相关论文: Path-integral evolution of multivariate systems wi…
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…
This paper leverages recent advances in high derivatives reconstruction from noisy-time series and sparse multivariate polynomial identification in order to improve the process of parsimoniously identifying, from a small amount of data,…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the…
We consider several issues related to the multidimensional integration using a network of heterogeneous computers. Based on these considerations, we develop a new general purpose scheme which can significantly reduce the time needed for…
Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational…
The study of multiplicative noise models has a long history in control theory but is re-emerging in the context of complex networked systems and systems with learning-based control. We consider linear system identification with…
We discuss the improvement in the accuracy of a Monte Carlo integration that can be obtained by optimization of the `a-priori weights' of the various channels. These channels may be either the strata in a stratified-sampling approach, or…
Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor's diffusion in…
In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…
In the computational sciences, one must often estimate model parameters from data subject to noise and uncertainty, leading to inaccurate results. In order to improve the accuracy of models with noisy parameters, we consider the problem of…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
Langevin algorithms are gradient descent methods augmented with additive noise, and are widely used in Markov Chain Monte Carlo (MCMC) sampling, optimization, and machine learning. In recent years, the non-asymptotic analysis of Langevin…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…