muradulislam/PhyGAT-15k-Geometric-Nanofluids

PhyGAT-15k: Zero-Shot Geometric Nanofluid Dynamics Dataset

Overview

This dataset contains 15,000 highly relational PyTorch Geometric (.pt) graphs representing steady-state computational fluid dynamics (CFD) and convective heat transfer of 5-component hybrid nanofluids. It is specifically designed to train and evaluate Geometric Foundation Models for physics-informed machine learning, enabling zero-shot generalization across varying topologies.

The dataset overcomes the limitations of fixed-mesh surrogates by introducing procedurally generated geometries with dynamic boundaries, explicit Signed Distance Fields (SDFs), surface normals, and dimensionless thermodynamic parameterizations.

Physics & Thermodynamics

The dataset models a continuous fluid domain subject to the steady-state Navier-Stokes and Energy equations, solved via the FEniCS finite element framework.

• Nanoparticles: $Al_{2}O_{3}$, Cu, $TiO_{2}$, $SiO_{2}$, Multi-Walled Carbon Nanotubes (MWCNT).
• Dilute Limit: Total volumetric concentration $\phi \le 4%$.
• Properties: Density and specific heat are modeled via the Principle of Mixtures. Dynamic viscosity utilizes the Brinkman model. Thermal conductivity utilizes the Hamilton-Crosser model (accounting for anisotropic cylindrical MWCNTs).
• Convective Regime: Reynolds Number uniformly sampled between $Re = 40.0$ and $Re = 120.0$.

Procedural Geometry

Each of the 15,000 graphs features a unique geometry:

• Macrochannels: Straight, Converging (Funnel), and Step-Expansion.
• Internal Obstacles: Randomized counts (1 to 3) and shapes (Circles, Squares, Triangles) acting as heat sources $(T=1.0)$.
• Meshing: Unstructured triangular meshes generated via Gmsh, with typical resolutions ranging from 3,000 to 6,000 nodes per graph.

Graph Feature Structure

To enable true geometric generalization, standard absolute coordinates have been replaced with a rich, 32-dimensional relational node representation.

Node Features data.x (Shape: [N, 32])

Index	Feature	Description
0-1	Spatial	Absolute Cartesian coordinates $(x, y)$.
2-5	Boundary Flags	Binary flags for [Inlet, Outlet, Wall, Obstacle].
6-8	Dirichlet BCs	Explicit boundary conditions $[u_x, u_y, T]$.
9-11	Wall Vector SDF	Distance to nearest adiabatic wall, and unit direction vector $[dist, v_x, v_y]$.
12-14	Obs Vector SDF	Distance to nearest heated obstacle, and unit direction vector $[dist, v_x, v_y]$.
15-16	Surface Normals	Inward-pointing normal vectors for boundary nodes $[n_x, n_y]$.
17	Nodal Area	Finite element nodal integration weight (for continuous loss formulations).
18-22	Nanofluid Composition	Volume fractions $[\phi_{Al2O3}, \phi_{Cu}, \phi_{TiO2}, \phi_{SiO2}, \phi_{MWCNT}]$.
23-27	Thermodynamic	Effective mixture properties $[Re, \rho_{eff}, \mu_{eff}, k_{eff}, (\rho C_p)_{eff}]$.
28-31	Dimensionless	Kinematic viscosity, Thermal diffusivity, Prandtl, Péclet $[\nu, \alpha, Pr, Pe]$.

Edge Attributes data.edge_attr (Shape: [E, 9])

Index	Feature	Description
0-1	Displacement	Relative vector between source and destination node $[\Delta x, \Delta y]$.
2	Distance	Absolute edge length $L_2$ norm.
3-4	Unit Vector	Normalized displacement $[\Delta x / dist, \Delta y / dist]$.
5-8	Boundary Edges	Binary flags indicating if the edge lies entirely on a [Wall, Obstacle, Inlet, Outlet].

Target Features data.y (Shape: [N, 10])

All targets are extracted directly from the converged FEniCS Newton solver.

Index	Feature	Description
0-1	Velocity	$u_x, u_y$ [m/s].
2	Pressure	Static pressure $p$ [Pa].
3	Temperature	Non-dimensional temperature $T$.
4	Velocity Magnitude	$|u|$.
5	Vorticity	$\nabla \times u$.
6-7	Temperature Gradient	$\nabla T_x, \nabla T_y$.
8-9	Pressure Gradient	$\nabla p_x, \nabla p_y$.

Usage

These graphs are natively compatible with PyTorch Geometric (PyG). Due to the explicit inclusion of spatial gradients in the target matrix (data.y), models can be trained using pure supervised Mean Squared Error (MSE), or constrained via Physics-Informed Neural Network (PINN) loss functions without requiring auto-differentiation through the network.