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.

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 ...

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An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by Partial Differential Equation (PDE), and its loading/ response mapping can be solved using Finite Element Analysis (FEA). Based on this, a special type of deep convolutional neural network (DCNN) is proposed that takes advantage of our prior knowledge in physics to build data-driven models whose architectures are of physics meaning. This type of network is named as FEA-Net and is used to solve the mechanical response under external loading. Thus, the identification of a mechanical system parameters and the computation of its responses are treated as the learning and inference of FEA-Net, respectively. Case studies on multi-physics (e.g., coupled mechanical-thermal analysis) and multi-phase problems (e.g., composite materials with random micro-structures) are used to demonstrate and verify the theoretical and computational advantages of the proposed method.