Surrogate-Based Differentiable Pipeline for Shape Optimization

2025-11-13

AI Summary

In engineering design, the non-differentiability of conventional CAE workflows—particularly mesh generation and physics simulation—hinders gradient-based high-dimensional optimization. To address this, we propose an end-to-end differentiable shape optimization framework: geometry is represented via signed distance fields (SDFs), and a 3D U-Net serves as a full-field surrogate model that directly learns the mapping from SDFs to physical fields (e.g., pressure, velocity), thereby bypassing non-differentiable components without requiring differentiable solvers or adjoint methods. The surrogate is embedded within a differentiable optimization pipeline, enabling backpropagation to compute gradients with respect to design parameters. Evaluated on aerodynamic shape optimization, our method achieves fully gradient-driven, efficient iterative design refinement. Results demonstrate substantial improvements in optimization efficiency and validate the framework’s feasibility and advantages in complex engineering applications.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Replaces non-differentiable CAE components with differentiable surrogates
• Enables gradient-based shape optimization without adjoint methods
• Trains 3D U-Net to map shape representations to physical fields

Innovation

• Replaces non-differentiable components with differentiable surrogates
• Uses 3D U-Net surrogate for meshing and simulation
• Enables gradient-based optimization without differentiable solvers