperform unguided generation at other scales (e.g., lambda=10 with the MSE-trained predictor). The abstract presents this fitted maximum as a general generation gain, which is misleading.
  3. [Sec. 2.5, Theorem 2.3] The entire SA-MC method rests on the assumption that secant pairs (s_k, r_k) from the ODE trajectory yield an accurate positive-definite approximation B_k to the Jacobian grad_{x_t} v_t and hence to the conditional covariance. This assumption is load-bearing but is not validated independently. In the 2D controlled study (Sec. 4.2), where the true velocity field and Jacobian are computable, the paper does not report the error between B_k and the ground-truth Jacobian, nor the sensitivity of guidance to the secant initialization and memory length. Without this validation, the quantitative generation results cannot be attributed to the proposed covariance estimator.
minor comments (5)
  1. [Sec. 3.1 heading] The heading 'Optimzation' contains a typo; should be 'Optimization'.
  2. [Algorithm 6] The computed sigma(t) on line 4 is never used. Either remove it or apply it as sqrt(sigma_t^2/alpha_t) to the perturbation, and update the surrounding text accordingly.
  3. [Sec. 4.1 / Table 1] The baseline grouping in Table 1 is somewhat coarse; the text states that existing car-shape optimization methods are 'instantiations or variants' of DPS/LGD-MC/SIM-MC, but no explicit mapping is provided for each baseline. This makes the comparison hard to reproduce.
  4. [Sec. 2.2, Eq. (8)] The softmax notation is used before defining w_B^(J,lambda). Consider moving the weight definition earlier to avoid confusion.
  5. [Appendix H, Table 6] The offline RL results report only the best score over a hyperparameter sweep, with some entries missing (marked '–'). This is acceptable for an exploratory comparison, but the absence of a fixed-configuration evaluation weakens the claim of 'best average score'.

Circularity Check

1 steps flagged · score 4.0 of 10

Partially circular empirical reporting: generation gains are best-λ selections on the evaluation set, while the theoretical derivation is self-contained.

  1. fitted input called prediction [Sec. 4.4 (Fig. 5c) and abstract generation claims; also Sec. 4.3 (Fig. 4c)]
    "To mirror practice, we select the best λ∈{1,10,100} for each method."

    The abstract's generation improvements (vehicle drag -3.0%; aircraft Cd/Cl -68.6%) are the best results after sweeping the guidance scale λ on the same OpenFOAM evaluation set used to report them. The reported 'prediction' is the maximum over the fitted hyperparameter, so the headline gain is selected rather than predicted; the comparison is statistically forced by the choice of the best λ.

full rationale

The derivation chain (Gibbs target, SKL loss, density-gradient optimization, secant-based covariance guidance) is not definitionally circular: the target q∝p exp(-λJ) is fixed by external CFD costs, and the optimization/generation claims are checked with independent OpenFOAM and wind-tunnel evaluations. The paper also does not rely on load-bearing self-citations; all cited foundations are external. The circularity score is raised only by the empirical reporting protocol for generation: the headline gains are obtained by selecting the best guidance scale λ∈{1,10,100} on the same evaluation set used to report them, so those numbers are best-of-n selections rather than independent predictions. Separate from circularity, Algorithm 6 computes σ(t)=√(σ_t^2/α_t) but never applies it to ξ^(i)=L ε^(i), so the implemented perturbation covariance is B_k rather than Eq. 20's Σ_t=(σ_t^2/α_t)B_k; this is an implementation/theory mismatch and a correctness risk, not a circular dependence.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central method relies on a pretrained generative model and supervised cost labels; the only truly new invented quantity is the online secant covariance estimator, which is an approximation rather than a new physical entity.

