Accelerating metamaterial topology optimization using deep super-resolution networks

TL;DR

This paper tackles the high computational cost of metamaterial topology optimization by learning a mapping from low-resolution designs to high-resolution topologies using Enhanced Deep Super-Resolution (EDSR). It builds a SIMP-based data pipeline to generate LR–HR pairs across four mechanical objectives and trains a CNN with residual blocks to predict HR designs from LR inputs. The work introduces a 12-block, 128-channel EDSR architecture with a 2x upscaling module, validated on 4000 training samples and 150-test samples, achieving IoU above 0.9 and pixel errors around 2–3% while reducing computation to about 5–7% of conventional SIMP TO. This approach yields manufacturable, high-fidelity HR metamaterial designs at a fraction of the time, with potential extensions to physics-informed and multi-physics optimization to broaden applicability.

Abstract

Designing metamaterials for extreme mechanical behavior involves the optimal selection of design parameters. However, identifying these optimal parameters through topology optimization (TO) across a large parametric space requires extensive computational resources. To address this challenge, we propose a novel deep learning framework for metamaterial topology optimization using an enhanced deep super-resolution (EDSR) approach. Generating low-resolution topologies significantly reduces computational cost compared to high-resolution designs. Therefore, an EDSR network is trained to learn the mapping between low- and high-resolution metamaterial topologies. The training dataset is generated using solid isotropic material with penalization (SIMP)-based TO. We demonstrate the proposed approach for the design of mechanical metamaterials targeting objectives such as maximization of bulk modulus, shear modulus, and elastic modulus, and minimization of Poisson's ratio. Quantitative assessments -including (i) pixel value error, (ii) objective function error, (iii) intersection over union, and (iv) volume fraction error -validate the accuracy of the EDSR-based TO. Our framework predicts high-resolution topologies of size $192 \times 192$ from optimized low-resolution topologies of size $48 \times 48$. Once trained, the proposed network predicts these high-resolution topologies with only $5-7\%$ of the computational cost required by conventional SIMP-based TO at the same resolution. Moreover, by adding upscale blocks, the framework can generate smoother, higher-resolution topologies suitable for 3D printing. This approach offers a scalable and efficient solution with strong potential for multidisciplinary metamaterial design applications.

Figures (15)

• Figure 1: Illustration of a material constituted by periodically arranged microstructures.
• Figure 2: Dirichlet boundary conditions (DBC's): (a)DBC1$:[u_{x}=0 \text{ on } \Gamma_L, u_{y}=0 \text{ on } \Gamma_T, u_{y}=0 \text{ on } \Gamma_B, u_{x}=1 \text{ on } \Gamma_R]$. (b) DBC2$:[u_{x}=0 \text{ on } \Gamma_L, u_{y}=1 \text{ on } \Gamma_T, u_{y}=0 \text{ on } \Gamma_B, u_{x}=0 \text{ on } \Gamma_R]$.
• Figure 3: Cone filter. The cone filter functions by performing a weighted averaging of parameter values from neighboring elements or cells located within a defined radius. (Top) Elements denoted as $ele_b$ within the vicinity of $ele_a$ are taken into account for the density filtering process. (Bottom) The weight factor ($W_b$) varies as the distance from $ele_a$ increases. It is important to observe that the weight factor becomes zero beyond the filter zone indicated by $r_{min}$.
• Figure 4: Illustrating a convolution operation instance featuring a $3 \times 3$ kernel size, same padding, and a stride of one. In this procedure, the kernel moves across the input tensor, and at each location, it performs an element-wise multiplication with the input tensor. The results are added together to obtain the output value at the respective position in the output tensor, commonly known as a feature map.
• Figure 5: Illustrating the detailed flow of an enhanced deep super-resolution (EDSR) and its key component, it shows the step-by-step process of enhancing image resolution.