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.

翻译：基于梯度的工程设计优化受到典型计算机辅助工程（CAE）流程中不可微分组件的限制，该流程从设计参数计算性能指标。虽然基于梯度的方法在高维设计空间中能提供显著的加速，但网格划分、物理仿真及其他常见组件的代码即使其底层数学或物理原理是可微的，本身仍不可微分。我们提出用本质上可微分的代理模型替代不可微分的流程组件。通过一个空气动力学形状优化的示例，我们展示了一个端到端的可微分流程：通过训练一个3D U-Net全场代理模型，学习从形状的有符号距离场（SDF）到目标场之间的映射，从而替代网格划分和仿真步骤。该方法实现了无需可微分求解器的基于梯度的形状优化，适用于伴随方法不可用或难以实施的情况。