Session: 12-06-02: Scientific Machine Learning (SciML) for Characterization, Modeling, and Design of Structures and Materials
Paper Number: 144057
144057 - Neural Topology Optimization Based on Differential Programming With Principled Constrained Optimization
Topology optimization (TO) seeks to determine the optimal distribution of material within a specified design domain for maximizing the structural performance while adhering to predefined constraints. Recent advancements in deep learning and neural network representations have shown significant promise in approximating PDE solutions, opening up a new avenue for synergy between these technologies and TO. In this study, we introduce a differential programming-based TO framework that leverages effective non-convex optimization with the deep image prior (DIP) approach for the re-parameterization of the density field, with a focus on addressing the inherent challenges of TO due to combinatorial constraints. The proposed TO algorithm is developed based on a in-house non-convex optimization algorithm PyGranso, which provides a robust optimization method with the ability to handle non-convex, non-smooth and non-linear constrained optimization problems; thus, it enables higher effectiveness in navigating the complex constraint space for TO problems and enabling the discovery of optimal designs. Furthermore, the employment of DIP to parameterize the density field enhances the capacity of design representation and enforces higher smoothness as it leverages the latent structure of convolutional neural networks (CNNs).
Compared with other (conventional and machine learning based) TO methods, our experimental results demonstrate the superiority of our proposed framework, especially in accurately preserving the constraints. By systematically evaluating its performance across a range of classical TO problems, including (1) MBB beam, (2) complex cases such as L-shaped structures with tricky loading paths, and (3) situations requiring the use of multiple materials in one design, the MBB beam, L-shaped structure with complex loading path, and the multi-material design problem, we have shown that our approach not only yields improved design in terms of material efficiency and structural integrity but also significantly enhances the feasibility of the optimization solutions. Our evaluation of TO methods is based on three key metrics: objective function (compliance), binary constraint adherence and volume constraint adherence. We compare our proposed method against the established Solid Isotropic Material with Penalization (SIMP) approach coupled with the Method of Moving Asymptotes (MMA). For example, in the case of the Cantilever Beam, MMA achieves a compliance of 255.66, incurs a binary constraint violation of 0.0609, and meets the volume constraint at 0.0. In contrast, our method achieves an improved compliance of 223.65 with zero violations in both binary and volume constraints. These results are consistent across various structures, highlighting our method’s ability to generate stiff and feasible designs.
Presenting Author: Ryan Devera University of Minnesota
Presenting Author Biography: Ryan Devera is currently in his second year as a PhD student in Computer Science & Engineering at University of Minnesota, working with Prof. Ju Sun on constrained deep learning and AI for science and engineering at large. Before this, he worked for eight years as a senior data scientist, project manager, and technical mentor in various start-up companies. He holds a master degree in applied mathematics and bachelor degrees in mathematics and physics.
Authors:
Ryan Devera University of MinnesotaBuyun Liang University of Minnesota
Binyao Guo University of Minnesota
Qizhi He University of Minnesota
Ju Sun University of Minnesota
Neural Topology Optimization Based on Differential Programming With Principled Constrained Optimization
Paper Type
Technical Presentation