free parameters (6)
  • guidance_scale_lambda = lambda in {1,10,100} (best selected per method on evaluation set)
    Controls strength of cost reweighting; generation results report best-of-lambda, a post-hoc selection.
  • MC_sample_size_S = 32 for 3D, up to 128 for D4RL
    Number of perturbations in the tilted-mean estimator; chosen by method/task.
  • memory_queue_length_m = not stated beyond fixed capacity
    Determines rank r=2m of the compact secant form; no ablation or stated value.
  • damping_bounds_sigma2_sigma3 = sigma2, sigma3 in (0,1), values not given
    Ensures positive definiteness in Alg. 3; numerical constants.
  • time_annealing_bounds = t_min >= 0.02, t_max <= 0.98
    Chosen to stabilize score estimate in Eq. 12.
  • optimization_step_size_eta_and_steps_K = not stated
    Gradient descent hyperparameters for Alg. 2.
assumptions (5)
  • domain assumption p0 = p (data distribution)
    Sec. 2.1 sets the prior to the data distribution to enforce shape preservation; assumes the training data covers the design region of interest.
  • domain assumption Pretrained Hunyuan3D Shape-VAE/DiT provides a faithful latent generative model of car/aircraft shapes
    Sec. 3.1 uses open-source weights; the score -grad log p is estimated from this model, so any distributional error transfers to optimization/generation.
  • standard math Tweedie/covariance identity Sigma_t = sigma_t^2/alpha_t * grad_{x_t} E[x1] holds for the flow-matching conditional
    Eq. 20 and Theorem 2.1 rely on the Gaussian forward kernel and interchange of differentiation/integration; stated in App. B.
  • ad hoc to paper Secant pairs from the ODE trajectory approximate the Jacobian of the velocity field
    Theorem 2.3 imposes a least-change/secant condition on grad v along one sample trajectory; this is the paper's main new approximation and is not validated independently.
  • domain assumption CFD labels (OpenFOAM/FUN3D) in DrivAerNet++ and BlendedNet are accurate enough as ground truth
    Used to train and evaluate the cost predictor; no convergence or uncertainty analysis is given in this paper.

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Cite this review

Pith. "Pith review of Optimization and Generation in Aerodynamics Inverse Design." pith.science (2026). https://pith.science/paper/EN3G6ON2

@misc{pith2026260203582,
  author       = {Pith},
  title        = {Pith review of: Optimization and Generation in Aerodynamics Inverse Design},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EN3G6ON2}},
  note         = {Machine review of arXiv:2602.03582}
}
read the original abstract

Aerodynamic inverse design can improve vehicle and aircraft efficiency, but practical design rarely seeks performance alone: vehicle refinement must reduce drag while preserving visual features linked to design language, brand recognition and user perception. Traditional CFD-driven optimization is accurate but slow for broad exploration, and current learning-based methods are still largely performance-driven and lack a coherent target linking optimization, generation and visual consistency. Here we formulate visual preservation and aerodynamic improvement as one probability target. Designs consistent with a reference shape or view define a learned visual design distribution, which is reweighted by aerodynamic cost. Optimization then refines an initial geometry toward a low-cost, high-probability design, whereas guided generation samples lower-cost 3D candidates from the same input view. OpenFOAM evaluation shows that visual-feature-preserving optimization reduces vehicle drag by 5.8\% relative to the initial vehicle and reduces the best valid aircraft drag-to-lift objective by 28.8\% relative to the initial aircraft while preserving input visual features. For view-based generation, guidance reduces vehicle drag by 3.0\% and the aircraft drag-to-lift objective by 68.6\% relative to direct generation from the same view, while maintaining visual consistency. Wind-tunnel tests with 3D-printed vehicle prototypes provide an independent wake-level check, and controlled analyses explain the distributional mechanisms behind these results. This work provides a probabilistic foundation and practical route for visual-feature-preserving aerodynamic refinement and early-stage 3D design exploration.

Figures

Figures reproduced from arXiv: 2602.03582 by the authors.

