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We introduce a path sampling method for the computation of rate constants for systems with a highly diffusive character. Based on the recently developed algorithm of transition interface sampling (TIS) this procedure increases the…
We present a novel Recurrent Graph Network (RGN) approach for predicting discrete marked event sequences by learning the underlying complex stochastic process. Using the framework of Point Processes, we interpret a marked discrete event…
We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a…
In this paper, a new fractional step method is proposed for simulating stiff and nonstiff chemically reacting flows. In stiff cases, a well-known spurious numerical phenomenon, i.e. the incorrect propagation speed of discontinuities, may be…
The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
We use importance sampling in a redefined way to highlight and investigate rare events in the form of trajectories trapped inside a target coherent set. We take a transfer operator approach to finding these sets on a reconstructed…
We consider linear hyperbolic balance law that describe gas flow. Stochastic influences are introduced by series of orthogonal functions. A deterministic stabilization concept, which makes deviations at steady states decay exponentially…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…
A novel approach termed \emph{stochastic truncated amplitude flow} (STAF) is developed to reconstruct an unknown $n$-dimensional real-/complex-valued signal $\bm{x}$ from $m$ `phaseless' quadratic equations of the form…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
We study large deviations of a ratio observable in discrete-time reset processes. The ratio takes the form of a current divided by the number of reset steps and as such it is not extensive in time. A large deviation rate function can be…
We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…
We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…
Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…
The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states, which are visited subsequently by the system in a Markov-type hopping process. In the present work, we analyze the…
We investigate numerically the configurational statistics of strings. The algorithm models an ensemble of global $U(1)$ cosmic strings, or equivalently vortices in superfluid $^4$He. We use a new method which avoids the specification of…