Related papers: Embedded operator splitting methods for perturbed …
We formulate the discovery of Lax integrability of Hamiltonian dynamical systems as a symbolic regression problem, which, loosely speaking, seeks to maximize the compatibility between a pair of Lax operators and the known Hamiltonian of the…
OPUS is a branch and bound search algorithm that enables efficient admissible search through spaces for which the order of search operator application is not significant. The algorithm's search efficiency is demonstrated with respect to…
Quasiperiodic elliptic operators (QEOs) serve as fundamental models in both mathematics and physics, as exemplified by their role in the numerical modeling of one-dimensional photonic quasicrystals. However, distinct from periodic elliptic…
In this paper, we develop a novel {\bf ho}moto{\bf p}y {\bf s}moothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering…
A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
Splitting schemes are numerical integrators for Hamiltonian problems that may advantageously replace the St\"ormer-Verlet method within Hamiltonian Monte Carlo (HMC) methodology. However, HMC performance is very sensitive to the step size…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…
Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called,…
We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…
We consider {\em discretized} Hamiltonian PDEs associated with a Hamiltonian function that can be split into a linear unbounded operator and a regular nonlinear part. We consider splitting methods associated with this decomposition. Using a…
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…
We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…
We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schr\"odinger (DDNLS)…
Ising machines as hardware solvers of combinatorial optimization problems (COPs) can efficiently explore large solution spaces due to their inherent parallelism and physics-based dynamics. Many important COP classes such as satisfiability…