dCG -- differentiable connected geometries for AI-compatible multi-domain optimization and inverse design

TL;DR

This paper introduces differentiable Connected Geometries (dCG), a novel framework enabling automatic differentiation in multi-domain geometric optimization, demonstrated through toy and photonic design examples to enhance scientific and engineering optimization tasks.

Contribution

The paper presents the concept of differentiable Connected Geometries (dCG), integrating geometric design with automatic differentiation for the first time in multi-domain optimization.

Findings

dCG is compatible with deep learning frameworks.

Demonstrated improved optimization in photonic design.

Provides a systematic approach for geometric optimization.

Abstract

In the domain of geometry and topology optimization, discovering geometries that optimally satisfy specific problem criteria is a complex challenge in both engineering and scientific research. In this work, we propose a new approach for the creation of multidomain connected geometries that are designed to work with automatic differentiation. We introduce the concept of differentiable Connected Geometries (dCG), discussing its theoretical aspects and illustrating its application through a simple toy examples and a more sophisticated photonic optimization task. Since these geometries are built upon the principles of automatic differentiation, they are compatible with existing deep learning frameworks, a feature we demonstrate via the application examples. This methodology provides a systematic way to approach geometric design and optimization in computational fields involving dependent geometries, potentially improving the efficiency and effectiveness of optimization tasks in scientific and engineering applications.