An Indirect Design Representation for Topology Optimization Using Variational Autoencoder and Style Transfer

Abstract

In this paper we propose an indirect low-dimension design representation to enhance topology optimization capabilities. Established topology optimization methods, such as the Solid Isotropic Material with Penalization (SIMP) method, can solve large-scale topology optimization problems efficiently, but only for certain problem formulation types (e.g., those that are amenable to efficient sensitivity calculations). The aim of the study presented in this paper is to overcome some of these challenges by taking a complementary approach: achieving efficient solution via targeted design representation dimension reduction, enabling the tractable solution of a wider range of problems (e.g., those where sensitivities are expensive or unavailable). A new data-driven design representation is proposed that uses an augmented Variational Autoencoder (VAE) to encode 2D topologies into a lower-dimensional latent space, and to decode samples from this space back into 2D topologies. Optimization is then performed in the latent space as opposed to the image space. Established topology optimization methods are used here as a tool to generate a data set for training by changing problem conditions systematically. The data is generated using problem formulations that are solvable by SIMP, and are related to (but distinct from) the desired design problem. We further introduce augmentations to the VAE formulation to reduce unrealistic scattering of small material clusters during topology generation, while ensuring diversity of the generated topologies. We compare computational expense for solving a heat conduction design problem (with respect to the latent design variables) using different optimization algorithms. The new non-dominated points obtained via the VAE representation were found and compared with the known attainable set, indicating that use of this new design representation can simultaneously improve computational efficiency and solution quality.

Deep learning for synthetic microstructure generation in a materials-by-design framework for heterogeneous energetic materials

“…The approach also provides control over the generated morphology, including the ability to spatially vary the morphological properties seamlessly. Compared to the recent deep learning based material synthesis methods 51,53,54,[56][57][58] , the advantage of the present method is the ability to scale to arbitrary size without stitching or quilting, to produce a linear and continuous control of morphology, and an ability to generate a microstructure with spatially controlled morphology. There are several avenues for further development of the current approach.…”

“…This poses a critical limitation in generating a large ensemble of microstructures that can span the space of candidate material morphologies. In another deep learning approach, Cang et al 53 and Guo et al 54 employed an encoder-decoder architecture to generate Synµ S. The encoder-decoder architecture develops a codified representation of micro-morphology by learning to compress the image pixels (encoder) and reconstruct it back to the original one (decoder). The code values learned by encoder-decoder networks parameterize micro-morphology, allowing the generation and manipulation of Synµ S by "turning knobs, " where the code values act as the knob control parameters.…”

One-shot generation of near-optimal topology through theory-driven machine learning

“…And based on these two, (3) how do we search for a good design? Challenges in answering these questions include high-dimensional or ill-defined design spaces such as for topologies [10,11], material microstructures [12,13,14], or complex geometries [15,16], expensive evaluations of designs and their sensitivities, e.g., due to model nonlinearity [17,18], coupled materials or physics [19,20,21], or subjective goodness measures [22,23], or search inefficiency due to the absence of sensitivities [24,25,26] or the existence of random variables [27].…”

“…10 Derive x * for s * by solving (TO); 11 Record δB as the number of Ku = s solved in solving (TO) and computing Eq. (6); 12 Update the budget B = B − δB;…”

Topology optimization of conductive heat transfer problems using parametric L-systems

“…Their objective is to minimize the thermal compliance of the design domain, which is discretized using both structured and unstructured meshes. Guo et al (2018) proposed a generative encoding approach based on artificial neural networks. The approach uses a variational autoencoder (Kingma and Welling 2013), the purpose of which is to reduce the dimensionality of the design via its latent layers, and deep convolutional neural networks (Krizhevsky et al 2012), to prevent the appearance of disconnected high conductive material in the designs.…”