Related papers: Most probable escape paths in perturbed gradient s…
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…
The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two…
For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent…
We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…
We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic…
Using path-integral methods, a formula is deduced for the noise-induced escape rate from an attracting fixed point across an unstable fixed point in one-dimensional maps. The calculation starts from the trace formula for the eigenvalues of…
We present a comprehensive theoretical analysis of first-order methods for escaping strict saddle points in smooth non-convex optimization. Our main contribution is a Perturbed Saddle-escape Descent (PSD) algorithm with fully explicit…
We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of…
The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport…
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these…
In this thesis we consider stochastic resonance for a diffusion with drift given by a potential, which has two metastable states and two pathways between them. Depending on the direction of the forcing the height of the two barriers, one…
Studying the properties of stochastic noise to optimize complex non-convex functions has been an active area of research in the field of machine learning. Prior work has shown that the noise of stochastic gradient descent improves…
Properties of the noise-driven escape kinetics are mainly determined by the stochastic component of the system dynamics. Nevertheless, the escape dynamics is also sensitive to deterministic forces. Here, we are exploring properties of the…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
Using the path integral representation of the non-equilibrium dynamics, we compute the most probable path between arbitrary starting and final points, followed by an active particle driven by persistent noise. We focus our attention on the…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
We reveal the escape mechanism of orbits in a Hamiltonian system with four exit channels composed of two-dimensional perturbed harmonic oscillators. We distinguish between trapped chaotic, non-escaping regular and escaping orbits by…
We study a fixed step-size noisy distributed gradient descent algorithm for solving optimization problems in which the objective is a finite sum of smooth but possibly non-convex functions. Random perturbations are introduced to the…
The complex dynamics of an increasing number of systems is attributed to the emergence of a rugged energy landscape with an exponential number of metastable states. To develop this picture into a predictive dynamical theory I discuss how to…