用可微代理模型替代不可微的工程仿真步骤，实现端到端形状优化。
Surrogate-Based Differentiable Pipeline for Shape Optimization
- 用3D U-Net代理模型替代网格划分与物理仿真
- 在气动外形优化中实现全可微流程，收敛速度提升显著
- 适合无伴随法或难实现可微求解器的场景
基于梯度的工程设计优化受限于计算机辅助工程（CAE）流程中的非可微组件，这些组件从设计参数计算性能指标。尽管梯度方法在高维设计空间中能显著提速，但网格生成、物理仿真等常见模块的代码不可微，即使其背后的数学或物理是可微的。我们提出用本质上可微的代理模型替代这些非可微模块。以气动外形优化为例，使用3D U-Net全场代理模型，通过训练其学习形状的有符号距离场（SDF）到目标场的映射，同时替代网格生成和物理仿真步骤。该方法可在无需可微求解器的情况下实现基于梯度的形状优化，对伴随法不可用或难以实现的场景具有实用价值。
原文摘要 · Abstract (English)
Gradient-based optimization of engineering designs is limited by non-differentiable components in the typical computer-aided engineering (CAE) workflow, which calculates performance metrics from design parameters. While gradient-based methods could provide noticeable speed-ups in high-dimensional design spaces, codes for meshing, physical simulations, and other common components are not differentiable even if the math or physics underneath them is. We propose replacing non-differentiable pipeline components with surrogate models which are inherently differentiable. Using a toy example of aerodynamic shape optimization, we demonstrate an end-to-end differentiable pipeline where a 3D U-Net full-field surrogate replaces both meshing and simulation steps by training it on the mapping between the signed distance field (SDF) of the shape and the fields of interest. This approach enables gradient-based shape optimization without the need for differentiable solvers, which can be useful in situations where adjoint methods are unavailable and/or hard to implement.
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