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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…
Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs
Dinh Dũng, Van Kien Nguyen, Duong Thanh Pham
We investigate non-adaptive methods of deep ReLU neural network approximation in Bochner spaces of functions on taking values i…
A posteriori error estimates for hypersingular integral equation on spheres with spherical splines
Duong Thanh Pham, Tung Le
A posteriori residual and hierarchical upper bounds for the error estimates were proved when solving the hypersingular integral equation on the unit sphere by using the Galerkin me…
A shape calculus based method for a transmission problem with random interface
Alexey Chernov, Duong Pham, Thanh Tran
The present work is devoted to approximation of the statistical moments of the unknown solution of a class of elliptic transmission problems in with randomly perturbe…