Figure 1
Figure 1. Inverse-design optimality and covariance-aware guidance. The left panel illustrates two classical paradigms in inverse design, point design and distributional design, and highlights their connection. The blue boxes indicate the organization of our theoretical sections. The right panel compares four representative guidance mechanisms, showing their computational graphs and differences. The schematic plots on the far … view at source ↗
Figure 2
Figure 2. Method overview. a, Latent shape-preserving optimization in the Shape-VAE space. b, Guided flow-matching generation with a cost predictor. c, Cost predictor conditioned on geometry, operating conditions and λ. d, Detailed modules in Transformer predictor. 3.2. Generation Instantiation As shown in Fig. 2b and Alg. 1, at step k we first query the DiT velocity field, vk = vtk (xk), and form the one-step prediction xb k… view at source ↗
Figure 3
Figure 3. a illustrates the setup: p is the data distribution and cost defines the objective landscape. The target distribution q ⋆ follows Eq. 4. Using the ground-truth cost gives qreal. Replacing it with a predictor trained on samples from p yields qMSE (MSE training) and qSKL (SKL training). Rela￾tive to qreal, qMSE misses several modes, whereas qSKL better preserves the target structure. Fig. 3b visualizes guided generati… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Vehicle aerodynamic optimization and generation. a, Drag reduction after optimization under different gradient and predictor training losses. b, Shape fidelity during optimization (Chamfer distance); dashed line marks an empirical plausibility boundary. c, Generation p…
Figure 5
Figure 5. Figure 5: Aircraft aerodynamic optimization and generation. a, Optimized drag-to-lift ratio (Cd/Cl); cost-gradient guidance can yield negative lift (< 0). b, Shape fidelity during optimization (Chamfer distance); dashed line marks an empirical plausibility boundary. c, Best gene…
Figure 6
Figure 6. Figure 6: OOD Exp. (Kyogre). a, Input and OpenFOAM velocity magnitude (w/ and w/o guidance); SA-MC reduces the wake deficit. b, Cd/Cl versus guidance scale λ; SA-MC performs best overall. ory usage across guidance schemes. For a single sample, SA-MC is relatively fast; meanwhile…
Figure 7
Figure 7. Figure 7: CFD setup. Top: computational domain and boundary conditions. Bottom: hex-dominant mesh with local refinement around the vehicle and near-wake. Boundary labels correspond to OpenFOAM patches: Velocity Inlet (ffminx), Pressure Out (ffmaxx), Symmetry (ffminy), Freestream…
Figure 8
Figure 8. Figure 8: CFD setup for the Blender car. Top: computational domain and boundary conditions: Velocity Inlet (ffminx), Pressure Out (ffmaxx), Symmetry (ffminy), and Freestream slip walls (ffmaxy, ffminz, ffmaxz). Bottom: hex-dominant mesh with local refinement around the vehicle a…
Figure 9
Figure 9. Figure 9: Physical evaluation with a miniature wind tunnel. (a) An example 3D-printed car used for testing. (b) Experimental pipeline: the fan-driven flow is seeded by a smoke generator and conditioned by a grille/flow straightener before entering the test section containing the…
Figure 10
Figure 10. Figure 10: Out-of-support generalization explains the drift of MSE-based guidance. Top: the data density p (contours), samples x ∼ p, and the base noise distribution N used to initialize generation. Bottom: cost landscapes over the entire domain: ground-truth (Real Cost), SKL-tr…
Figure 11
Figure 11. Figure 11: Runtime overhead of guidance on D4RL locomotion. Wall-clock time (seconds) to generate a 1,000-step trajectory. The dashed line denotes the unconditional baseline (w/o g). Lower is better. 38 [PITH_FULL_IMAGE:figures/full_fig_p038_11.png]

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Forward citations

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Reference graph

Works this paper leans on

28 extracted references · 15 linked inside Pith · cited by 2 Pith papers

  1. [2]

    17 Optimization and Generation in Aerodynamics Inverse Design B.3

    Taking expectation underq (Jt) t and substitutinge t(xt) =∥∆ t(xt)∥2 2 gives ∥gLGD t −g SIM t ∥2 2 ≤b 2 t ∥Σ−1 t ∥2 2 Eq(Jt ) t ∥zt∥2 2 et(xt), which concludes the proof. 17 Optimization and Generation in Aerodynamics Inverse Design B.3. Proof of Theorem 2.3 Proof.Recall that ∇xt Ep1|t(x1|xt)[x1] =− at bt I+ 1 bt ∇xt vt(xt).(51) At iterationk, letJ k ≈ ∇x...

