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Register a new userInverse design of two-dimensional materials with invertible neural networks
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The ability to readily design novel materials with chosen functional properties on-demand represents a next frontier in materials discovery. However, thoroughly and efficiently sampling the entire design space in a computationally tractable manner remains a highly challenging task. To tackle this problem, we propose an inverse design framework (MatDesINNe) utilizing invertible neural networks which can map both forward and reverse processes between the design space and target property. This approach can be used to generate materials candidates for a designated property, thereby satisfying the highly sought-after goal of inverse design. We then apply this framework to the task of band gap engineering in two-dimensional materials, starting with MoS2. Within the design space encompassing six degrees of freedom in applied tensile, compressive and shear strain plus an external electric field, we show the framework can generate novel, high fidelity, and diverse candidates with near-chemical accuracy. We extend this generative capability further to provide insights regarding metal-insulator transition, important for memristive neuromorphic applications among others, in MoS2 which is not otherwise possible with brute force screening. This approach is general and can be directly extended to other materials and their corresponding design spaces and target properties.
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The large-scale search for high-performing candidate 2D materials is limited to calculating a few simple descriptors, usually with first-principles density functional theory calculations. In this work, we alleviate this issue by extending and generalizing crystal graph convolutional neural networks to systems with planar periodicity, and train an ensemble of models to predict thermodynamic, mechanical, and electronic properties. To demonstrate the utility of this approach, we carry out a screening of nearly 45,000 structures for two largely disjoint applications: namely, mechanically robust composites and photovoltaics. An analysis of the uncertainty associated with our methods indicates the ensemble of neural networks is well-calibrated and has errors comparable with those from accurate first-principles density functional theory calculations. The ensemble of models allows us to gauge the confidence of our predictions, and to find the candidates most likely to exhibit effective performance in their applications. Since the datasets used in our screening were combinatorically generated, we are also able to investigate, using an innovative method, structural and compositional design principles that impact the properties of the structures surveyed and which can act as a generative model basis for future material discovery through reverse engineering. Our approach allowed us to recover some well-accepted design principles: for instance, we find that hybrid organic-inorganic perovskites with lead and tin tend to be good candidates for solar cell applications.
Locally resonant elastic metamaterials (LREM) can be designed, by optimizing the geometry of the constituent self-repeating unit cells, to potentially damp out vibration in selected frequency ranges, thus yielding desired bandgaps. However, it remains challenging to quickly arrive at unit cell designs that satisfy any requested bandgap specifications within a given global frequency range. This paper develops a computationally efficient framework for (fast) inverse design of LREM, by integrating a new type of machine learning models called invertible neural networks or INN. An INN can be trained to predict the bandgap bounds as a function of the unit cell design, and interestingly at the same time it learns to predict the unit cell design given a bandgap, when executed in reverse. In our case the unit cells are represented in terms of the widths of the outer matrix and middle soft filler layer of the unit cell. Training data on the frequency response of the unit cell is provided by Bloch dispersion analyses. The trained INN is used to instantaneously retrieve feasible (or near feasible) inverse designs given a specified bandgap constraint, which is then used to initialize a forward constrained optimization (based on sequential quadratic programming) to find the bandgap satisfying unit cell with minimum mass. Case studies show favorable performance of this approach, in terms of the bandgap characteristics and minimized mass, when compared to the median scenario over ten randomly initialized optimizations for the same specified bandgaps. Further analysis using FEA verify the bandgap performance of a finite structure comprised of $8times 8$ arrangement of the unit cells obtained with INN-accelerated inverse design.
The combination of high throughput computation and machine learning has led to a new paradigm in materials design by allowing for the direct screening of vast portions of structural, chemical, and property space. The use of these powerful techniques leads to the generation of enormous amounts of data, which in turn calls for new techniques to efficiently explore and visualize the materials space to help identify underlying patterns. In this work, we develop a unified framework to hierarchically visualize the compositional and structural similarities between materials in an arbitrary material space with representations learned from different layers of graph convolutional neural networks. We demonstrate the potential for such a visualization approach by showing that patterns emerge automatically that reflect similarities at different scales in three representative classes of materials: perovskites, elemental boron, and general inorganic crystals, covering material spaces of different compositions, structures, and both. For perovskites, elemental similarities are learned that reflects multiple aspects of atom properties. For elemental boron, structural motifs emerge automatically showing characteristic boron local environments. For inorganic crystals, the similarity and stability of local coordination environments are shown combining different center and neighbor atoms. The method could help transition to a data-centered exploration of materials space in automated materials design.
Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is a major form of inverse design, where we optimize a designed geometry to achieve targeted properties and the geometry is parameterized by a density function. This optimization is challenging, because it has a very high dimensionality and is usually constrained by partial differential equations (PDEs) and additional inequalities. Here, we propose a new deep learning method -- physics-informed neural networks with hard constraints (hPINNs) -- for solving topology optimization. hPINN leverages the recent development of PINNs for solving PDEs, and thus does not rely on any numerical PDE solver. However, all the constraints in PINNs are soft constraints, and hence we impose hard constraints by using the penalty method and the augmented Lagrangian method. We demonstrate the effectiveness of hPINN for a holography problem in optics and a fluid problem of Stokes flow. We achieve the same objective as conventional PDE-constrained optimization methods based on adjoint methods and numerical PDE solvers, but find that the design obtained from hPINN is often simpler and smoother for problems whose solution is not unique. Moreover, the implementation of inverse design with hPINN can be easier than that of conventional methods.
The relation between unusual Mexican-hat band dispersion, ferromagnetism and ferroelasticity is investigated using a combination of analytical, first-principles and phenomenological methods. The class of material with Mexican-hat band edge is studied using the $alpha$-SnO monolayer as a prototype. Such band edge causes a van Hove singularity diverging with $frac{1}{sqrt{E}}$, and in p-type material leads to spatial and/or time-reversal spontaneous symmetry breaking. We show that an unexpected multiferroic phase is obtained in a range of hole density for which the material presents ferromagnetism and ferroelasticity simultaneously.
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