Topology optimization automatically tunes design hyperparameters during optimization
Bilevel Optimization of Topology and Hyperparameters (BOTH)
Machine Learning
Summary
Designing objects often involves picking settings called hyperparameters, which are usually hard to choose and need lots of trial and error. The authors show how to automatically adjust these settings while designing, by calculating how small changes affect the design quality. This approach uses information from just a few optimization steps and can handle many hyperparameters efficiently. It helps create better designs by tuning settings alongside the main design process without extra guesswork.
What this means in practice
- •For mechanical design engineers: Automatically tune critical design parameters during topology optimization to improve structural prototypes and reduce trial-and-error time.
- •For machine learning model builders: Use differentiable topology optimization with neural density parameterization to jointly optimize design and model hyperparameters for improved performance.
Authors
Suryanarayanan Manoj Sanu, Miguel Anibal Bessa, Alejandro Marcos Aragón
Abstract
Topology optimization (TO) represents a significant step towards automating the design process: given a working simulation, TO can produce a viable prototype at the press of a button by differentiating the simulation and iteratively improving the design. In practice, however, TO is riddled with ``magic numbers''---hyperparameters whose tuning significantly affects the outcome. Finding the right values typically requires not only deep problem-specific knowledge but also extensive trial-and-error. While practitioners can use surrogate-assisted hyperparameter optimization as an alternative, this approach requires strictly limiting the number of hyperparameters through careful problem formulation. Here, we propose differentiating TO itself using automatic differentiation. This yields ``hypergradients'' that allow us to tune these hyperparameters in tandem with the primary optimization. We show that evaluating just one or two steps of TO is sufficiently informative and that the method scales favorably to thousands of hyperparameters at an expense comparable to only a few standard TO runs. We demonstrate this approach on stress-constrained and compliance problems, with the latter utilizing a neural parameterization of the density field.