Inverse design with physics-based objectives is challenging because it couples high-dimensional geometry with expensive simulations, as exemplified by aerodynamic shape optimization for drag reduction. We revisit inverse design through two canonical solutions, the optimal design point and the optimal design distribution, and relate them to optimization and guided generation. Building on this view, we propose a new training loss for cost predictors and a density-gradient optimization method that improves objectives while preserving plausible shapes. We further unify existing training-free guided generation methods. To address their inability to approximate conditional covariance in high dimensions, we develop a time- and memory-efficient algorithm for approximate covariance estimation. Experiments on a controlled 2D study and high-fidelity 3D aerodynamic benchmarks (car and aircraft), validated by OpenFOAM simulations and miniature wind-tunnel tests with 3D-printed prototypes, demonstrate consistent gains in both optimization and guided generation. Additional offline RL results further support the generality of our approach.

翻译：基于物理目标的逆设计具有挑战性，因为它将高维几何与昂贵的仿真计算相耦合，以降低阻力的气动外形优化为例证。我们通过两个典型解——最优设计点与最优设计分布——重新审视逆设计，并将其与优化及引导生成联系起来。基于这一视角，我们提出了一种用于成本预测器的新训练损失函数，以及一种在保持合理外形的同时优化目标的密度梯度优化方法。我们进一步统一了现有的免训练引导生成方法。针对这些方法在高维条件下难以近似条件协方差的问题，我们开发了一种时间和内存高效的近似协方差估计算法。在受控二维研究和高保真三维空气动力学基准（汽车与飞机）上的实验，通过OpenFOAM仿真及采用3D打印原型的小型风洞测试验证，证明了我们的方法在优化和引导生成方面均能取得持续提升。额外的离线强化学习结果进一步支持了我们方法的普适性。