Related papers: Sensitivity analysis of fractional linear systems …
In this paper, we develop a highly parallel and derivative-free fractional neural walk-on-spheres method (FNWoS) for solving high-dimensional fractional Poisson equations on irregular domains. We first propose a simplified fractional…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…
Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
Inverse optimal control can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…
In this paper, we present a novel approach based on the random walk process for finding meaningful representations of a graph model. Our approach leverages the transient behavior of many short random walks with novel initialization…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
This article presents a novel perspective along with a scalable methodology to design a fault detection and isolation (FDI) filter for high dimensional nonlinear systems. Previous approaches on FDI problems are either confined to linear…
The accuracy of floating-random-walk (FRW) based capacitance extraction stands only when the recursive FRW transitions are sampled unbiasedly according to surrounding dielectrics. Advanced technology profiles, featuring complicated…
Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
We give faster algorithms for producing sparse approximations of the transition matrices of $k$-step random walks on undirected, weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of…
A class of discrete time random walks has recently been introduced to provide a stochastic process based numerical scheme for solving fractional order partial differential equations, including the fractional subdiffusion equation. Here we…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
Perception of time from sequentially acquired sensory inputs is rooted in everyday behaviors of individual organisms. Yet, most algorithms for time-series modeling fail to learn dynamics of random event timings directly from visual or audio…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…