  Complex design problems are common in the scientific and industrial fields.
In practice, objective functions or constraints of these problems often do not
have explicit formulas, and can be estimated only at a set of sampling points
through experiments or simulations. Such optimization problems are especially
challenging when design parameters are high-dimensional due to the curse of
dimensionality. In this work, we propose a data-informed deep optimization
(DiDo) approach as follows: first, we use a deep neural network (DNN)
classifier to learn the feasible region; second, we sample feasible points
based on the DNN classifier for fitting of the objective function; finally, we
find optimal points of the DNN-surrogate optimization problem by gradient
descent. To demonstrate the effectiveness of our DiDo approach, we consider a
practical design case in industry, in which our approach yields good solutions
using limited size of training data. We further use a 100-dimension toy example
to show the effectiveness of our model for higher dimensional problems. Our
results indicate that the DiDo approach empowered by DNN is flexible and
promising for solving general high-dimensional design problems in practice.

Optimization and Control;Machine Learning