Self-Learning Monte Carlo Method

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of general and efficient update algorithm for large size systems close to phase transition or with strong frustrations, for which local updates perform badly. In this work, we propose a new general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup.Comment: add more refs and correct some typo

PiCANet: Learning Pixel-wise Contextual Attention for Saliency Detection

Contexts play an important role in the saliency detection task. However, given a context region, not all contextual information is helpful for the final task. In this paper, we propose a novel pixel-wise contextual attention network, i.e., the PiCANet, to learn to selectively attend to informative context locations for each pixel. Specifically, for each pixel, it can generate an attention map in which each attention weight corresponds to the contextual relevance at each context location. An attended contextual feature can then be constructed by selectively aggregating the contextual information. We formulate the proposed PiCANet in both global and local forms to attend to global and local contexts, respectively. Both models are fully differentiable and can be embedded into CNNs for joint training. We also incorporate the proposed models with the U-Net architecture to detect salient objects. Extensive experiments show that the proposed PiCANets can consistently improve saliency detection performance. The global and local PiCANets facilitate learning global contrast and homogeneousness, respectively. As a result, our saliency model can detect salient objects more accurately and uniformly, thus performing favorably against the state-of-the-art methods

Self-Learning Monte Carlo Method in Fermion Systems

We develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly-efficient update algorithm, which we design and dub "cumulative update", to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From general analysis and numerical study of the double exchange model as an example, we find the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates

Self-Learning Determinantal Quantum Monte Carlo Method

Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we implement this method in the framework of determinantal quantum Monte Carlo simulation of interacting fermion systems. Guided by a self-learned bosonic effective action, our method uses a cumulative update [arXiv:1611.09364] algorithm to sample auxiliary field configurations quickly and efficiently. We demonstrate that self-learning determinantal Monte Carlo method can reduce the auto-correlation time to as short as one near a critical point, leading to $\mathcal{O}(N)$-fold speedup. This enables to simulate interacting fermion system on a $100\times 100$ lattice for the first time, and obtain critical exponents with high accuracy.Comment: 5 pages, 4 figure

Weak Topological Insulators in PbTe/SnTe Superlattices

It is desirable to realize topological phases in artificial structures by engineering electronic band structures. In this paper, we investigate $(PbTe)_m(SnTe)_{2n-m}$ superlattices along [001] direction and find a robust weak topological insulator phase for a large variety of layer numbers m and 2n-m. We confirm this topologically non-trivial phase by calculating Z2 topological invariants and topological surface states based on the first-principles calculations. We show that the folding of Brillouin zone due to the superlattice structure plays an essential role in inducing topologically non-trivial phases in this system. This mechanism can be generalized to other systems in which band inversion occurs at multiple momenta, and gives us a brand-new way to engineer topological materials in artificial structures.Comment: 6 pages, 4 figures, another author adde

Self-Learning Monte Carlo Method: Continuous-Time Algorithm

The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement this method in the framework of continuous time Monte Carlo method with auxiliary field in quantum impurity models. We introduce and train a diagram generating function (DGF) to model the probability distribution of auxiliary field configurations in continuous imaginary time, at all orders of diagrammatic expansion. By using DGF to propose global moves in configuration space, we show that the self-learning continuous-time Monte Carlo method can significantly reduce the computational complexity of the simulation.Comment: 6 pages, 5 figures + 2 page supplemental materials, to be published in Phys. Rev. B Rapid communication sectio

Study on Risk Zoning Technology of Major Environmental Risk Sources in Urban Scale and Its Application in Shanghai, China

AbstractBecause of the inherent characteristics of the cities, such as high population density, complicated traffic, numerous pollution sources, etc., it has become very important to conduct environmental risk zoning in urban scale. Based on analyzing the current research situation of the regional environmental risk assessment and regional environmental risk zoning, this paper constructed the index system and the quantitative model of environmental risk zoning which are fit for urban scale, applies AHP to weight index and comprehensive evaluation method to calculate comprehensive risk index value. Then applying the method to Shanghai, and with the clustering function of SPSS and the visualization of GIS, the quantitative risk zoning map of Shanghai was obtained. The result can provide reference for environmental risk management of Shanghai

Accelerating Diffusion-based Combinatorial Optimization Solvers by Progressive Distillation

Graph-based diffusion models have shown promising results in terms of generating high-quality solutions to NP-complete (NPC) combinatorial optimization (CO) problems. However, those models are often inefficient in inference, due to the iterative evaluation nature of the denoising diffusion process. This paper proposes to use progressive distillation to speed up the inference by taking fewer steps (e.g., forecasting two steps ahead within a single step) during the denoising process. Our experimental results show that the progressively distilled model can perform inference 16 times faster with only 0.019% degradation in performance on the TSP-50 dataset

Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model

Self-learning Monte Carlo method (SLMC), using a trained effective model to guide Monte Carlo sampling processes, is a powerful general-purpose numerical method recently introduced to speed up simulations in (quantum) many-body systems. In this work, we further improve the efficiency of SLMC by enforcing physical symmetries on the effective model. We demonstrate its effectiveness in the Holstein Hamiltonian, one of the most fundamental many-body descriptions of electron-phonon coupling. Simulations of the Holstein model are notoriously difficult due to the combination of the typical cubic scaling of fermionic Monte Carlo and the presence of extremely long autocorrelation times. Our method addresses both bottlenecks. This enables simulations on large lattices in the most difficult parameter regions, and evaluation of the critical point for the charge density wave transition at half-filling with high precision. We argue that our work opens a new research area of quantum Monte Carlo (QMC), providing a general procedure to deal with ergodicity in situations involving Hamiltonians with multiple, distinct low energy states.Comment: 4 pages, 3 figures with 2 pages supplemental materia