    2006

  2. [7]

    and Nichol, A

    Jun, H. and Nichol, A. Shap-e: Generating conditional 3d implicit functions.arXiv preprint arXiv:2305.02463,

    arXiv

  3. [9]

    Reinforcement learning and control as proba- bilistic inference: Tutorial and review.arXiv preprint arXiv:1805.00909,

    Levine, S. Reinforcement learning and control as proba- bilistic inference: Tutorial and review.arXiv preprint arXiv:1805.00909,

    arXiv

  4. [11]

    T., Lopez-Paz, D., Ben-Hamu, H., and Gat, I

    Lipman, Y ., Havasi, M., Holderrieth, P., Shaul, N., Le, M., Karrer, B., Chen, R. T., Lopez-Paz, D., Ben-Hamu, H., and Gat, I. Flow matching guide and code.arXiv preprint arXiv:2412.06264,

    arXiv

  5. [13]

    P., Kumar, A., Er- mon, S., and Poole, B

    Song, Y ., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Er- mon, S., and Poole, B. Score-based generative modeling through stochastic differential equations.arXiv preprint arXiv:2011.13456,

    arXiv 2011

  6. [15]

    Tripoptimizer: Generative 3d shape optimization and drag prediction using triplane vae networks.arXiv preprint arXiv:2509.12224,

    Vatani, P., Elrefaie, M., Nazarpour, F., and Ahmed, F. Tripoptimizer: Generative 3d shape optimization and drag prediction using triplane vae networks.arXiv preprint arXiv:2509.12224,

    arXiv

  7. [16]

    Tran- solver: A fast transformer solver for pdes on general geometries.arXiv preprint arXiv:2402.02366,

    Wu, H., Luo, H., Wang, H., Wang, J., and Long, M. Tran- solver: A fast transformer solver for pdes on general geometries.arXiv preprint arXiv:2402.02366,

    arXiv

  8. [17]

    3d shapenets: A deep representation for volumetric shapes

    Wu, Z., Song, S., Khosla, A., Yu, F., Zhang, L., Tang, X., and Xiao, J. 3d shapenets: A deep representation for volumetric shapes. InProceedings of the IEEE conference on computer vision and pattern recognition, pp. 1912– 1920,

    1912

Show all 28 references
  1. [20]

    Hunyuan3d 2.0: Scaling diffusion models for high resolution textured 3d assets generation.arXiv preprint arXiv:2501.12202,

    Zhao, Z., Lai, Z., Lin, Q., Zhao, Y ., Liu, H., Yang, S., Feng, Y ., Yang, M., Zhang, S., Yang, X., et al. Hunyuan3d 2.0: Scaling diffusion models for high resolution textured 3d assets generation.arXiv preprint arXiv:2501.12202,

    arXiv

  2. [21]

    15 B.2 Proof of Theorem 2.2

    11 Optimization and Generation in Aerodynamics Inverse Design Contents of Appendix A Related Work 13 B Proof 15 B.1 Proof of Theorem 2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 B.2 Proof of Theorem 2.2 . . . . . . . . . . . ...

    2007

  3. [22]

    Guided generation.As discussed in Sec

    and TRELLIS series(Xiang et al., 2025b;a), employ V AE to compress geometry into compact latent feature fields, and subsequently utilize diffusion models as the generative prior, enabling high-fidelity geometric synthesis with scalable compute. Guided generation.As discussed i...

    2022

  4. [25]

    +O S Cfwd J , where C fwd J denotes the cost of a single forward pass of the cost predictor. The remaining operations (computing ℓmax, forming the normalized weights, and the weighted sum) contribute O(S) scalar work and O(Sd) vector accumulations, which are dominated by the t...

    2024

  5. [90]

    34 Optimization and Generation in Aerodynamics Inverse Design G

    and report both representative snapshots and their time-averaged image for comparison. 34 Optimization and Generation in Aerodynamics Inverse Design G. Additional Analysis of Experiment Results G.1. Why do guided methods with an MSE-trained predictor exhibit a consistent drift...

    2025

  6. [95]

    step size

    22 Optimization and Generation in Aerodynamics Inverse Design Theorem C.2 highlights two regimes. For small λ, SKL behaves like a (scaled) variance of the prediction error and is therefore controlled by MSE. For large λ, SKL depends primarily on how well Jθ matches therelative...

    2006

  7. [256]

    The critic shares the same backbone and uses the last token as the value head; it is trained for 104 steps with batch size 64 and learning rate 2×10 −4

    It is trained for 105 steps with batch size 32, learning rate 2×10 −4, and cosine-annealing scheduling. The critic shares the same backbone and uses the last token as the value head; it is trained for 104 steps with batch size 64 and learning rate 2×10 −4. The discount factor ...

