The problem of efficient design of material microstructures exhibiting desired properties spans a variety of engineering and science applications. An ability to rapidly generate microstructures that exhibit user-specified property distributions transforms the iterative process of traditional microstructure-sensitive design. We reformulate the microstructure design process as a constrained Generative Adversarial Network (GAN). This approach explicitly encodes invariance constraints within a GAN to generate two-phase morphologies for photovoltaic applications obeying design specifications: specifically, various short circuit current density and fill-factor combinations. Such invariance constraints can be represented by deep learning-based surrogates of full physics models mapping microstructure to photovoltaic properties. To circumvent data generation bottlenecks, we utilize a multi-fidelity surrogate that reduces the requirements of expensive labels by 5X. Our approach enables fast generation of microstructures (in ≈190ms) with user-defined properties. Such physics-aware data-driven methods for inverse design problems are expected to democratize and accelerate the field of microstructure-sensitive design.

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The problem of efficient design of material microstructures exhibiting desired properties spans a variety of engineering and science applications. An ability to rapidly generate microstructures that exhibit user-specified property distributions transforms the iterative process of traditional microstructure-sensitive design. We reformulate the microstructure design process as a constrained Generative Adversarial Network (GAN). This approach explicitly encodes invariance constraints within a GAN to generate two-phase morphologies for photovoltaic applications obeying design specifications: specifically, various short circuit current density and fill-factor combinations. Such invariance constraints can be represented by deep learning-based surrogates of full physics models mapping microstructure to photovoltaic properties. To circumvent data generation bottlenecks, we utilize a multi-fidelity surrogate that reduces the requirements of expensive labels by 5X. Our approach enables fast generation of microstructures (in~190ms) with user-defined properties. Such physics-aware data-driven methods for inverse design problems are expected to democratize and accelerate the field of microstructure-sensitive design.

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Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention. However, the large majority of neural PDE solvers only apply to rectilinear domains, and do not systematically address the imposition of Dirichlet/Neumann boundary conditions over irregular domain boundaries. In this paper, we present a framework to neurally solve partial differential equations over domains with irregularly shaped (nonrectilinear) geometric boundaries. Our network takes in the shape of the domain as an input (represented using an unstructured point cloud, or any other parametric representation such as Non-Uniform Rational B-Splines) and is able to generalize to novel (unseen) irregular domains; the key technical ingredient to realizing this model is a novel approach for identifying the interior and exterior of the computational grid in a differentiable manner. We also perform a careful error analysis which reveals theoretical insights into several sources of error incurred in the model-building process. Finally, we showcase a wide variety of applications, along with favorable comparisons with ground truth solutions.