Related papers: Efficient Computation of Higher-Order Variational …
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on…
Gaussian wavepacket dynamics has proven to be a useful semiclassical approximation for quantum simulations of high-dimensional systems with low anharmonicity. Compared to Heller's original local harmonic method, the variational Gaussian…
In this article, we investigate the convergence rate of the discrete-time Clark--Ocone formula provided by Akahori--Amaba--Okuma [1]. In that paper, they mainly focus on the $L_{2}$-convergence rate of the first-order error estimate related…
This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…
This paper proposes a novel and efficient optimization-based method for generating near time-optimal trajectories for holonomic vehicles navigating through complex but structured environments. The approach aims to solve the problem of…
As a model of more general contour integration problems we consider the numerical calculation of high-order derivatives of holomorphic functions using Cauchy's integral formula. Bornemann (2011) showed that the condition number of the…
There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
This paper considers the problem of real-time mode scheduling in linear time-varying switched systems subject to a quadratic cost functional. The execution time of hybrid control algorithms is often prohibitive for real-time applications…
We consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
Accelerated gradient methods have had significant impact in machine learning -- in particular the theoretical side of machine learning -- due to their ability to achieve oracle lower bounds. But their heuristic construction has hindered…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…
We introduce a systematic construction of higher-order matrix product operator (MPO) approximations of the time evolution operator for generic (short and long range) one-dimensional Hamiltonians. We demonstrate the utility of our…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
In this study, we consider a numerical implementation of the nonlinear Rosenbluth-Trubnikov collision operator for particle simulations in plasma physics in the framework of the finite element method (FEM). The relevant particle evolution…
In this paper, we present an~algorithm that computes funnels along trajectories of systems of ordinary differential equations. A funnel is a time-varying set of states containing the given trajectory, for which the evolution from within the…