Related papers: A convergent discretisation method for transition …
We present a data-driven point of view for rare events, which represent conformational transitions in biochemical reactions modeled by over-damped Langevin dynamics on manifolds in high dimensions. We first reinterpret the transition state…
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC…
Diffusion trajectory distillation accelerates sampling by training a student model to approximate the multi-step denoising trajectories of a pretrained teacher model using far fewer steps. Despite strong empirical results, the trade-off…
Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of…
Diffusion-based re-ranking methods are effective in modeling the data manifolds through similarity propagation in affinity graphs. However, positive signals tend to diminish over several steps away from the source, reducing discriminative…
Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…
This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and…
Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…
We consider special upwinding Petrov-Galerkin discretizations for convection-diffusion problems. For the one dimensional case with a standard continuous linear element as the trial space and a special exponential bubble test space, we prove…
Sampling from complex target distributions is a challenging task fundamental to Bayesian inference. Parallel tempering (PT) addresses this problem by constructing a Markov chain on the expanded state space of a sequence of distributions…
In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…
We propose a diffusion approximation method to the continuous-state Markov Decision Processes (MDPs) that can be utilized to address autonomous navigation and control in unstructured off-road environments. In contrast to most…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
The Transition Path Theory (TPT) of complex systems has proven a robust means for statistically characterizing the ensemble of trajectories that connect any two preset flow regions, say $\mathcal A$ and $\mathcal B$, directly. More…
Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…