Omkar2118/datasets huggingface dataset:
CylinderFlow
Full name: CylinderFlow with dynamic grid

This dataset captures incompressible fluid dynamics around a 2D circular cylinder within a channel:
\begin{align}
    \nabla \cdot \mathbf{u} &= 0, \\
    \partial_t \mathbf{u} + (\mathbf{u} \cdot \nabla) \mathbf{u} &= \nu \nabla^2 \mathbf{u} - \frac{1}{\rho} \nabla p,
\end{align}
with boundary conditions set for velocity and pressure. It features 100 snapshots per case, with 7600 training, 1000 validation, and 1000 test samples.

Introducing paper: Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries
Poisson Equation
Full name: Poisson Equation with unstructured grid

\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.

Introducing paper: Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries