Related papers: The Kramers equation simulation algorithm I. Opera…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical…
We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
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…
The Multiple Try Metropolis (MTM) method is a generalization of the classical Metropolis-Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
We propose a new approach to computing global minimizers of singular value functions in two real variables. Specifically, we present new algorithms to compute the Kreiss constant of a matrix and the distance to uncontrollability of a linear…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
The simplest technique for simulating a quantum algorithm - QA described based on the direct matrix representation of the quantum operators. Using this approach, it is relatively simple to simulate the operation of a QA and to perform…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for…
The physics of crystalline membranes, i.e. fixed-connectivity surfaces embedded in three dimensions and with an extrinsic curvature term, is very rich and of great theoretical interest. To understand their behavior, numerical simulations…
By means of Metropolis Monte Carlo simulations of a coarse-grained model for flexible polymers, we investigate how the integrated autocorrelation times of different energetic and structural quantities depend on the temperature. We show…
Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
In this paper, an efficient parallel splitting method is proposed for the optimal control problem with parabolic equation constraints. The linear finite element is used to approximate the state variable and the control variable in spatial…