    2025

  8. [2005]

    URL https://epubs.siam

    doi: 10.1137/ 1.9780898717921. URL https://epubs.siam. org/doi/abs/10.1137/1.9780898717921. Tran, J., Fukami, K., Inada, K., Umehara, D., Ono, Y ., Ogawa, K., and Taira, K. Aerodynamics-guided machine learning for design optimization of electric vehicles.Com- munications Engin...

    doi

  9. [2007]

    B., and Levine, S

    Janner, M., Du, Y ., Tenenbaum, J. B., and Levine, S. Plan- ning with diffusion for flexible behavior synthesis.arXiv preprint arXiv:2205.09991,

    arXiv

  10. [2009]

    D4rl: Datasets for deep data-driven reinforcement learning.arXiv preprint arXiv:2004.07219,

    Fu, J., Kumar, A., Nachum, O., Tucker, G., and Levine, S. D4rl: Datasets for deep data-driven reinforcement learning.arXiv preprint arXiv:2004.07219,

    2004 arXiv

  11. [2013]

    Hunyuan3d 2.1: From images to high-fidelity 3d as- sets with production-ready pbr material.arXiv preprint arXiv:2506.15442,

    Hunyuan3D, T., Yang, S., Yang, M., Feng, Y ., Huang, X., Zhang, S., He, Z., Luo, D., Liu, H., Zhao, Y ., et al. Hunyuan3d 2.1: From images to high-fidelity 3d as- sets with production-ready pbr material.arXiv preprint arXiv:2506.15442,

    arXiv

  12. [2015]

    J., et al

    Xiang, J., Chen, X., Xu, S., Wang, R., Lv, Z., Deng, Y ., Zhu, H., Dong, Y ., Zhao, H., Yuan, N. J., et al. Native and compact structured latents for 3d generation.arXiv preprint arXiv:2512.14692, 2025a. Xiang, J., Lv, Z., Xu, S., Deng, Y ., Wang, R., Zhang, B., Chen, D., Tong...

    arXiv

  13. [2016]

    T., Klasky, M

    Chung, H., Kim, J., Mccann, M. T., Klasky, M. L., and Ye, J. C. Diffusion posterior sampling for general noisy in- verse problems.arXiv preprint arXiv:2209.14687,

    arXiv

  14. [2018]

    Fourier neural operator for parametric partial differential equa- tions.arXiv preprint arXiv:2010.08895,

    Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhat- tacharya, K., Stuart, A., and Anandkumar, A. Fourier neural operator for parametric partial differential equa- tions.arXiv preprint arXiv:2010.08895,

    2010 arXiv

  15. [2019]

    Physgen: Physically grounded 3d shape generation for industrial design.arXiv preprint arXiv:2512.00422,

    You, Y ., Zhao, C., Zhang, H., Xu, M., and Fua, P. Physgen: Physically grounded 3d shape generation for industrial design.arXiv preprint arXiv:2512.00422,

  16. [2020]

    Hyperparameters are tuned per method following Feng et al

    (Feng et al., 2025). Hyperparameters are tuned per method following Feng et al. (2025): covariance- gradient guidances sweep multiple λt schedules (e.g., constant/decay families) and global scales; gMC sweeps the reward scaling and uses up to 128 Monte Carlo samples with a sma...

    2025

  17. [2021]

    Point-e: A system for generating 3d point clouds from complex prompts.arXiv preprint arXiv:2212.08751,

    Nichol, A., Jun, H., Dhariwal, P., Mishkin, P., and Chen, M. Point-e: A system for generating 3d point clouds from complex prompts.arXiv preprint arXiv:2212.08751,

    arXiv

  18. [2023]

    Kingma, D. P. and Welling, M. Auto-encoding variational bayes.arXiv preprint arXiv:1312.6114,

    arXiv

  19. [2024]

    On the guid- ance of flow matching.arXiv preprint arXiv:2502.02150,

    Feng, R., Yu, C., Deng, W., Hu, P., and Wu, T. On the guid- ance of flow matching.arXiv preprint arXiv:2502.02150,

    arXiv

  20. [2025]

    and Martinelli, L

    Jameson, A. and Martinelli, L. Aerodynamic shape opti- mization techniques based on control theory. InComputa- tional Mathematics Driven by Industrial Problems: Lec- tures given at the 1st Session of the Centro Internazionale Matematico Estivo (CIME) held in Martina Franca, It...

    1999

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.