Related papers: Level Set Methods for Stochastic Discontinuity Det…
Large-scale nonconvex and nonsmooth problems have attracted considerable attention in the fields of compress sensing, big data optimization and machine learning. Exploring effective methods is still the main challenge of today's research.…
In this paper we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify: (i) the discontinuity points of systems described by piecewise dynamical equations…
Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and…
This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a class of nonlocal Hamilton--Jacobi equations and establish a…
In this paper, we consider the stochastic optimal control problem for jump diffusion systems with state constraints. In general, the value function of such problems is a discontinuous viscosity solution of the Hamilton-Jacobi-Bellman (HJB)…
We present a novel approach to determine the evolution of level sets under uncertainties in the velocity fields. This leads to a stochastic description of the level sets. To compute the quantiles of random level sets, we use the stochastic…
This paper extends the deterministic Lyapunov-based stabilization framework to random hyperbolic systems of conservation laws, where uncertainties arise in boundary controls and initial data. Building on the finite volume discretization…
This paper constructs and analyzes a boundary correction finite element method for the Stokes problem based on the Scott-Vogelius pair on Clough-Tocher splits. The velocity space consists of continuous piecewise quadratic polynomials, and…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…
This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less…
This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for…
We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
In this paper, we study a new model of nonlocal geometric equations which appears in tomographic reconstruction when using the level-set method. We treat two additional difficulties which make the work original. On one hand, the level lines…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
Highly concentrated patterns have been observed in a spatially heterogeneous, nonlocal, model of BGK type implementing a velocity-jump process. We study both a linear and a nonlinear case and describe the concentration profile. In…
Let $H$ be a bounded and Lipschitz continuous function. We consider discontinuous viscosity solutions of the Hamilton-Jacobi equation $U_{t}+H(U_x)=0$ and signed Radon measure valued entropy solutions of the conservation law…
This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…