Surrogate-Based Differentiable Pipeline for Shape Optimization

Andrin Rehmann, Nolan Black, Josiah Bjorgaard, Alessandro Angioi, Andrei Paleyes, Niklas Heim, Dion Häfner, Alexander Lavin

Keywords: gradient-based optimization, shape optimization, neural surrogates, computational fluid dynamics, differentiable physics programming

TL;DR: We introduce a fully differentiable pipeline for shape optimization by replacing non-differentiable components with a surrogate model trained to predict flow fields directly from signed distance functions.

Abstract:

Gradient-based optimization of engineering designs is limited by non-differentiable
components in the typical CAE workflow, which calculates performance metrics
from design parameters. While gradient-based methods could provide noticeable
speed-ups in high-dimensional design spaces, commonly-used codes for meshing,
physical simulations, and so on, 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 simu-
lation steps by training it on the mapping between the 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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Submission Number: 53