Accelerated Stochastic Sampling of Discrete Statistical Systems

We propose a method to reduce the relaxation time towards equilibrium in stochastic sampling of complex energy landscapes in statistical systems with discrete degrees of freedom by generalizing the platform previously developed for continuous systems. The method starts from a master equation, in contrast to the Fokker-Planck equation for the continuous case. The master equation is transformed into an imaginary-time Schr\"odinger equation. The Hamiltonian of the Schr\"odinger equation is modified by adding a projector to its known ground state. We show how this transformation decreases the relaxation time and propose a way to use it to accelerate simulated annealing for optimization problems. We implement our method in a simplified kinetic Monte Carlo scheme and show an acceleration by an order of magnitude in simulated annealing of the symmetric traveling salesman problem. Comparisons of simulated annealing are made with the exchange Monte Carlo algorithm for the three-dimensional Ising spin glass. Our implementation can be seen as a step toward accelerating the stochastic sampling of generic systems with complex landscapes and long equilibration times.Comment: 18 pages, 6 figures, to appear in Phys. Rev.

Stochastic Sampling Simulation for Pedestrian Trajectory Prediction

Urban environments pose a significant challenge for autonomous vehicles (AVs) as they must safely navigate while in close proximity to many pedestrians. It is crucial for the AV to correctly understand and predict the future trajectories of pedestrians to avoid collision and plan a safe path. Deep neural networks (DNNs) have shown promising results in accurately predicting pedestrian trajectories, relying on large amounts of annotated real-world data to learn pedestrian behavior. However, collecting and annotating these large real-world pedestrian datasets is costly in both time and labor. This paper describes a novel method using a stochastic sampling-based simulation to train DNNs for pedestrian trajectory prediction with social interaction. Our novel simulation method can generate vast amounts of automatically-annotated, realistic, and naturalistic synthetic pedestrian trajectories based on small amounts of real annotation. We then use such synthetic trajectories to train an off-the-shelf state-of-the-art deep learning approach Social GAN (Generative Adversarial Network) to perform pedestrian trajectory prediction. Our proposed architecture, trained only using synthetic trajectories, achieves better prediction results compared to those trained on human-annotated real-world data using the same network. Our work demonstrates the effectiveness and potential of using simulation as a substitution for human annotation efforts to train high-performing prediction algorithms such as the DNNs.Comment: 8 pages, 6 figures and 2 table

Stochastic Sampling Simulation for Pedestrian Trajectory Prediction

Urban environments pose a significant challenge for autonomous vehicles (AVs) as they must safely navigate while in close proximity to many pedestrians. It is crucial for the AV to correctly understand and predict the future trajectories of pedestrians to avoid collision and plan a safe path. Deep neural networks (DNNs) have shown promising results in accurately predicting pedestrian trajectories, relying on large amounts of annotated real-world data to learn pedestrian behavior. However, collecting and annotating these large real-world pedestrian datasets is costly in both time and labor. This paper describes a novel method using a stochastic sampling-based simulation to train DNNs for pedestrian trajectory prediction with social interaction. Our novel simulation method can generate vast amounts of automatically-annotated, realistic, and naturalistic synthetic pedestrian trajectories based on small amounts of real annotation. We then use such synthetic trajectories to train an off-the-shelf state-of-the-art deep learning approach Social GAN (Generative Adversarial Network) to perform pedestrian trajectory prediction. Our proposed architecture, trained only using synthetic trajectories, achieves better prediction results compared to those trained on human-annotated real-world data using the same network. Our work demonstrates the effectiveness and potential of using simulation as a substitution for human annotation efforts to train high-performing prediction algorithms such as the DNNs.Comment: 8 pages, 6 figures and 2 table

Sampled-data synchronization control of dynamical networks with stochastic sampling

Copyright @ 2012 IEEEThis technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61028008, 60974030, 61134009 and 61104125, the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany

Monte Carlo simulation of boson lattices

Boson lattices are theoretically well described by the Hubbard model. The basic model and its variants can be effectively simulated using Monte Carlo techniques. We describe two newly developed approaches, the Stochastic Series Expansion (SSE) with directed loop updates and continuous--time Diffusion Monte Carlo (CTDMC). SSE is a formulation of the finite temperature partition function as a stochastic sampling over product terms. Directed loops is a general framework to implement this stochastic sampling in a non--local fashion while maintaining detailed balance. CTDMC is well suited to finding exact ground--state properties, applicable to any lattice model not suffering from the sign problem; for a lattice model the evolution of the wave function can be performed in continuous time without any time discretization error. Both the directed loop algorithm and the CTDMC are important recent advances in development of computational methods. Here we present results for a Hubbard model for anti--ferromagnetic spin--1 bosons in one dimensions, and show evidence for a dimerized ground state in the lowest Mott lobe.Comment: 3 pages, 5 figur