1 citations · 2 across the 9 of their papers we have counts for
10 papers
Elliptic PDEs on log-Gaussian Shapes: Sparsity and Finite Element Discretization
Dinh Dũng, Helmut Harbrecht, Van Kien Nguyen +1
In this article, we consider the solution to elliptic diffusion problems on a class of random domains obtained by log-Gaussian random homothety of the unit disk respectively an ann…
Piecewise-polynomial interpolations and quadratures for parametric PDEs with log-Laplace random inputs
Dinh Dũng
We establish a sparsity in terms of -summability and weighted -summability for the coefficients of the Laguerre generalized piecewise-polynomial chaos expansion of…
Sparsity for parametric PDEs with log-gamma random inputs and applications
Dinh Dũng, Van Kien Nguyen, Viet Ha Hoang
We propose a novel method for establishing the sparsity of the coefficients of the Laguerre generalized polynomial chaos expansion of solutions to parametric elliptic PDEs with log…
Approximation of PDE solution manifolds: Sparse-grid interpolation and quadrature
Dinh Dũng, Van Kien Nguyen, Duong Thanh Pham +1
We study fully-discrete approximations and quadratures of infinite-variate functions in abstract Bochner spaces associated with a Hilbert space and an infinite-tensor-product J…
Weighted approximate sampling recovery and integration based on B-spline interpolation and quasi-interpolation
Dinh Dũng
We propose novel methods for approximate sampling recovery and integration of functions in the Freud-weighted Sobolev space . The approximation error of samp…
Computation complexity of deep ReLU neural networks in high-dimensional approximation
Dinh Dũng, Van Kien Nguyen, Mai Xuan Thao
The purpose of the present paper is to study the computation complexity of deep ReLU neural networks to approximate functions in Hölder-Nikol'skii spaces of mixed smoothness $H_\in…