Related papers: A global algorithm for the computation of travelin…
We study theoretically the effects of dissipation on the performances of a variational quantum algorithm used to approximately solve a combinatorial optimization problem, the Maximum Independent Set, on a platform of neutral atoms. We take…
Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of…
Route choice is often modelled as a two-step procedure in which travellers choose their routes from small sets of promising candidates. Many methods developed to identify such choice sets rely on assumptions about the mechanisms behind the…
With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…
The initial value problem P0, in all of the space, for the spatio - temporal FitzHugh - Nagumo equations is analyzed. When the reaction kinetics of the model can be outlined by means of piecewise linear approximations, then the solution of…
This paper presents a fast method for global search of atomic structures at ab initio level. The structures global optimization (SGO) engine consists of a high-efficiency differential evolution algorithm, accelerated local relaxation…
We use soliton perturbation theory and collective coordinate ansatz to investigate the mechanism of soliton ratchets in a driven and damped asymmetric double sine-Gordon equation. We show that, at the second order of the perturbation…
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional DeepParticle (BDP) method to learn and generate solutions…
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
We develop a hierarchical functional derivative method to investigate the reduced dynamics of a quantum dissipative system within the framework of a stochastic decoupling description. Keeping only the lowest order truncation of the…
This paper constructs a predictor-corrector technique with orthogonal spline collocation finite element method for simulating a FitzHugh-Nagumo system subject to suitable initial and boundary conditions. The developed computational…
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…
Multidimensional hypoelliptic diffusions arise naturally in different fields, for example to model neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. In this paper we…
The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear…
We present an algorithm to compute stabilizing minimum dwell times for discrete-time switched linear systems without the explicit knowledge of state-space models of their subsystems. Given a set of finite traces of state trajectories of the…