Related papers: The Study on the Nonlinear Computations of the DQ …
We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as…
A finite element method for solving nonlinear differential equations on a grid, with potential applicability to computational fluid dynamics (CFD), is developed and tested. The current method facilitates the computation of solutions of a…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
This paper deals with the numerical computations of two space dimensional time dependent parabolic partial differential equations by adopting adopting an optimal five stage fourth-order strong stability preserving Runge Kutta (SSP-RK54)…
We present a new method to solve nonlinear Hammerstein equations with weakly singular kernels. The process to approximate the solution, followed usually, consists in adapting the discretization scheme from the linear case in order to obtain…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
The Hadamard product of two tensors in the tensor-train (TT) format is a fundamental operation across various applications, such as TT-based function multiplication for nonlinear differential equations or convolutions. However, conventional…
Dynamical Decoupling (DD) is perhaps the simplest and least resource-intensive error suppression strategy for improving quantum computer performance. Here we report on a large-scale survey of the performance of 60 different DD sequences…
We derive a numerical method for Darcy flow, hence also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is…
The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative…
In the paper an efficient semi-analytical approach based on the method of steps and differential transformation is proposed for numerical approximation of solutions of retarded logistic models of delayed and neutral type, including models…
Conventional multiply-accumulate (MAC) operations have long dominated computation time for deep neural networks (DNNs), espcially convolutional neural networks (CNNs). Recently, product quantization (PQ) has been applied to these workloads,…
An extension of the product operator formalism of NMR is introduced, which uses the Hadamard matrix product to describe many simple spin 1/2 relaxation processes. The utility of this formalism is illustrated by deriving NMR…
This article presents a unified approach to quadratic optimal control for both linear and nonlinear discrete-time systems, with a focus on trajectory tracking. The control strategy is based on minimizing a quadratic cost function that…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
The inherent diversity of computation types within the deep neural network (DNN) models often requires a variety of specialized units in hardware processors, which limits computational efficiency, increasing both inference latency and power…
In this paper, a novel Hermite radial basis function-based differential quadrature method (H-RBF-DQ) is presented. This new method is designed to treat derivative boundary conditions accurately. The developed method is very different from…