Universal Machine Learning for Topology Optimization

Topology optimization is a powerful computational tool that has been extensively implemented in several major commercial software, and successfully used in many industrial applications (e.g. aerospace and automotive). Because topology optimization is an iterative procedure, a major limitation of it is its computational expense. A topology optimization problem typically involves hundreds of design iterations, and in order to update the current design, the structural response needs to be solved to compute the sensitivity (gradient) information. To handle large-scale topology optimization problems (e.g., problems involves millions of design variables and beyond), the associated computational cost could be enormous, and one typically needs to resort to parallel computing, advanced iterative solvers, or multi-scale and multi-resolution approaches.

In this talk, we will introduce a general machine learning-based topology optimization framework which utilizes the concept of online learning to greatly accelerate the design process of large-scale problems in 3D. The proposed framework has several unique and novel features. First, unlike many existing machine learning-based frameworks in the topology optimization literature, where the machine learning model is trained offline prior to topology optimization via expensive data collection procedures, the machine learning module of the proposed framework is trained online during the topology optimization. Second, the proposed framework adopts a tailored multi-scale discretization setup which enables a training strategy which is based on local data. More specifically, the architecture of the Neural Network (NN) is designed such that only the local information (e.g., state and design variables) in the neighborhood region of a given design variable is used to predict its corresponding sensitivity. This localized training strategy is shown to improve both the scalability and accuracy of the proposed framework. Third, the framework incorporates an online update scheme which continuously reinforces the machine learning module with new physics-based simulation data to improve its prediction accuracy. The proposed machine learning-based topology optimization framework is universal in the sense that it can work with any suitable machine learning model and has the potential to be applied in wide range of topology optimization problems (e.g., minimum compliance, compliant mechanism, maximum thermal conductivity, and so on) without worrying the generalizability of the learned mapping. Through numerical investigations and several design examples of various problem size, we demonstrate that the proposed framework is accurate and highly scalable and can efficiently handle design problem with a wide range of discretization levels and types, different load and boundary conditions, and various design considerations.