Related papers: On the matching of eigensolutions to parametric pa…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
A local and parallel algorithm based on the multilevel discretization is proposed in this paper to solve the eigenvalue problem by the finite element method. With this new scheme, solving the eigenvalue problem in the finest grid is…
The reliability is of the most importance when employing a numerical method to solve the eigenvalue integral equations. In this paper, we present one type of particular singularities (pseudosingularities) existing in eigenvalue integral…
We consider the problem of numerically approximating the solutions to a partial differential equation (PDE) when there is insufficient information to determine a unique solution. Our main example is the Poisson boundary value problem, when…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
This research presents a novel method using an adversarial neural network to solve the eigenvalue topology optimization problems. The study focuses on optimizing the first eigenvalues of second-order elliptic and fourth-order biharmonic…
The focus is on a model reduction framework for parameterized elliptic eigenvalue problems by a reduced basis method. In contrast to the standard single output case, one is interested in approximating several outputs simultaneously, namely…
In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
In our previous work [Singler, SIAM J. Numer. Anal. 52 (2014), no. 2, 852-876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous…
In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…
In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters $\omega$ and we are interested in the…
The main focus of the present work is the inclusion of spatial adaptivity for the snapshot computation in the offline phase of model order reduction utilizing Proper Orthogonal Decomposition (POD-MOR) for nonlinear parabolic evolution…
Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…
We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order…
In this paper, we discuss approximating the eigenvalue problem of biharmonic equation. We first present an equivalent mixed formulation which admits amiable nested discretization. Then, we construct multi-level finite element schemes by…
It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…
We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…