IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures

Abstract

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologicallyoptimized, functionally graded structures, particularly when those structures are represented as discrete density maps. One naïve approach to creating variable-density cellular structures is simply replacing the discrete density map with an unselective type of unit cells having corresponding densities. However, doing so breaks the desired mechanical behavior, as equivalent density alone does not guarantee equivalent mechanical properties. Another approach uses homogenization methods to estimate each pre-defined unit cell's effective properties and remaps the unit cells following a scaling law. However, a scaling law merely mitigates the problem by performing an indirect and inaccurate mapping from the material property space to singletype unit cells. In contrast, we propose a deep generative model that resolves this problem by automatically learning an accurate mapping and generating diverse cellular unit cells conditioned on desired properties (i.e., Young's modulus and Poisson's ratio). We demonstrate our method via the use of implicit function-based unit cells and conditional generative adversarial networks. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (relative error < 5%), 2) create functionally graded cellular structures with high-quality interface connectivity (98.7% average overlap area at interfaces), and 3) improve the structural performance over the conventional topology-optimized variabledensity structure (84.4% reduction in concentrated stress and extra 7% reduction in displacement).

t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning

“…On the other hand, the corresponding property distributions in Figure 2(c) show considerable imbalance, which epitomizes that data balance in parametric shape space does not ensure that in property space. By extension, we argue that such property imbalance is prevalent in many metamaterial datasets generated by space-filling design in parametric shape space [16,11,17,22,23]. We claim that: (i) any metamaterial dataset collected based on naive sampling in parametric shape space are subject to substantial property bias [16,11,17,22,23], and more importantly, (ii) this is highly likely to hold true for datasets with generic design representations -other than parametric ones -as well [11,19,10,24,25].…”

“…Underestimating the risk, common practice in DDMD typically resorts to a large number of space-filling designs in the shape space spanned by the shape parameters. This inevitably hosts imbalance -distributional bias of data -in the property space [15,16,11,17] formed by the property vectors. The succeeding tasks involving a data-driven modeltraining, validation, and deployment to design -follow mostly without rigorous assessment on data quality in terms of diversity, design quality, feasibility, etc.…”

Range-GAN: Range-Constrained Generative Adversarial Network for Conditioned Design Synthesis

“…While we validated our proposed model on a 3D shape synthesis example, the method is not restricted to this application. For example, by replacing the latent vector with parameters of unit cell shapes, this model can also help address the inverse design problem of cellular structures [24].…”

“…This allows us to generate many designs conditioned on any performance requirement; i.e., the mapping from the performance space to the design space can be one-to-many. This technique has been used for the inverse design of metasurfaces, metamaterials, and cellular structures [12,13,24]. As pointed out in [25], however, conditional generative models with continuous conditions may fail.…”

“…Similar to the idea of adding an auxiliary classifier/regressor to the cGAN [36,24] to improve generation quality or enforce accurate conditioning, we use a label estimator to guide the generator during training to generate designs that meet input con-straints. In this way, we utilize the discriminator's insight into the data distribution to promote synthesis of realistic designs while simultaneously using the estimator's insight to guide the generator towards meeting input requirements.…”