IF-TONIR: iteration-free topology optimization based on implicit neural representations

Abstract

Topology optimization holds great significance as a research topic in the field of mechanical engineering, aiming to design and optimize structures to achieve desired performance while adhering to specific constraints. However, its high computational complexity and iterative optimization process severely impact the efficiency, which presents substantial obstacles to its practical applications. To tackle this challenge, recent research is dedicated to the advancement of iteration-free topology optimization methods that leverage neural networks and deep learning, aiming to directly predict optimal structures through optimization problem configurations. In this paper, we propose IF-TONIR, a novel data-driven topology optimization method that utilizes implicit neural representations. Our approach employs signed distance fields to represent structures, offering compact and smooth representations that effectively eliminate the checkerboard phenomenon commonly observed in density-based methods. IF-TONIR leverages Conditional Variational Autoencoders, which use a CNN-based encoder and a MLP-based decoder to learn and reconstruct optimal structures. We employ the features extracted from physical information as conditions to guide the decoder in generating optimal structures that adhere to specific design domain shapes and boundary conditions. Furthermore, we propose the integration of a topological loss based on persistent homology to train the model. This loss function effectively penalizes the existence of structural disconnections in the reconstructed output, thereby enhancing the overall physical reliability of the generated structures. Various experiments have demonstrated that our iteration-free topology optimization method based on implicit representations can accurately identify regions of high strain energy and generate continuous structures with low compliance. The methods also holds the theoretical capability of outputting optimal structures at any desired resolution. Our code and dataset are available on https://github.com/jbHu67/IF-TONIR.git