When is it actually worth learning Inverse Design?

Design optimization, and particularly adjoint-based multi-physics shape and topology optimization, is time-consuming and often requires expensive iterations to converge to desired designs. In response, researchers have developed Machine Learning (ML) approaches—often referred to as Inverse Design methods—to either replace or accelerate tools like Topology Optimization (TO). However, these methods have their own hidden, non-trivial costs, including those of data generation, training, and refinement of ML-produced designs. This begs the question: when is it actually worth learning Inverse Design (ID), compared to just optimizing designs without ML assistance? This paper quantitatively addresses this question by comparing the costs and benefits of three different ID ML models on a TO task, compared to just running the optimizer by itself. We explore the relationship between the size of training data and the predictive power of each ML model, as well as the computational costs of the models, and the extent to which they accelerate or hinder TO convergence. The results demonstrate that simpler models, such as K-Nearest Neighbors and Random Forests, are more effective for TO warm-starting with limited training data. In contrast, more complex models, such as Deconvolutional Neural Networks, are preferable with more data. We also emphasize the need to balance the benefits of using larger training sets with the data generation costs when selecting the appropriate ID model. Finally, the paper addresses some challenges that arise when using ML predictions to warm-start optimization, and provides some suggestions for resource management.