3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization

TL;DR

The paper tackles 3D inverse design in aerodynamics, where direct 3D exploration is hampered by high dimensionality and costly simulations.It introduces a Physics–Geometry VAE (PG-VAE) that jointly encodes geometry and physical fields into a continuous latent, enabling a compact, expressive 3D representation via triplanes.A two-stage optimization—gradient-guided diffusion over the latent space followed by topology-preserving refinement using a differentiable surrogate—drives designs toward target objectives while preserving mesh topology.Empirical results on the DrivAerNet++ dataset show 3DID achieves superior drag reduction and design novelty, outperforming baselines and validating the effectiveness of the unified representation and diffusion-plus-refinement pipeline.

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 objective-driven, 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.

Figures (11)

• Figure 1: Motivation of 3DID. Existing 3D inverse‐design methods either rely on reduced‐dimensional representations (2D projections or fixed parameterizations) that constrain design freedom, or require an initial geometry as a starting point for local refinement, which highly constrains the search space. In contrast, 3DID overcomes these limitations by directly exploring the full 3D design space from random initialization.
• Figure 2: The overview of PG-VAE. We use transformers to encode the design geometry and its associated physical field, along with learnable tokens, into a compact triplane latent representation $z$. A decoder then upsamples the latent $z$ into high-resolution triplane feature maps, which can be reshaped into three orthogonal planes. Finally, a physics–geometry mapping network is applied to reconstruct both the occupancy field and the corresponding physical field from these feature maps.
• Figure 3: The optimization framework of 3DID. Starting from noise, we guide diffusion using objective gradients to steer the latent toward high-performance regions. The decoded triplane then yields an initial mesh $\bm{M}_0$ and its surface physical field $\bm{\varphi}$, which is then refined via backpropagation over a free-form deformation lattice to improve performance while preserving topology.
• Figure 4: Qualitative comparisons of different representations. Each row shows four candidates with geometry (left) and simulated velocity field (right) with Sim-Drag in the top-right. Despite equal resolution, voxel methods incur higher drag and often yield non-watertight shapes (red box) due to coarse discretization. Our continuous latent representation produces watertight, smooth designs with superior aerodynamic performance, outperforming both voxel-based and geometry-only approaches.
• Figure 5: Qualitative comparisons of topology-preserving refinement. Each row presents two design candidates comparisons with their geometry and simulated velocity field heatmaps. Sim-Drag values are shown in the top-right corner of each panel. Refined designs exhibit a more significant fastback profile (yellow box), reduced low-velocity recirculation zones (blue box), and stronger downward flow (green box), indicating improved aerodynamic performance.