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The controlled introduction of elastic strains is an appealing strategy for modulating the physical properties of semiconductor materials. With the recent discovery of large elastic deformation in nanoscale specimens as diverse as silicon and diamond, employing this strategy to improve device performance necessitates first-principles computations of the fundamental electronic band structure and target figures-of-merit, through the design of an optimal straining pathway. Such simulations, however, call for approaches that combine deep learning algorithms and physics of deformation with band structure calculations to custom-design electronic and optical properties. Motivated by this challenge, we present here details of a machine learning framework involving convolutional neural networks to represent the topology and curvature of band structures in k-space. These calculations enable us to identify ways in which the physical properties can be altered through “deep” elastic strain engineering up to a large fraction of the ideal strain. Algorithms capable of active learning and informed by the underlying physics were presented here for predicting the bandgap and the band structure. By training a surrogate model with ab initio computational data, our method can identify the most efficient strain energy pathway to realize physical property changes. The power of this method is further demonstrated with results from the prediction of strain states that influence the effective electron mass. We illustrate the applications of the method with specific results for diamonds, although the general deep learning technique presented here is potentially useful for optimizing the physical properties of a wide variety of semiconductor materials. Nanyang Technological University Published version The computations involved in this work were conducted on the computer cluster at Skolkovo Institute of Science and Technology (Skoltech) CEST Multiscale Molecular Modelling group and Massachusetts Institute of Technology (MIT) Nuclear Science Engineering department. E.T., Z.S., A.S., and J.L. acknowledge support by the Skoltech-MIT Next Generation Program 2016-7/NGP. E.T. and A.S. acknowledge support by the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy Office of Science by Los Alamos National Laboratory (Contract 89233218CNA000001) and Sandia National Laboratories (Contract DE-NA-0003525). M.D. acknowledges support from MIT J-Clinic for Machine Learning and Health. S.S. acknowledges support from Nanyang Technological University through the Distinguished University Professorship.

Significance Identifying the conditions for complete metallization of diamond solely through mechanical strain is an important scientific objective and technological demonstration. Through quantum mechanical calculations, continuum mechanics simulations validated by experiments, and machine learning, we show here that reversible metallization can be achieved in diamond deformed below threshold elastic strain levels for failure or phase transformation. The general method outlined here for deep elastic strain engineering is also applicable to map the strain conditions for indirect-to-direct bandgap transitions. Our method and findings enable extreme alterations of semiconductor properties via strain engineering for possible applications in power electronics, optoelectronics, and quantum sensing., Experimental discovery of ultralarge elastic deformation in nanoscale diamond and machine learning of its electronic and phonon structures have created opportunities to address new scientific questions. Can diamond, with an ultrawide bandgap of 5.6 eV, be completely metallized, solely under mechanical strain without phonon instability, so that its electronic bandgap fully vanishes? Through first-principles calculations, finite-element simulations validated by experiments, and neural network learning, we show here that metallization/demetallization as well as indirect-to-direct bandgap transitions can be achieved reversibly in diamond below threshold strain levels for phonon instability. We identify the pathway to metallization within six-dimensional strain space for different sample geometries. We also explore phonon-instability conditions that promote phase transition to graphite. These findings offer opportunities for tailoring properties of diamond via strain engineering for electronic, photonic, and quantum applications.

Nanoscale specimens of semiconductor materials as diverse as silicon and diamond are now known to be deformable to large elastic strains without inelastic relaxation. These discoveries harbinger a new age of deep elastic strain engineering of the band structure and device performance of electronic materials. Many possibilities remain to be investigated as to what pure silicon can do as the most versatile electronic material and what an ultrawide bandgap material such as diamond, with many appealing functional figures of merit, can offer after overcoming its present commercial immaturity. Deep elastic strain engineering explores full six-dimensional space of admissible nonlinear elastic strain and its effects on physical properties. Here we present a general method that combines machine learning and ab initio calculations to guide strain engineering whereby material properties and performance could be designed. This method invokes recent advances in the field of artificial intelligence by utilizing a limited amount of ab initio data for the training of a surrogate model, predicting electronic bandgap within an accuracy of 8 meV. Our model is capable of discovering the indirect-to-direct bandgap transition and semiconductor-to-metal transition in silicon by scanning the entire strain space. It is also able to identify the most energy-efficient strain pathways that would transform diamond from an ultrawide-bandgap material to a smaller-bandgap semiconductor. A broad framework is presented to tailor any target figure of merit by recourse to deep elastic strain engineering and machine learning for a variety of applications in microelectronics, optoelectronics, photonics, and energy technologies. Published version

We develop a new compact scheme for second-order PDE (parabolic and Schr\"odinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary problems are considered. The relative finite-difference operator is almost self-adjoint., Comment: v2

In this work, we consider the problem of uncertainty estimation for Transformer-based models. We investigate the applicability of uncertainty estimates based on dropout usage at the inference stage (Monte Carlo dropout). The series of experiments on natural language understanding tasks shows that the resulting uncertainty estimates improve the quality of detection of error-prone instances. Special attention is paid to the construction of computationally inexpensive estimates via Monte Carlo dropout and Determinantal Point Processes.

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A compact difference scheme on a three-point stencil for an unknown function is proposed. The scheme approximates a second-order linear differential equation with a variable smooth coefficient. Our numerical experiment confirms the fourth order of accuracy of the solution of the difference scheme and of the approximation of the eigenvalues of the boundary problem. The difference operator is almost self-adjoint and its spectrum is real. Richardson extrapolation helps to increase the order of accuracy.

Testing of distributed systems is a complex task, which is hampered by the impossibility of guaranteed reproduction of errors associated with race conditions. Even minor instrumentation of the system significantly changes its characteristics, which becomes critical, especially for load testing. All of that increases the importance of quality control methods based on the system log analysis. In this paper, we present our experience of semi-automated analysis of the behavior of clearing and settlement system by utilizing its logs for the purpose of identifying and classifying errors.

Active learning methods for neural networks are usually based on greedy criteria, which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one active learning iteration, or retraining the neural network after adding each data point, which is computationally inefficient. Moreover, uncertainty estimates for neural networks sometimes are overconfident for the points lying far from the training sample. In this work, we propose to approximate Bayesian neural networks (BNN) by Gaussian processes (GP), which allows us to update the uncertainty estimates of predictions efficiently without retraining the neural network while avoiding overconfident uncertainty prediction for out-of-sample points. In a series of experiments on real-world data, including large-scale problems of chemical and physical modeling, we show the superiority of the proposed approach over the state-of-the-art methods.

Active learning is relevant and challenging for high-dimensional regression models when the annotation of the samples is expensive. Yet most of the existing sampling methods cannot be applied to large-scale problems, consuming too much time for data processing. In this paper, we propose a fast active learning algorithm for regression, tailored for neural network models. It is based on uncertainty estimation from stochastic dropout output of the network. Experiments on both synthetic and real-world datasets show comparable or better performance (depending on the accuracy metric) as compared to the baselines. This approach can be generalized to other deep learning architectures. It can be used to systematically improve a machine-learning model as it offers a computationally efficient way of sampling additional data.