We demonstrate a first-principles method to study magnetotransport in materials by solving the Boltzmann transport equation (BTE) in the presence of an external magnetic field. Our approach employs ab initio electronphonon interactions and takes spin-orbit coupling into account. We apply our method to various semiconductors (Si and GaAs) and two-dimensional (2D) materials (graphene) as representative case studies. The magnetoresistance, Hall mobility, and Hall factor in Si and GaAs are in very good agreement with experiments. In graphene, our method predicts a large magnetoresistance, consistent with experiments. Analysis of the steady-state electron occupations in graphene shows the dominant role of optical phonon scattering and the breaking of the relaxation time approximation. Our paper provides a detailed understanding of the microscopic mechanisms governing magnetotransport coefficients, establishing the BTE in a magnetic field as a broadly applicable first-principles tool to investigate transport in semiconductors and 2D materials.
Noise and uncertainty are usually the enemy of machine learning, noise in training data leads to uncertainty and inaccuracy in the predictions. However, we develop a machine learning architecture that extracts crucial information out of the noise itself to improve the predictions. The phenomenology computes and then utilizes uncertainty in one target variable to predict a second target variable. We apply this formalism to PbZr0.7Sn0.3O3 crystal, using the uncertainty in dielectric constant to extrapolate heat capacity, correctly predicting a phase transition that otherwise cannot be extrapolated. For the second example – single-particle diffraction of droplets – we utilize the particle count together with its uncertainty to extrapolate the ground truth diffraction amplitude, delivering better predictions than when we utilize only the particle count. Our generic formalism enables the exploitation of uncertainty in machine learning, which has a broad range of applications in the physical sciences and beyond.
Development of robust concrete mixes with a lower environmental impact is challenging due to natural variability in constituent materials and a multitude of possible combinations of mix proportions. Making reliable property predictions with machine learning can facilitate performance-based specification of concrete, reducing material inefficiencies and improving the sustainability of concrete construction. In this work, we develop a machine learning algorithm that can utilize intermediate target variables and their associated noise to predict the final target variable. We apply the methodology to specify a concrete mix that has high resistance to carbonation, and another concrete mix that has low environmental impact. Both mixes also fulfill targets on the strength, density, and cost. The specified mixes are experimentally validated against their predictions. Our generic methodology enables the exploitation of noise in machine learning, which has a broad range of applications in structural engineering and beyond.
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