Abstract
This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a one-scale design on a fine mesh, we avoid solving the least square problems associated with traditional de-homogenization approaches and save time correspondingly. To train the neural network, a two-step custom loss function has been developed which ensures a periodic output field that follows the local lamination orientations. A key feature of the proposed method is that the training is carried out without any use of or reference to the underlying structural optimization problem, which renders the proposed method robust and insensitive wrt domain size, boundary conditions, and loading. A post-processing procedure utilizing a distance transform on the output field skeleton is used to project the desired lamination widths onto the output field while ensuring a predefined minimum length-scale and volume fraction. To demonstrate that the deep learning approach has excellent generalization properties, numerical examples are shown for several different load and boundary conditions. For an appropriate choice of parameters, the de-homogenized designs perform within 7–25% of the homogenization-based solution at a fraction of the computational cost. With several options for further improvements, the scheme may provide the basis for future interactive high-resolution topology optimization.
Highlights
In many ways the fields of computer vision and topology optimization are closely related, e.g. in both cases, the optimization domain constitutes a set of elements/pixels in a grid, and the problem can be formulated as minimizing a functional to obtain an optimized configuration
Due to the closeness of the tasks, it is only reasonable to assume that some of the impact which deep learning has had on the field of computer vision will transfer to the field of topology optimization
Deep learning has yet to make a major impact within topology optimization, and only performs at a similar level to traditional topology optimization methods at very low design resolutions, or for highly restricted problem domains and boundary conditions, where the cost of generating a synthetic dataset and training a neural network is not prohibitive
Summary
In many ways the fields of computer vision and topology optimization are closely related, e.g. in both cases, the optimization domain constitutes a set of elements/pixels in a grid, and the Figure 2: Data pipeline from orientation field to intermediate density field on to one-scale design. For end-to-end machine learning to have a significant impact on the field of topology optimization, it is clearly a requirement that it is faster and scales better, and that the solutions produced are of comparable quality to those computed using more conventional optimization methods [9] This must be true even when the network is provided inputs that are very different from those in the training data. We report on a deep learning approach that allows for problem definition generalization and which is capable of producing high resolution and detailed designs The key to this achievement lies in the fact that the proposed method does not provide an end-to-end topology optimization approach.
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