Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session S39: Machine learning for quantum matter IVFocus
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Sponsoring Units: DCOMP GDS DMP Chair: Linda Hung, Toyota Research Institute Room: 703 |
Thursday, March 5, 2020 11:15AM - 11:51AM |
S39.00001: Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines Invited Speaker: Estelle Inack Projective quantum Monte Carlo (QMC) simulations have been successfully used to simulate various relevant quantum many-body systems. They are systematically implemented in a two-step approach, in which a variational ansatz inspired by theory is first optimized using traditional variational optimization techniques. Later, the optimized ansatz is used as a guiding wave function in projective QMC simulations. In this work, we present a novel method that uses unsupervised machine learning techniques to combine the two steps above. It adaptively trains the guiding wave function (represented by a restricted Boltzmann machine) within QMC simulations, thus avoiding the need for separate variational optimization. On the one hand, this approach greatly increases the efficiency and accuracy of projective QMC simulations. On the other hand, it provides a new way to develop ground-state ansatzes, complementary to the common variational optimization schemes. We present extensive benchmarks that demonstrate the efficiency of our self-learning method. |
Thursday, March 5, 2020 11:51AM - 12:03PM |
S39.00002: Self-learning Hybrid Monte Carlo method for first-principles molecular simulations Yuki Nagai, Masahiko Okumura, Keita Kobayashi, Motoyuki Shiga We propose a novel approach called Self-Learning Hybrid Monte Carlo (SLHMC)[1] which is a general method to make use of machine learning potentials to accelerate the statistical sampling of first-principles density-functional-theory (DFT) simulations. The trajectories are generated on an approximate machine learning (ML) potential energy surface. The trajectories are then accepted or rejected by the Metropolis algorithm based on DFT energies. In this way the statistical ensemble is sampled exactly at the DFT level for a given thermodynamic condition. Meanwhile the ML potential is improved on the fly by training to enhance the sampling, whereby the training data set, which is sampled from the exact ensemble, is created automatically. |
Thursday, March 5, 2020 12:03PM - 12:15PM |
S39.00003: On-the-fly machine learning algorithm for accelerating Monte Carlo sampling: Application to the stochastic analytical continuation Hongkee Yoon, Myung Joon Han We present a new Monte Carlo method whose sampling is assisted by modern machine learning (ML) technique. In order to improve the MC sampling efficiency in high dimensional problems, we suggest ML generative model as being a part of MC sampler. We apply this ML+MC method to a long-standing numerical problem in quantum many-body physics, namely, analytic continuation. In our scheme, ML sampler naturally satisfies physical constraints such as detailed balance because it is combined with the conventional Markov chain MC procedure. Furthermore, massive data sets generated by MC procedure provides the on-the-fly ‘learnings’ for ML sampler. Remarkable improvement has been achieved in terms of both convergence speed and the quality of continuation result. The same approach can be applicable to various other problems for which MC algorithm has been used. |
Thursday, March 5, 2020 12:15PM - 12:27PM |
S39.00004: Automatic Differentiable Monte Carlo: Theory Shixin Zhang, Zhou-Quan Wan, Hong Yao Differentiable programming emerges as the new programming paradigm empowering the rapid development of deep learning as it has been shown equally powerful in computational physics. Here we propose a general theory framework with detach function techniques enabling infinite order automatic differentiation on Monte Carlo expectations with unnormalized probability distributions. By introducing automatic differentiable Monte Carlo (ADMC), we can leverage state-of-the-art machine learning framework and toolbox to traditional Monte Carlo approaches in statistics and physics by simply implementing relevant Monte Carlo algorithms on computation graphs. |
Thursday, March 5, 2020 12:27PM - 12:39PM |
