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Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches

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Published on: December 15, 2023

Data-informed deep optimization.

Lulu Zhang¹, Zhi-Qin John Xu^1,2, Yaoyu Zhang^1,2,3

¹School of Mathematical Sciences, Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China.

|June 23, 2022

Summary

Deep learning tackles complex optimization problems without explicit formulas. The data-informed deep optimization (DiDo) approach effectively handles high-dimensional design challenges with implicit objectives and constraints.

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Area of Science:

Computational Science
Optimization
Machine Learning

Background:

Deep learning excels in various applications, yet struggles with optimization problems lacking explicit objective functions and constraints.
High-dimensional design problems with implicit objectives and constraints are challenging due to the curse of dimensionality.

Purpose of the Study:

To propose a novel data-informed deep optimization (DiDo) approach for solving high-dimensional optimization problems with implicit objectives and constraints.
To adaptively fit the feasible region using deep neural networks (DNNs).

Main Methods:

A DNN-based adaptive fitting approach to learn an accurate DNN classifier of the feasible region.
Utilizing the DNN classifier for efficient sampling of feasible points and training a DNN surrogate of the objective function.
Employing gradient descent to find optimal points of the DNN surrogate optimization problem.

Main Results:

The DiDo approach yields effective solutions for a practical industrial design case with limited data.
Demonstrated effectiveness for high-dimensional problems using a 100-dimension toy example.
The method successfully addresses the challenge of fitting the feasible region.

Conclusions:

The DiDo approach is a flexible and promising deep learning-based method for high-dimensional design problems with implicit objectives and constraints.
Accurate feasible region fitting is crucial for the success of DNN-based optimization.