Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs the interior conductivity distribution of samples from a set of voltage measurements performed on the sample boundary. EIT reconstruction is a non-linear and ill-posed inverse problem. Consequently, the non-linearity results in a high computational cost of solution, while regularisation and the most informative measurements must be used to overcome ill-posedness. To build the foundation of future research into EIT applications for 2D materials, such as graphene, we designed and implemented a novel approach to measurement optimisation via a machine learning adaptive electrode selection algorithm (A-ESA). Furthermore, we modified the forward solver of a python-based EIT simulation software, pyEIT, to include the complete electrode model (CEM) and employed it on 2D square samples [1, 2]. In addition, the Deep D-Bar U-Net convolutional neural network architecture was applied to post-process conductivity map reconstructions from the GREIT algorithm [3, 4]. The A-ESA offered around 20% lower reconstruction losses in fewer measurements than the standard opposite-adjacent electrode selection algorithm, on both simulated data and when applied to a real graphene-based device. The CEM enhanced forward solver achieved a 3% lower loss compared to the original pyEIT forward model. Finally, an experimental evaluation was performed on a graphene laminate film. Overall, this work demonstrates how EIT could be applied to 2D materials and highlights the utility of machine learning in both the experimental and analytical aspects of EIT.
Many-body physics of electron-electron correlations plays a central role in condensed mater physics, it governs a wide range of phenomena, stretching from superconductivity to magnetism, and is behind numerous technological applications. To explore this rich interaction-driven physics, two-dimensional (2D) materials with flat electronic bands provide a natural playground thanks to their highly localised electrons. Currently, thousands of 2D materials with computed electronic bands are available in open science databases, awaiting such exploration. Here we used a new machine learning algorithm combining both supervised and unsupervised machine intelligence to automate the otherwise daunting task of materials search and classification, to build a genome of 2D materials hosting flat electronic bands. To this end, a feedforward artificial neural network was employed to identify 2D flat band materials, which were then classified by a bilayer unsupervised learning algorithm. Such a hybrid approach of exploring materials databases allowed us to reveal completely new material classes outside the known flat band paradigms, offering new systems for in-depth study on their electronic interactions.
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