Related papers: Strong convergence for split-step methods in stoch…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…
Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…
There exist several methods for simulating biological and physical systems as represented by chemical reaction networks. Systems with low numbers of particles are frequently modelled as discrete-state Markov jump processes and are typically…
In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant…
Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying…
The Langevin dynamics is a diffusion process extensively used, in particular in molecular dynamics simulations, to sample Gibbs measures. Some alternatives based on (piecewise deterministic) kinetic velocity jump processes have gained…
We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
Tau leaping is a popular method for performing fast approximate simulation of certain continuous time Markov chain models typically found in chemistry and biochemistry. This method is known to perform well when the transition rates satisfy…
We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is…
In this paper we propose new numerical algorithms in the setting of unconstrained optimization problems and we study the rate of convergence in the iterates of the objective function. Furthermore, our algorithms are based upon splitting and…
Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov chain on a general state space. Focusing on a class of…
We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…
Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection is a challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it…
We propose a novel, tractable latent state inference scheme for Markov jump processes, for which exact inference is often intractable. Our approach is based on an entropic matching framework that can be embedded into the well-known…
This paper considers the speed of convergence (mixing) of a finite Markov kernel $P$ with respect to the Kullback-Leibler divergence (entropy). Given a Markov kernel one defines either a discrete-time Markov chain (with the $n$-step…
We present a framework for the scale-invariance characterization of stochastic processes in reconstructed finite-dimensional phase spaces. This framework analyses the structural and dynamical properties of the phase space and is based on a…
A combination of a steady-state preserving operator splitting method and a semi-implicit integration scheme is proposed for efficient time stepping in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical…