Title: 3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization
Venue: NeurIPS 2025
Accepted: yes
Keywords: Inverse Design

Aerodynamic Shape Optimization
Abstract: Inverse design aims to design the input variables of a physical system to optimize
a specified objective function, typically formulated as a search or optimization
problem. However, in 3D domains, the design space grows exponentially, rendering
exhaustive grid-based searches infeasible. Recent advances in deep learning have
accelerated inverse design by providing powerful generative priors and differentiable surrogate models. Nevertheless, current methods tend to approximate the
3D design space using 2D projections or fine-tune existing 3D shapes. These
approaches sacrifice volumetric detail and constrain design exploration, preventing
true 3D design from scratch. In this paper, we propose a 3D Inverse Design (3DID)
framework that directly navigates the 3D design space by coupling a continuous
latent representation with a physics-aware optimization strategy. We first learn a
unified physics–geometry embedding that compactly captures shape and physical
field data in a continuous latent space. Then, we introduce a two-stage strategy to
perform physics-aware optimization. In the first stage, a gradient-guided diffusion
sampler explores the global latent manifold. In the second stage, an objectivedriven, topology-preserving refinement further sculpts each candidate toward the
target objective. This enables 3DID to generate high-fidelity 3D geometries, outperforming existing methods in both solution quality and design versatility.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper performs inverse design of car geometries for optimizing aerodynamics properties, e.g., drag. The paper creates a latent space that encodes both the geometry of the cars and the simulated physical fields around the car geometry. The paper then uses this latent space for optimizing for a new shape (in the latent space). As a final post processing step, the paper further optimizes the obtained design through a shape optimization that preserves the topology. The paper compares its method to two other inverse design method and reports superiority. It also studies some of its own design decision through ablations.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths: \n- The choice of the problem: this problem is inherently difficult and underrepresented in ML. \n\n- Validation is relatively good and the paper has done the right thing by including how a ground-truth (and not only surrogate) rates the optimized design, through 'Sim-Drag' metric. \n\nWeaknesses: \n- The two main contributions of the paper could have been more discussed. For example, there should have been references to the works that encode both design and physical properties as well as works that do refinement. \n\n- An important missing evaluation that acts as a sanity check is to compare the performance of the optimized design with the best performing design in the training dataset. \n\n- The whole point of surrogation is to amortize its training during inference. Is this the case in this paper? The paper shows the best performing shape through surrogate but what if we optimize for 1000 different drags and show the statistics? Ideally, this must be coupled with other objectives and have a multi-objective optimization. \n\n- I am not sure why this method is called a physics-aware optimization. The fact that the physical fields are used jointly for training the encoder, does not fit the (loose) definition of physics-aware. \n\n- Minor, but the title is a bit too broad by not including the context (car geometries and aerodynamics).\n\nQUESTIONS:\n- On the amortization note above, how general the surrogation is? With the 8000 training data, can one use the trained surrogates for slightly changed conditions/applications? \n\n- How much topology variation exist in the training data and how much the topology of optimized designs is different from the training data? Are we talking about mesh-topology or the more macro-scale car topology? \n\n- I had difficulty understanding 2D projection part. Some clarification would be helpful to the paper. \n\n- Equation 1 is hard to parse mathematically. Please check the correctness.\n\nLIMITATIONS:\nNot much discussed in the main paper. Some of the points raised in Strengths/Weakness section above could potentially be used.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-19"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a new 3D inverse design method with physics-aware optimization, differentiating from prior work in two aspects: (1) avoiding 2D projection; (2) abstaining from fine-tuning existing 3D shapes. The 3DID framework employs a unified latent representation within a VAE to encode both shape geometry and induced physical fields. It performs two-stage generation: (1) direct latent space sampling via guided diffusion models; (2) topology-preserving mesh refinement under constraint. Results on vehicle aerodynamic shape design validate 3DID’s effectiveness.\n\nSTRENGTHS AND WEAKNESSES:\n1. Strengths\n\n   (1) The proposed method is novel.  The Physics-Geometry VAE unifies shape and physical field encoding in a latent space, ensuring physical consistency during design. The two-stage generation process combines objective-guided diffusion with topology-preserving refinement, addressing prior limitations.\n\n   (2) The empirical results on vehicle aerodynamic shape optimization is significant, as shown in Table 1/2/3 and Figure 4/5.\n\n2. Weaknesses\n\n   (1) As a general 3D inverse design method, the current validation is limited to a single task (vehicle aerodynamics). To establish generality, at least one additional engineering task is required—e.g., 3D aircraft design, a well-studied problem in physics-based engineering design.\n\n   (2) The motivation for the topology preserving refinement stage is ambiguously stated as \"biases from training data prior,\" lacking clear theoretical grounding. The authors should clarify: Why is refinement needed after objective-guided sampling? A visual/intuitive illustration of the refinement process (e.g., fine-grid visualizations) is essential for understanding.\n\nQUESTIONS:\nTwo critical questions:\n\n(1) should provide one more task for evaluation.\n\n(2) should clarify the necessity of the topology preserving refinement stage.\n\nOther questions:\n\n(1) In Eq (2), how to formulate \"constraints, such as volume, manufacturability, and boundary conditions\"?\n\n(2) In Eq (5), the = should be replaced by $\\propto$\n\n(3) What does the KL divergence mean in Eq. (3)?\n\n(4) how does the hyperparameter $\\gamma$ effect the performance? Too large $\\gamma$ may make generated shape deviated from the manifold and adversarial artifacts, and too small $\\gamma$  has little effect on optimizing the objective.\n\n(5) How to pretrain the surrogate model $f_\\text{GNN}$? How does it deal with out-of-distribution prediction?\n\n(6) In Figure 4, Voxel+PCA produces non-watertight shapes. How doese 3DID guarantee watertightness?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors learn a unified latent representation that compactly encodes both the 3D shape geometry and its associated physical field (such as flow pressure). This latent space significantly reduces the dimensionality of the design problem while preserving fine geometric details and high-fidelity physics information. Building on this representation, 3DID employs a two-stage optimization pipeline: (1) a gradient-guided diffusion sampler that generates diverse candidate shapes from scratch by guiding a 3D diffusion model with the gradient of the target objective, thus biasing generation toward high-performance designs, and (2) a topology-preserving refinement stage that fine-tunes each candidate via physics-aware gradient descent (using a differentiable surrogate model) to further improve performance while maintaining the shape’s structural integrity.\n\nSTRENGTHS AND WEAKNESSES:\nA core contribution is the learned latent space that jointly encodes geometry and physics (e.g., flow fields) in a compact form. The paper introduces a clever optimization strategy that balances global exploration with local refinement. The first stage, a gradient-guided diffusion sampler, leverages the generative power of diffusion models and steers them using objective gradients. \n\nWhile this work is largely empirical, adding theoretical underpinnings where possible would improve its rigor. For example, providing a convergence analysis for the refinement stage (even if simplified, like proving that the FFD gradient descent will locally improve the objective under certain smoothness assumptions) would lend more credibility. Similarly, formalizing the guided diffusion by referencing known results in score-based generative modeling would address theoretical concerns. If exact analysis is intractable, even a conceptual discussion of failure modes (e.g., how too-strong guidance can lead to off-manifold samples) and how the method mitigates them (via the chosen hyperparameter) shows theoretical awareness. Grounding each algorithmic choice in either theory or established literature would dispel any impression of ad-hoc design.\n\nAblations to establish the impact of different hyperparameters are needed due to the complex workflow.\n\nIt is not clear how the method compares against a well-formulated optimization-only pipeline (FFD+adjoints or FFD+heuristic search), which avoids data collection, training, and the limited generalizability challenge. These methods are commonly used in aerospace and vehicle design. What are the key benefits that will convince practitioners to adopt this methodology compared to existing optimization-only approaches?\n\nQUESTIONS:\nDemonstrating any degree of generalization or adaptability would greatly strengthen the work’s impact. The authors are requested to test two conditions: 1) Cluster Drivaernet++ using parameters and completely hold out one of the clusters as the test set. 2) Test the method on a different dataset (e.g., ShapeNet geometries) to demonstrate the degree of generalization.\n\nHyperparameter tuning: The paper has a complex workflow, and ablations for more key design choices are needed to understand the outcome. For example, an ablation on the effect of the objective guidance strength (the coefficient in diffusion guidance) would show sensitivity to that hyperparameter and help answer, “How does the strength of this guidance impact the downstream optimization results?” Another ablation could remove or vary the regularizers in the refinement stage (smoothness and volume preservation) to demonstrate their effect on the design outcome.\n\nWhile the approach is “physics-aware” in that it uses training data from simulations, it doesn’t enforce the physical laws during generation – it relies on the surrogate’s learned approximation. If one wanted to apply 3DID to a new domain, one would have to retrain the entire model and ensure the surrogate is accurate, which could be a barrier. It will help if the authors discuss this issue.\n\nHow accurate does the encoding surrogate have to be for integration in the full pipeline?\n\nLIMITATIONS:\nA current limitation is the narrow scope of testing. A rigorous study would test generalization in multiple ways. One suggestion is cross-generalization: train the model on one subset of shapes or one objective, and test its performance on a slightly different scenario. How well does the method work on out-of-distribution geometries?", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

