Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session R34: Machine Learning in Condensed Matter Physics IVFocus

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Sponsoring Units: DCOMP DCMP Chair: Lei Wang, Chinese Academy of Sciences Room: LACC 409A 
Thursday, March 8, 2018 8:00AM  8:36AM 
R34.00001: Tensor Network Machine Learning Models Invited Speaker: Edwin Stoudenmire Tensor networks are an efficient approach to representing complicated manybody wavefunctions in terms of many smaller tensors, and they lead to powerful algorithms for studying strongly correlated systems. But tensor networks could be applied much more broadly than just for representing wavefunctions. Large tensors similar to wavefunctions appear naturally in certain classes of models studied extensively in machine learning. Decomposing the model parameters as a tensor network leads to interesting algorithms for training models on realworld data which scale better than existing approaches. In addition to training models directly for recognizing labeled data, tensor network realspace renormalization approaches can be used to extract statistically significant "features" for subsequent learning tasks. I will also highlight other benefits of the tensor network approach such as the flexibility to blend different approaches and to interpret trained models. 
Thursday, March 8, 2018 8:36AM  8:48AM 
R34.00002: Unifying Quantum Tensor Network and Convolutional Neural Network Yahui Zhang The success of deep convolutional neural network (CNN) in computer vision especially image classification problems requests a new information theory for function of image, instead of image itself. In this article, after establishing a deep mathematical connection between image classification problem and quantum spin model, we propose to use entanglement entropy, a generalization of classical BoltzmannShannon entropy, as a powerful tool to characterize the information needed for representation of general function of image. We prove that there is a subvolumelaw bound for entanglement entropy of target functions of reasonable image classification problems.The concept of entanglement entropy can also be useful to characterize the expressive power of different neural networks. 
Thursday, March 8, 2018 8:48AM  9:00AM 
R34.00003: Efficient Representation of Matrx Product State with Restricted Boltzmann Machine Zhengyu Zhang, Xun Gao, Luming Duan One of the fundamental problems in manybody physics is the lack of an efficient representational ansatz for highly entangled quantum states. Tensor network state is potentially one of such ansatzes, especially in onedimensional(1D) case, as its 1D form, matrix product state, has been proven an efficient representation of ground states of gapped 1D systems and seen a lot of applications in both numerical and analytical work. On the other hand, Restricted Boltzmann Machine (RBM), a probabilistic model widely used in machine learning, has recently drawn a lot of attentions as a successful variational ansatz in computing some manybody ground states. Here we prove that RBM can efficiently represent almost all matrix product states asymptotically thus serving as a new ansatz for quantum manybody states. We also give numerical experimental results as a support to our claim and concrete examples for useful manybody highly entangled states. 
Thursday, March 8, 2018 9:00AM  9:12AM 
R34.00004: Machine Learning Spatial Geometry from Entanglement Features Yizhuang You, Zhao Yang, Xiaoliang Qi Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum manybody state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum manybody state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS_{3} spatial geometry) as we tune the fermion system towards the gapless critical point (CFT_{2} point). 
Thursday, March 8, 2018 9:12AM  9:24AM 
R34.00005: Thermodynamicsinspired unsupervised clustering of objects Jorge Munoz The goal of unsupervised machine learning is to find the underlying structure that describes a dataset. Realworld applications include the clustering of customers by the ads they click on or the movies they watch. We treat unsupervised learning as an optimization problem by designing a morphism to transform data attributes into a mathematical graph and defining a graph entropy that is minimized when only relatively few nodes are highly connected. The thermodynamics of such system are derived and simulated annealing is used to cluster similar data together. The methodology is applied to network traffic patterns and scientific literature and results are discussed. 
Thursday, March 8, 2018 9:24AM  9:36AM 
R34.00006: Designing ErrorCorrection Codes by Machine Learning YeHua Liu Errorcorrection codes are essential to faulttolerant computational devices. The errorcorrection model consists of an encoder, an erroneous channel and a decoder. Given a channel and a humandesigned encoder, it could be hard to find an efficient decoder, and this problem has been studied with insights from machine learning. Here we move forward and use machine learning to design both the encoder and the decoder. The errorcorrection capability of the machinedesigned encoder and decoder, for a fixed channel, increases during training, which means the machine learns to exploit the redundancy in the transmitted bit string. 
Thursday, March 8, 2018 9:36AM  9:48AM 
R34.00007: MorseSmale Systems and Machine Learning Kyle Kawagoe, Arvind Murugan Recurrent Neural Networks (RNNs) are seen as a powerful tool in dealing with time series data generated by physical systems with dynamics because RNNs have their own internal dynamics. However, they are limited in the tasks they can perform and are often difficult to train. Since RNNs effectively simulate a dynamical system, some of their inherent drawbacks are due to their heavily constrained energy landscape. We introduce and explore an alternative, nonneuron based learning method using a broader class of dynamical systems called MorseSmale systems. The extra freedom in the complexity of the energy landscape allows for a more efficient use of dimensions, leading to significant learning even in two dimensions. In this talk, we will show that MorseSmale systems have significant advantages over conventional neural networks in classifying time series data, which show up across condensed matter physics. This shows how dynamical systems can improve algorithms, which are in turn used to analyze dynamical data from physical systems. 
