1 code implementation • 30 Jun 2023 • Vinh Hoang, Luis Espath, Sebastian Krumscheid, Raúl Tempone
A-optimality is a widely used and easy-to-interpret criterion for Bayesian experimental design.
no code implementations • 21 Feb 2023 • Luis Espath, Pouria Behnoudfar, Raul Tempone
In this work, we further develop the Physics-informed Spectral Learning (PiSL) by Espath et al. \cite{Esp21} based on a discrete $L^2$ projection to solve the discrete Hodge--Helmholtz decomposition from sparse data.
no code implementations • 25 Oct 2022 • Hamed Saidaoui, Luis Espath, Rául Tempone
In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing Dirichlet boundary conditions.
no code implementations • 22 Sep 2021 • Luis Espath, Sebastian Krumscheid, Raúl Tempone, Pedro Vilanova
In this study, we demonstrate that the norm test and inner product/orthogonality test presented in \cite{Bol18} are equivalent in terms of the convergence rates associated with Stochastic Gradient Descent (SGD) methods if $\epsilon^2=\theta^2+\nu^2$ with specific choices of $\theta$ and $\nu$.