S39.00005: Automatic Differentiable Monte Carlo: Applications Zhouquan Wan, Shixin Zhang, Hong Yao Differentiable programming emerges as the new programming paradigm empowering the rapid development of deep learning as it has been shown equally powerful in computational physics. By introducing automatic differentiable Monte Carlo (ADMC), we can leverage state-of-the-art machine learning frameworks and techniques to traditional Monte Carlo approaches in statistics and physics by simply implementing relevant Monte Carlo algorithms on computation graphs. We show the power of ADMC by three specific applications from physics and statistics: 1. Locate the critical temperature for 2D Ising model; 2. Compute Fisher matrix with automatic differentiation setup; 3. End-to-end, easy-to-implement, automatic differentiable variational Monte Carlo on 2D Heisenberg model with general neural network wavefunction anstaz. We further discuss about other potential possibilities that ADMC bring us in the innovations and breakthroughs of Monte Carlo methods. |
Thursday, March 5, 2020 12:39PM - 12:51PM |
S39.00006: Optimal Real-Space Renormalization-Group Transformations with Artificial Neural Networks Jui-Hui Chung, Ying-Jer Kao We introduce a general method for optimizing real-space renormalization-group transformations to study the critical properties of a classical system.The scheme is based on minimizing the Kullback-Leibler divergence between the distribution of the system and the normalizing factor of the transformation parametrized by a restricted Boltzmann machine. We compute the thermal critical exponent of the two-dimensional Ising model using the trained optimal projector and obtain a very accurate exponent yt=1.0001(11) after the first step of the transformation. |
Thursday, March 5, 2020 12:51PM - 1:03PM |
S39.00007: Machine-learning-accelerated predictions of optical properties of condensed systems based on many-body perturbation theory Sijia Dong, Marco Govoni, Giulia Galli Accurate and efficient predictions of absorption spectra of molecules and solids are essential for the understanding and rational design of broad classes of materials, including photo-absorbers in solar and photo-electrochemical cells and defective insulators and semiconductors hosting optically addressable spin-defects. We present an approach to improve the efficiency of first principles calculations of absorption spectra of complex materials at finite temperature, based on the solution of the Bethe-Salpeter equation (BSE) [1]. We use machine learning techniques to predict the spectra of snapshots extracted from ab initio molecular dynamics simulations, and we use data generated by explicitly solving the BSE for a small subset of snapshots. We present results for nanoclusters, solids, liquids, including water, and semiconductor-water interfaces. |
Thursday, March 5, 2020 1:03PM - 1:15PM |
S39.00008: Machine Learned Spectral Functions for the Quantum Impurity Problem Erica Sturm, Matthew R Carbone, Deyu Lu, Andreas Weichselbaum, Robert Konik Machine learning techniques can greatly reduce simulation times by providing highly accurate approximations, thus circumventing the need for more expensive models. This work leverages a feed-forward neural network (NN) to predict the spectral functions of the single impurity Anderson model (SIAM) as a function of five physical parameters including the Coulomb interaction U, hybridization constant Γ, impurity energy εd, magnetic field B, and temperature T. The NN was trained on ~670,000 unique SIAM system spectral functions generated by Wilson’s Numerical Renormalization Group (NRG). The NN predicts the spectral function with a mean absolute difference of less than 3% compared to the ground truth. The ability to efficiently predict a spectral function for the quantum impurity problem can improve the computation time for dynamical mean field theory and related methods that investigate strong correlation in condensed matter systems. |
Thursday, March 5, 2020 1:15PM - 1:27PM |
S39.00009: Finding New Mixing Strategies for Self Consistent Field Procedures Using Reinforcement Learning Daniel Abarbanel, Hong Guo Density mixing is a technique to improve the convergence for self-consistent field (SCF) procedures, and is used extensively to calculate electronic structure and transport properties in the context of density functional theory (DFT). Typically, a single mixing method will be chosen for the whole of a SCF calculation, but recent research suggests that alternating the mixing strategy between subsequent SCF iterations can improve the time of convergence. There are many untested SCF mixing methods beyond those already discovered that can be constructed using combinations of established methods. We present a new method to discover mixing strategies by applying a reinforcement learning algorithm (RLA). The state space of the RLA consists of SCF parameters such as the density, potential and convergence error. The action space of the RLA consists of previously developed mixing methods including simple mixing, Broyden mixing and Pulay mixing, with the crucial point being that the RLA is able to alter the mixing strategy in situ. |
