Towards deep generation of guided wave representations for composite materials

Laminated composite materials are widely used in most fields of engineering. Wave propagation analysis plays an essential role in understanding the short-duration transient response of composite structures. The forward physics-based models are utilized to map from elastic properties space to wave propagation behavior in a laminated composite material. Due to the high-frequency, multi-modal, and dispersive nature of the guided waves, the physics-based simulations are computationally demanding. It makes property prediction, generation, and material design problems more challenging. In this work, a forward physics-based simulator such as the stiffness matrix method is utilized to collect group velocities of guided waves for a set of composite materials. A variational autoencoder (VAE)-based deep generative model is proposed for the generation of new and realistic polar group velocity representations. It is observed that the deep generator is able to reconstruct unseen representations with very low mean square reconstruction error. Global Monte Carlo and directional equally-spaced samplers are used to sample the continuous, complete and organized low-dimensional latent space of VAE. The sampled point is fed into the trained decoder to generate new polar representations. The network has shown exceptional generation capabilities. It is also seen that the latent space forms a conceptual space where different directions and regions show inherent patterns related to the generated representations and their corresponding material properties

Smoothing the Rough Edges: Evaluating Automatically Generated Multi-Lattice Transitions

Additive manufacturing is advantageous for producing lightweight components while addressing complex design requirements. This capability has been bolstered by the introduction of unit lattice cells and the gradation of those cells. In cases where loading varies throughout a part, it may be beneficial to use multiple, distinct lattice cell types, resulting in multi-lattice structures. In such structures, abrupt transitions between unit cell topologies may cause stress concentrations, making the boundary between unit cell types a primary failure point. Thus, these regions require careful design in order to ensure the overall functionality of the part. Although computational design approaches have been proposed, smooth transition regions are still difficult to achieve, especially between lattices of drastically different topologies. This work demonstrates and assesses a method for using variational autoencoders to automate the creation of transitional lattice cells, examining the factors that contribute to smooth transitions. Through computational experimentation, it was found that the smoothness of transition regions was strongly predicted by how closely the endpoints were in the latent space, whereas the number of transition intervals was not a sole predictor.Comment: 23 Pages, 8 Figure

Hybrid Geometry/Property Autoencoders for Multi-Lattice Transitions

Additive manufacturing has revolutionized structural optimization by enhancing component strength and reducing material requirements. One approach used to achieve these improvements is the application of multi-lattice structures. The performance of these structures heavily relies on the detailed design of mesostructural elements. Many current approaches use data-driven design to generate multi-lattice transition regions, making use of models that jointly address the geometry and properties of the mesostructures. However, it remains unclear whether the integration of mechanical properties into the data set for generating multi-lattice interpolations is beneficial beyond geometry alone. To address this issue, this work implements and evaluates a hybrid geometry/property machine learning model for generating multi-lattice transition regions. We compare the results of this hybrid model to results obtained using a geometry-only model. Our research determined that incorporating physical properties decreased the number of variables to address in the latent space, and therefore improves the ability of generative models for developing transition regions of multi-lattice structures.Mechanical Engineerin

Microstructure reconstruction of 2D/3D random materials via diffusion-based deep generative models

Microstructure reconstruction serves as a crucial foundation for establishing Process-Structure-Property (PSP) relationship in material design. Confronting the limitations of variational autoencoder and generative adversarial network within generative modeling, this study adopted the denoising diffusion probability model (DDPM) to learn the probability distribution of high-dimensional raw data and successfully reconstructed the microstructures of various composite materials, such as inclusion materials, spinodal decomposition materials, chessboard materials, fractal noise materials, and so on. The quality of generated microstructure was evaluated using quantitative measures like spatial correlation functions and Fourier descriptor. On this basis, this study also successfully achieved the regulation of microstructure randomness and the generation of gradient materials through continuous interpolation in latent space using denoising diffusion implicit model (DDIM). Furthermore, the two-dimensional microstructure reconstruction is extended to three-dimensional framework and integrates permeability as a feature encoding embedding. This enables the conditional generation of three-dimensional microstructures for random porous materials within a defined permeability range. The permeabilities of these generated microstructures were further validated through the application of the Boltzmann method

