相关论文: Path-integral evolution of multivariate systems wi…

We construct the exponential map associated to a nonholonomic system that allows us to define an exact discrete nonholonomic constraint submanifold. We reproduce the continuous nonholonomic flow as a discrete flow on this discrete…

The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…

Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…

We present a comparison of the performance of two non-local update algorithms for path integral Monte Carlo (PIMC) simulations, the multigrid Monte Carlo method and the staging algorithm. Looking at autocorrelation times for the internal…

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

A novel approach for vehicle tracking using a hybrid adaptive Kalman filter is proposed. The filter utilizes recurrent neural networks to learn the vehicle's geometrical and kinematic features, which are then used in a supervised learning…

We propose a two-step procedure to detect cointegration in high-dimensional settings, focusing on sparse relationships. First, we use the adaptive LASSO to identify the small subset of integrated covariates driving the equilibrium…

Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good…

We propose a Monte Carlo algorithm to promote Kennedy and Kuti's linear accept/reject algorithm which accommodates unbiased stochastic estimates of the probability to an exact one. This is achieved by adopting the Metropolis accept/reject…

A method of path integral construction without gauge fixing in the holomorphic representation is proposed for finite-dimensional gauge models. This path integral determines a manifestly gauge-invariant kernel of the evolution operator.

We prove a moderate deviation principle for the continuous time interpolation of discrete time recursive stochastic processes. The methods of proof are somewhat different from the corresponding large deviation result, and in particular the…

We consider a nonlinear filtering problem of multiscale non-Gaussian signal processes and observation processes with jumps. Firstly, we prove that the dimension for the signal system can be reduced by a homogenized approach. Secondly,…

Synchronization in a group of linear time-invariant systems is studied where the coupling between each pair of systems is characterized by a different output matrix. Simple methods are proposed to generate a (separate) linear coupling gain…

Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…

In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…

The evaluation of the path-integral representation for stochastic processes in the weak-noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics. We show that, even when the noise is…

Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…

A discrete analysis of the phase and dissipation errors of an explicit, semi-Lagrangian spectral element method is performed. The semi-Lagrangian method advects the Lagrange interpolant according the Lagrangian form of the transport…

We present a novel Monte Carlo algorithm which enhances equilibrization of low-temperature simulations and allows sampling of configurations over a large range of energies. The method is based on a non-Boltzmann probability weight factor…

In this article we revisit the problem of numerical integration for monotone bounded functions, with a focus on the class of nonsequential Monte Carlo methods. We first provide new a lower bound on the maximal $L^p$ error of nonsequential…