Thursday, March 5, 2020 1:27PM - 1:39PM |
S39.00010: Machine learning spin dynamics in the double-exchange systems Puhan Zhang, Preetha Saha, Gia-Wei Chern The double-exchange (DE) mechanism plays an important role in our understanding of the colossal magnetoresistance phenomenon. It describes itinerant electrons interacting with local magnetic moments through the Hund's rule coupling. Although extensive effort has been devoted to studying the equilibrium properties of the DE models, dynamical phenomena in these systems remain much less explored, partly due to the expensive computational cost of their microscopic simulations. For example, in Landau-Lifshitz dynamics (LLD) simulations of the DE systems, the electron tight-binding Hamiltonian has to be solved at every time-step in order to obtain the torque acting on the local spins. Here we propose a machine learning (ML) technique that can solve the dynamics of the DE model in linear time complexity. Our approach is similar to the ML-based force prediction in quantum molecular dynamics. In our method, a deep-learning neural network trained by dataset from small system simulations is used to directly predict the effective local exchange force. We will also present our ML-enabled large-scale LLD simulation of phase separation phenomena in DE systems. |
Thursday, March 5, 2020 1:39PM - 1:51PM |
S39.00011: Machine learning of high-throughput DFT electron densities Linda Hung, Daniel Schweigert, Arjun Bhargava, Chirranjeevi Gopal Kohn-Sham density functional theory (DFT) provides a good balance between accuracy and efficiency, and its utility has given rise to high-throughput DFT databases including the Materials Project and the Open Quantum Materials Database. In this talk, we demonstrate how electron density datasets from these databases can be used to train machine learning models that complement and enhance the capabilities of DFT. We quantify the accuracy of neural networks that predict electron densities, and also report the trends observed in electronic structure-property relationships. |
Thursday, March 5, 2020 1:51PM - 2:03PM |
S39.00012: Machine learning as a solution to the electronic structure problem Beatriz Gonzalez del Rio, Ramamurthy Ramprasad An essential component of materials research is the use of simulations based on density functional theory (DFT), which imposes severe limitations on the size of the system under study. A promising development in recent years is the use of machine learning (ML) methodologies to train surrogate models with DFT data to predict quantum-accurate results for larger systems. Many successful ML models have been created to predict higher-level DFT results such as the total potential energy and atomic forces, and initial steps have been taken to create deep-learning based ML methodologies that can predict fundamental DFT outputs such as the charge density, wave functions and corresponding energy levels [1]. Here, we explore the applicability of this latter methodology using convolutional and recurrent neural networks to learn and predict the electronic charge density and the density of states of carbon, for a large variety of allotropes spanning from metallic to insulating behavior. Further improvements to the speed, accuracy and versatility of this DFT-emulation methodology will also be presented. |
Thursday, March 5, 2020 2:03PM - 2:15PM |
S39.00013: Machine learning spectral indicators of topology Nina Andrejevic, Jovana Andrejevic, Christopher Rycroft, Mingda Li Topological materials discovery has emerged as an important frontier in condensed matter physics due to the exceptional properties arising from nontrivial band topology. Recent theoretical methods based on local and global symmetry indicators have been used to identify several thousand candidate topological materials, yet experimental determination of materials’ topological character often poses significant technical challenges. X-ray absorption spectroscopy (XAS) is a widely-used characterization technique of materials’ local geometric and electronic structure, as it is sensitive to the symmetry and local chemical environment of constituent atoms; thus, it is a potentially useful encoding of topological character. Here, we study the effectiveness of XAS as a predictor of topology using machine learning methods to disentangle key structural information from the complex spectral features. We discuss the utility of experimental spectra to inform materials’ topology and compare the predictive power of individual absorbing elements. |
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