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Register a new userBayesian Learning of Thermodynamic Integration and Numerical Convergence for Accurate Phase Diagrams
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Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy functions using data of various origin. Our framework allows for propagating statistical uncertainty from finite molecular dynamics trajectories to the phase diagram and automatically performing convergence with respect to simulation parameters. Furthermore, our approach provides a way for automatic optimal sampling in the simulation parameter space based on Bayesian optimization approach. We validate our methodology by constructing phase diagrams of two model systems, the Lennard-Jones and soft-core potential, and compare the results with existing works studies and our coexistence simulations. Finally, we construct the phase diagram of lithium at temperatures above 300 K and pressures below 30 GPa from a machine-learning potential trained on ab initio data. Our approach performs well when compared to coexistence simulations and experimental results.
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Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of interest in the image space or parameter space of computational models. The direct grid search of the parameter space tends to be extremely time-consuming, leading to the development of strategies balancing exploration of unknown parameter spaces and exploitation towards required performance metrics. However, classical Bayesian optimization strategies based on the Gaussian process (GP) do not readily allow for the incorporation of the known physical behaviors or past knowledge. Here we explore a hybrid optimization/exploration algorithm created by augmenting the standard GP with a structured probabilistic model of the expected systems behavior. This approach balances the flexibility of the non-parametric GP approach with a rigid structure of physical knowledge encoded into the parametric model. The fully Bayesian treatment of the latter allows additional control over the optimization via the selection of priors for the model parameters. The method is demonstrated for a noisy version of the classical objective function used to evaluate optimization algorithms and further extended to physical lattice models. This methodology is expected to be universally suitable for injecting prior knowledge in the form of physical models and past data in the Bayesian optimization framework
Machine learning promises to deliver powerful new approaches to neutron scattering from magnetic materials. Large scale simulations provide the means to realise this with approaches including spin-wave, Landau Lifshitz, and Monte Carlo methods. These approaches are shown to be effective at simulating magnetic structures and dynamics in a wide range of materials. Using large numbers of simulations the effectiveness of machine learning approaches are assessed. Principal component analysis and nonlinear autoencoders are considered with the latter found to provide a high degree of compression and to be highly suited to neutron scattering problems. Agglomerative heirarchical clustering in the latent space is shown to be effective at extracting phase diagrams of behavior and features in an automated way that aid understanding and interpretation. The autoencoders are also well suited to optimizing model parameters and were found to be highly advantageous over conventional fitting approaches including being tolerant of artifacts in untreated data. The potential of machine learning to automate complex data analysis tasks including the inversion of neutron scattering data into models and the processing of large volumes of multidimensional data is assessed. Directions for future developments are considered and machine learning argued to have high potential for impact on neutron science generally.
The analysis of defects and defect dynamics in crystalline materials is important for fundamental science and for a wide range of applied engineering. With increasing system size the analysis of molecular-dynamics simulation data becomes non-trivial. Here, we present a workflow for semi-automatic identification and classification of defects in crystalline structures, combining a new approach for defect description with several already existing open-source software packages. Our approach addresses the key challenges posed by the often relatively tiny volume fraction of the modified parts of the sample, thermal motion and the presence of potentially unforeseen atomic configurations (defect types) after irradiation. The local environment of any atom is converted into a rotation-invariant descriptive vector (fingerprint), which can be compared to known defect types and also yields a distance metric suited for classification. Vectors which cannot be associated to known structures indicate new types of defects. As proof-of-concept we apply our method on an iron sample to analyze the defects caused by a collision cascade induced by a 10 keV primary-knock-on-atom. The obtained results are in good agreement with reported literature values.
The discovery of topological features of quantum states plays an important role in modern condensed matter physics and various artificial systems. Due to the absence of local order parameters, the detection of topological quantum phase transitions remains a challenge. Machine learning may provide effective methods for identifying topological features. In this work, we show that the unsupervised manifold learning can successfully retrieve topological quantum phase transitions in momentum and real space. Our results show that the Chebyshev distance between two data points sharpens the characteristic features of topological quantum phase transitions in momentum space, while the widely used Euclidean distance is in general suboptimal. Then a diffusion map or isometric map can be applied to implement the dimensionality reduction, and to learn about topological quantum phase transitions in an unsupervised manner. We demonstrate this method on the prototypical Su-Schrieffer-Heeger (SSH) model, the Qi-Wu-Zhang (QWZ) model, and the quenched SSH model in momentum space, and further provide implications and demonstrations for learning in real space, where the topological invariants could be unknown or hard to compute. The interpretable good performance of our approach shows the capability of manifold learning, when equipped with a suitable distance metric, in exploring topological quantum phase transitions.
We applied the clustering technique using DTW (dynamic time wrapping) analysis to XRD (X-ray diffraction) spectrum patterns in order to identify the microscopic structures of substituents introduced in the main phase of magnetic alloys. The clustering is found to perform well to identify the concentrations of the substituents with successful rates (around 90%). The sufficient performance is attributed to the nature of DTW processing to filter out irrelevant informations such as the peak intensities (due to the incontrollability of diffraction conditions in polycrystalline samples) and the uniform shift of peak positions (due to the thermal expansions of lattices).
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