Thursday, March 8, 2018 9:48AM  10:00AM 
R34.00008: Selflearning Monte Carlo Method with Deep Neural Networks Junwei Liu, Huitao Shen, Liang Fu Selflearning Monte Carlo (SLMC) method is a general algorithm to speedup MC simulations. Its efficiency has been demonstrated in various systems by employing the effective model to propose global moves in configuration space. Here, we explicitly show that deep neural networks can be naturally embedded in SLMC as the effective model, and further extend the realm of SLMC. Without any prior physical knowledge, the neural network could accurately learn the dynamics of the original model in a quantitatively level. By extracting physical information from the trained neural networks, more efficient neural networks can further designed. For impurity models, we reduce the complexity of the conventional HirschFye algorithm and accelerate the simulation significantly. By deeply integrating the advanced machine learning techniques, SLMC can be expected to play a more important role in exploring the manybody physics. 
Thursday, March 8, 2018 10:00AM  10:12AM 
R34.00009: Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines Li Huang, Lei Wang Despite their exceptional flexibility and popularity, the Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and techniques from the machine learning community. We fit the unnormalized probability of the physical model to a feedforward neural network and reinterpret the architecture as a restricted Boltzmann machine. Then, exploiting its feature detection ability, we utilize the restricted Boltzmann machine for efficient Monte Carlo updates and to speed up the simulation of the original physical system. We implement these ideas for the FalicovKimball model and demonstrate improved acceptance ratio and autocorrelation time near the phase transition point. 
Thursday, March 8, 2018 10:12AM  10:24AM 
R34.00010: Model parameter learning using KullbackLeibler divergence Chungwei Lin, Chihkuan Tung In this presentation, we address the following problem: For a given set spin configurations whose probability distribution is of the Boltzmann type, how do we determine the model coupling parameters? We demonstrate that directly minimizing the KullbackLeibler divergence is a very efficient method. We test this method against the Ising and XY models on the onedimensional and twodimensional lattices, and provide two estimators to quantify the model quality. We apply this method to two types of problems. First we apply it to the realspace renormalization group (RG), and find that the obtained RG flow is sufficiently good for determining the phase boundary (within 1\% of the exact result) and the critical point, but not accurate enough for critical exponents. The proposed method provides a simple way to numerically estimate amplitudes of the interactions typically truncated in the realspace RG procedure. Second, we apply this method to the dynamical system composed of selfpropelled particles, where we extract the parameter of a statistical model (a generalized XY model) from a dynamical system described by the Viscek model. Our method is thus able to provide quantitative analysis of dynamical systems composed of selfpropelled particles. 
Thursday, March 8, 2018 10:24AM  10:36AM 
R34.00011: SchNet  A Deep Learning Architecture for Molecules and Materials Kristof Schütt, Huziel Sauceda, PieterJan Kindermans, Stefan Chmiela, KlausRobert Müller, Alexandre Tkatchenko Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks are the first choice for images, the atoms in molecules are not restricted to a grid. Instead, their precise locations contain essential chemical information. Thus, we propose continuousfilter convolutional layers that we apply in SchNet: a novel deep learning architecture for modeling quantum interactions in molecules and materials [1]. Using filtergenerating networks, we are able to encode prior knowledge about atom interactions, e.g. periodic boundary conditions, directly into the model. We predict chemical properties across compound space for molecules and materials as well as energyconserving force fields for MD trajectories. Beyond achieving highly accurate predictions, SchNet provides spatially and chemically resolved insights into quantummechanical properties of atomistic systems beyond those trivially contained in the training set [1,2]. 
Thursday, March 8, 2018 10:36AM  10:48AM 
R34.00012: Deep Potential Molecular Dynamics: a Scalable Model with the Accuracy of Quantum Mechanics Linfeng Zhang, Jiequn Han, Han Wang, Roberto Car, Weinan E We introduce a new scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a manybody potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is “first principlebased” in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DeePMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size. 
Thursday, March 8, 2018 10:48AM  11:00AM 
R34.00013: Translating accurate electronic structure calculations into an accurate calculation of dynamical properties in liquid water via the neural network. Yi Yao, Yosuke Kanai While firstprinciples molecular dynamics simulation has advanced greatly in the last few decades, accurate computation of the diffusion constant in liquid water remains highly challenging in practice. Underlying electronic structure calculation must be accurate, and the statistical sampling needs to be adequate enough at the same time. This is further complicated by the challenge of taking into account the nuclear quantum effect, which depends on both the underlying potential energy surface and the temperature. We will discuss how we are using the neural network potential for performing statisticallyconverged path integral molecular dynamics simulations in order to calculate selfdiffusivity of liquid water for a wide range of temperatures. We will discuss successes and limitations of employing the neural network potential approach in this study. 
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