Related papers: Time discretization and quantization methods for o…
This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization combines the Euler scheme for temporal approximation and the finite element method for spatial…
A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…
This paper deals with the problem of asymptotically optimal detection of changes in regime-switching stochastic models. We need to divide the whole obtained sample of data into several sub-samples with observations belonging to different…
This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation…
We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type…
Model-based experimental design is attracting increasing attention in chemical process engineering. Typically, an iterative procedure is pursued: an approximate model is devised, prescribed experiments are then performed and the resulting…
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
Choosing control inputs randomly can result in a reduced expected cost in optimal control problems with stochastic constraints, such as stochastic model predictive control (SMPC). We consider a controller with initial randomization, meaning…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
We propose a comprehensive framework for policy gradient methods tailored to continuous time reinforcement learning. This is based on the connection between stochastic control problems and randomised problems, enabling applications across…
In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
Gate-model quantum computers can allow quantum computations in near-term implementations. The stabilization of an optimal quantum state of a quantum computer is a challenge, since it requires stable quantum evolutions via a precise…
The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal…
We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence…
We address the problem of Bayesian inference for parameters in ordinary differential equation (ODE) models based on observational data. Conventional approaches in this setting typically rely on numerical solvers such as the Euler or…
In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional It\^{o} model when the discrete rebalancing dates are stopping times. We investigate the convergence,…