Optimization and Generation in Aerodynamics Inverse Design

TL;DR

This paper introduces a novel approach combining optimization and guided generation for aerodynamic inverse design, improving shape plausibility and efficiency in high-dimensional, simulation-expensive scenarios.

Contribution

It proposes a new training loss for cost predictors, a density-gradient optimization method, and unifies existing guided generation techniques, addressing high-dimensional covariance approximation.

Findings

Improved aerodynamic shape optimization results.

Enhanced guided generation quality and plausibility.

Validated methods on 2D and 3D aerodynamic benchmarks.

Abstract

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.