Related papers: Newton's method and its hybrid with machine learni…
We propose a Newton-based scheme, initialized by neural operator predictions, to accelerate the parametric solution of nonlinear problems in computational solid mechanics. First, a physics informed conditional neural field is trained to…
A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton's method to the system of nonlinear equations obtained by the corresponding first-order necessary optimality…
The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…
We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…
We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of…
A posteriori estimates for mixed finite element discretizations of the Navier-Stokes equations are derived. We show that the task of estimating the error in the evolutionary Navier-Stokes equations can be reduced to the estimation of the…
This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the…
The aim of this paper is to propose a systematic way to obtain convergent finite element schemes for the Darcy-Stokes flow problem by combining well-known mixed finite elements that are separately convergent for Darcy and Stokes problems.…
We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with non-globally Lipschitz and non-monotone nonlinearities,…
The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
In this paper, we present a Newton-like method based on model reduction techniques, which can be used in implicit numerical methods for approximating the solution to ordinary differential equations. In each iteration, the Newton-like method…
In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…