Mean Squared Error May Lead You Astray When Optimizing Your Inverse Design Methods

When performing time-intensive optimization tasks, such as those in topology or shape optimization, researchers have turned to machine-learned inverse design (ID) methods—i.e., predicting the optimized geometry from input conditions—to replace or warm start traditional optimizers. Such methods are often optimized to reduce the mean squared error (MSE) or binary cross entropy between the output and a training dataset of optimized designs. While convenient, we show that this choice may be myopic. Specifically, we compare two methods of optimizing the hyperparameters of easily reproducible machine learning models including random forest, k-nearest neighbors, and deconvolutional neural network model for predicting the three optimal topology problems. We show that under both direct inverse design and when warm starting further topology optimization, using MSE metrics to tune hyperparameters produces less performance models than directly evaluating the objective function, though both produce designs that are almost one order of magnitude better than using the common uniform initialization. We also illustrate how warm starting impacts both the convergence time, the type of solutions obtained during optimization, and the final designs. Overall, our initial results portend that researchers may need to revisit common choices for evaluating ID methods that subtly tradeoff factors in how an ID method will actually be used. We hope our open-source dataset and evaluation environment will spur additional research in those directions.