Related papers: Improving the stability and efficiency of high-ord…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation-discarding technique is proposed along with the stopping rule to significantly…
In this paper we present an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. We are motivated by dynamical systems, which occur in dynamics of the electrons in…
The three-operators splitting algorithm is a popular operator splitting method for finding the zeros of the sum of three maximally monotone operators, with one of which is cocoercive operator. In this paper, we propose a class of inertial…
We show how the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics (with accuracy of order $\tau^2$ for a timestep of length $\tau$) can be improved in a systematic manner without using the…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We propose and analyze an adaptive step-size variant of the Davis-Yin three operator splitting. This method can solve optimization problems composed by a sum of a smooth term for which we have access to its gradient and an arbitrary number…
Many existing methods for constructing optimal split-plot designs, such as D-optimal designs, only focus on minimizing the variances and covariances of the estimation for the fitted model. However, the underlying true model is usually…
Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…
Shor's algorithm is one of the most prominent quantum algorithms, yet finding efficient implementations remains an active research challenge. While many approaches focus on low-level modular arithmetic optimizations, a broader perspective…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
We consider Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part. We consider abstract splitting methods associated with this decomposition where no discretization in space is made. We prove a…
Trotter-Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error---the Trotter error. The Trotter…
Nonlinear parabolic equations are central to numerous applications in science and engineering, posing significant challenges for analytical solutions and necessitating efficient numerical methods. Exponential integrators have recently…
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…
Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled with numerical methods of different…
It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
The single-step explicit time integration methods have long been valuable for solving large-scale nonlinear structural dynamic problems, classified into single-solve and multi-sub-step approaches. However, no existing explicit single-solve…
Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference…