Poisson Equation

홈페이지 · 논문 2편

\subsection{Poisson Equation} The Poisson equation with Dirichlet boundary conditions is studied: \begin{align} -\Delta u &= f, \quad \text{in } \Omega = [0,1]^2, \\ u &= 0, \quad \text{on } \partial \Omega, \end{align} where \(f\) consists of a Gaussian superposition, with parameters \(\mu_{x,i}, \mu_{y,i} \sim \text{U}(0,1)\) and \(\sigma_i \sim \text{U}(0.025, 0.1)\). The dataset includes 4000 training, 500 validation, and 500 test samples.