Direct prediction of material properties from microstructures through statistical models has shown to be a potential approach to accelerating computational material design with large design spaces. However, statistical modeling of highly nonlinear mappings defined on highdimensional microstructure spaces is known to be data-demanding. Thus, the added value of such predictive models diminishes in common cases where material samples (in forms of 2D or 3D microstructures) become costly to acquire either experimentally or computationally. To this end, we propose a generative machine learning model that creates an arbitrary amount of artificial material samples with negligible computation cost, when trained on only a limited amount of authentic samples. The key contribution of this work is the introduction of a morphology constraint to the training of the generative model, that enforces the resultant artificial material samples to have the same morphology distribution as the authentic ones. We show empirically that the proposed model creates artificial samples that better match with the authentic ones in material property distributions than those generated from a state-of-the-art Markov Random Field model, and thus is more effective at improving the prediction performance of a predictive structure-property model.

Integrated Computational Materials Engineering (ICME) aims to accelerate optimal design of complex material systems by integrating material science and design automation. For tractable ICME, it is required that (1) a structural feature space be identified to allow reconstruction of new designs, and (2) the reconstruction process be property-preserving. The majority of existing structural presentation schemes rely on the designer's understanding of specific material systems to identify geometric and statistical features, which could be biased and insufficient for reconstructing physically meaningful microstructures of complex material systems. In this paper, we develop a feature learning mechanism based on convolutional deep belief network to automate a two-way conversion between microstructures and their lower-dimensional feature representations,and to achieve a 1000-fold dimension reduction from the microstructure space. The proposed model is applied to a wide spectrum of heterogeneous material systems with distinct microstructural features including Ti-6Al-4V alloy, Pb63-Sn37 alloy, Fontainebleau sandstone, and Spherical colloids, to produce material reconstructions that are close to the original samples with respect to 2-point correlation functions and mean critical fracture strength. This capability is not achieved by existing synthesis methods that rely on the Markovian assumption of material microstructures. * The paper is accepted by JMD 1 arXiv:1612.07401v3 [cond-mat.mtrl-sci]

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.

We introduce a theory-driven mechanism for learning a neural network model that performs generative topology design in one shot given a problem setting, circumventing the conventional iterative process that computational design tasks usually entail. The proposed mechanism can lead to machines that quickly response to new design requirements based on its knowledge accumulated through past experiences of design generation. Achieving such a mechanism through supervised learning would require an impractically large amount of problem-solution pairs for training, due to the known limitation of deep neural networks in knowledge generalization. To this end, we introduce an interaction between a student (the neural network) and a teacher (the optimality conditions underlying topology optimization): The student learns from existing data and is tested on unseen problems. Deviation of the student's solutions from the optimality conditions is quantified, and used for choosing new data points to learn from. We call this learning mechanism "theory-driven", as it explicitly uses domain-specific theories to guide the learning, thus distinguishing itself from purely data-driven supervised learning. We show through a compliance minimization problem that the proposed learning mechanism leads to topology generation with near-optimal structural compliance, much improved from standard supervised learning under the same computational budget. example, the design of vehicle body-in-white is often done by experienced structure engineers, since topology optimization (TO) on full-scale crash simulation is not yet fast enough to respond to requests from higher-level design tasks, e.g., geometry design with style and aerodynamic considerations, and thus may slow down the entire design process 1 .Research exists in developing deep neural network models that learn to create structured solutions in a one-shot fashion, circumventing the need of iterations (e.g., in solving systems of equations [1], simulating dynamical systems [2], or searching for optimal solutions [3,4,5]). Learning of such models through data, however, is often criticized to have limited generalization capability, especially when highly nonlinear input-output relations or highdimensional output spaces exist [6,7,8]. In the context of TO, this means that the network may create structures with unreasonably poor physical properties when it responds to new problem settings. More concretely, consider a topology with a tiny crack in one of its trusses. This design would be far from optimal if the goal is to lower compliance, yet standard datadriven learning mechanisms do not prevent this from happening, i.e., they don't know that they don't know (physics).Our goal is to create a learning mechanism that knows what it does not know, and thus can self-improve in an effective way. Specifically, we are curious about how physicsbased knowledge, e.g., in the forms of dynamical models, theoretical bounds, and optimality conditions, can be directly injected into the learning of networks that ...

Computational material design (CMD) aims to accelerate optimal design of complex material systems by integrating material science and design automation. For tractable CMD, it is required that (1) a feature space be identified to allow reconstruction of new designs, and (2) the reconstruction process be property-preserving. Existing solutions rely on the designer’s understanding of specific material systems to identify geometric and statistical features, which could be insufficient for reconstructing physically meaningful microstructures of complex material systems. This paper develops a feature learning mechanism that automates a two-way conversion between microstructures and their lower-dimensional feature representations. The proposed model is applied to four material systems: Ti-6Al-4V alloy, Pb-Sn alloy, Fontainebleau sandstone, and spherical colloids, to produce random reconstructions that are visually similar to the samples. This capability is not achieved by existing synthesis methods relying on the Markovian assumption of material systems. For Ti-6Al-4V alloy, we also show that the reconstructions preserve the mean critical fracture force of the system for a fixed processing setting. Source code and datasets are available.