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

arXiv: https://arxiv.org/abs/2512.08987 · HTML: https://mlsanity.com/paper/2512.08987/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 81 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Rodin: A Generative Model for Sculpting 3D Digital Avatars Using Diffusion](https://mlsanity.com/paper/2212.06135/) (2022)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Direct3D: Scalable Image-to-3D Generation via 3D Latent Diffusion Transformer](https://mlsanity.com/paper/2405.14832/) (2024)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks](https://mlsanity.com/paper/2406.09624/) (2024)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Learning to Accelerate Partial Differential Equations via Latent Global Evolution](https://mlsanity.com/paper/2206.07681/) (2022)
- [Geodesic Convolutional Shape Optimization](https://mlsanity.com/paper/1802.04016/) (2018)
- [Learning to Solve PDE-constrained Inverse Problems with Graph Networks](https://mlsanity.com/paper/2206.00711/) (2022)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [DrivAerNet: A Parametric Car Dataset for Data-Driven Aerodynamic Design and Prediction](https://mlsanity.com/paper/2403.08055/) (2024)
- [Compositional Generative Inverse Design](https://mlsanity.com/paper/2401.13171/) (2024)
- [Autoinverse: Uncertainty Aware Inversion of Neural Networks](https://mlsanity.com/paper/2208.13780/) (2022)
- [Surrogate Modeling of Car Drag Coefficient with Depth and Normal Renderings](https://mlsanity.com/paper/2306.06110/) (2023)
- [DEBOSH: Deep Bayesian Shape Optimization](https://mlsanity.com/paper/2109.13337/) (2021)
- [TripNet: Learning Large-scale High-fidelity 3D Car Aerodynamics with Triplane Networks](https://mlsanity.com/paper/2503.17400/) (2025)
- [Drag-guided diffusion models for vehicle image generation](https://mlsanity.com/paper/2306.09935/) (2023)

## Built on by (most cited first, 3 of 3)

- [Optimization and Generation in Aerodynamics Inverse Design](https://mlsanity.com/paper/2602.03582/) (2026)
- [Geometry-Aware Neural Optimizer for Shape Optimization and Inversion](https://mlsanity.com/paper/2605.04474/) (2026)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)

## Abstract (arXiv)

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.