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

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry-property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from geometry to properties. We further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (relative error <5%) and 2) improve the optimized structural performance over the conventional topology-optimized variable-density structure. Specifically, in the minimum compliance example, our IH-GAN generated structure achieves an 84.4% reduction in concentrated stress and an extra 7% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 24.2% and 44.4% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending

Image-based Artificial Intelligence empowered surrogate model and shape morpher for real-time blank shape optimisation in the hot stamping process

As the complexity of modern manufacturing technologies increases, traditional trial-and-error design, which requires iterative and expensive simulations, becomes unreliable and time-consuming. This difficulty is especially significant for the design of hot-stamped safety-critical components, such as ultra-high-strength-steel (UHSS) B-pillars. To reduce design costs and ensure manufacturability, scalar-based Artificial-Intelligence-empowered surrogate modelling (SAISM) has been investigated and implemented, which can allow real-time manufacturability-constrained structural design optimisation. However, SAISM suffers from low accuracy and generalisability, and usually requires a high volume of training samples. To solve this problem, an image-based Artificial-intelligence-empowered surrogate modelling (IAISM) approach is developed in this research, in combination with an auto-decoder-based blank shape generator. The IAISM, which is based on a Mask-Res-SE-U-Net architecture, is trained to predict the full thinning field of the as-formed component given an arbitrary blank shape. Excellent prediction performance of IAISM is achieved with only 256 training samples, which indicates the small-data learning nature of engineering AI tasks using structured data representations. The trained auto-decoder, trained Mask-Res-SE-U-Net, and Adam optimiser are integrated to conduct blank optimisation by modifying the latent vector. The optimiser can rapidly find blank shapes that satisfy manufacturability criteria. As a high-accuracy and generalisable surrogate modelling and optimisation tool, the proposed pipeline is promising to be integrated into a full-chain digital twin to conduct real-time, multi-objective design optimisation.Comment: 32 pages, 11 figure

Machine Learning of Implicit Combinatorial Rules in Mechanical Metamaterials

Combinatorial problems arising in puzzles, origami, and (meta)material design have rare sets of solutions, which define complex and sharply delineated boundaries in configuration space. These boundaries are difficult to capture with conventional statistical and numerical methods. Here we show that convolutional neural networks can learn to recognize these boundaries for combinatorial mechanical metamaterials, down to finest detail, despite using heavily undersampled training sets, and can successfully generalize. This suggests that the network infers the underlying combinatorial rules from the sparse training set, opening up new possibilities for complex design of (meta)materials

Learning from Invalid Data: On Constraint Satisfaction in Generative Models

Generative models have demonstrated impressive results in vision, language, and speech. However, even with massive datasets, they struggle with precision, generating physically invalid or factually incorrect data. This is particularly problematic when the generated data must satisfy constraints, for example, to meet product specifications in engineering design or to adhere to the laws of physics in a natural scene. To improve precision while preserving diversity and fidelity, we propose a novel training mechanism that leverages datasets of constraint-violating data points, which we consider invalid. Our approach minimizes the divergence between the generative distribution and the valid prior while maximizing the divergence with the invalid distribution. We demonstrate how generative models like GANs and DDPMs that we augment to train with invalid data vastly outperform their standard counterparts which solely train on valid data points. For example, our training procedure generates up to 98 % fewer invalid samples on 2D densities, improves connectivity and stability four-fold on a stacking block problem, and improves constraint satisfaction by 15 % on a structural topology optimization benchmark in engineering design. We also analyze how the quality of the invalid data affects the learning procedure and the generalization properties of models. Finally, we demonstrate significant improvements in sample efficiency, showing that a tenfold increase in valid samples leads to a negligible difference in constraint satisfaction, while less than 10 % invalid samples lead to a tenfold improvement. Our proposed mechanism offers a promising solution for improving precision in generative models while preserving diversity and fidelity, particularly in domains where constraint satisfaction is critical and data is limited, such as engineering design, robotics, and medicine