comments: SUMMARY:
The paper introduces 3DID, a framework for direct 3D inverse design that addresses the limitations of prior approaches constrained by 2D projections or initial geometry assumptions. Instead of operating in the raw high-dimensional space, 3DID first learns a compact, unified latent representation that couples geometry and physics through a triplane-based VAE. It then performs a two-stage optimization: (1) a gradient-guided diffusion sampler that generates diverse candidate designs in latent space with objective-aware steering, and (2) a topology-preserving refinement stage based on free-form deformation that further improves the design while maintaining geometric integrity. Applied to aerodynamic shape optimization, 3DID outperforms existing methods in objective quality, novelty, and simulation fidelity.

STRENGTHS AND WEAKNESSES:
The methodology is well presented and evaluated. Results on aerodynamic shape optimization show improvements in simulated drag and design novelty over baselines. The proposed physics-geometry triplane embedding and the gradient-guided diffusion and topology-preserving refinement look both novel.
Clarity is generally good, with clear figures. The work targets a challenging and relevant problem in scientific design and makes clear progress compared to existing methods. Overall, I find this to be a solid and well-executed paper with meaningful contributions, and I lean toward acceptance.

QUESTIONS:
While the diffusion process is guided by gradients of the objective, there is no explicit enforcement of hard physical or geometric constraints during sampling. This raises the question of how often does the sampling stage produce geometries that are physically invalid or impractical?

LIMITATIONS:
Yes.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-07-03