Surrogate-Based Differentiable Pipeline for Shape Optimization

TL;DR

This paper introduces a surrogate-based differentiable pipeline for shape optimization, replacing non-differentiable CAE components with trainable models to enable efficient gradient-based optimization in complex design workflows.

Contribution

It presents a novel end-to-end differentiable pipeline using a 3D U-Net surrogate to replace meshing and simulation steps in aerodynamic shape optimization.

Findings

Successfully trained a 3D U-Net surrogate for shape-to-field mapping.

Enabled gradient-based optimization without differentiable solvers.

Demonstrated effectiveness on a toy aerodynamic shape optimization example.

Abstract

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.