Initial dataset card

README.md

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+---
+tags:
+- physics
+- simulation
+- FEM
+- electromagnetics
+- neural-operator
+- scientific-computing
+size_categories:
+- 100K<n<1M
+pretty_name: MaxwellBench
+---
+
+# MaxwellBench
+
+A large-scale benchmark of 2D finite-element electromagnetic simulations for training and evaluating neural operators. Each sample is a complete FEM problem—geometry (unstructured triangular mesh), material properties (nonlinear B-H curves, conductivity), excitation sources, boundary conditions—paired with the solved magnetic flux density **B** field.
+
+## Dataset Summary
+
+| Property | Value |
+|---|---|
+| Domain | 2D Electromagnetic FEM |
+| Number of subsets | 14 |
+| Samples per subset | 11000 (10000 train / 1000 val) |
+| Total samples | 154000 |
+| File format | HDF5 (`.h5`) |
+| Simulation types | Stationary, Frequency-domain |
+| Coordinate systems | Cartesian (x, y), Cylindrical axisymmetric (r, z) |
+
+## Subsets
+
+| Subset Name | Device Type | Coordinate | Simulation Type |
+|---|---|---|---|
+| `Transformer_2D_UU` | Transformer (UU core) | x, y | Frequency-domain |
+| `Transformer_2D_PQ` | Transformer (PQ core) | r, z | Frequency-domain |
+| `Inductor_2D_I_gap` | Inductor (I core with gap) | x, y | Frequency-domain |
+| `Inductor_2D_EI_multi_gap` | Inductor (EI core, with gaps) | x, y | Frequency-domain |
+| `Inductor_2D_EE_multi` | Inductor (EE core, fixed center gap) | x, y | Frequency-domain |
+| `Inductor_2D_Circular_Small_Gap` | Inductor (circular small core, with gaps) | x, y | Frequency-domain |
+| `Inductor_2D_Circular_Large` | Inductor (circular large core, no gaps) | x, y | Frequency-domain |
+| `Inductor_2D_UU` | Inductor (UU core) | x, y | Frequency-domain |
+| `Electromagnet_2D` ⚠️ | Electromagnet | r, z | Stationary |
+| `ElectromagnetC_wire_2D` | Electromagnet (C core, wire) | x, y | Stationary |
+| `Transformer_2D_L` | Transformer (L core) | x, y | Frequency-domain |
+| `Inductor_2D_EI_multi` | Inductor (EI core, fixed gap) | x, y | Frequency-domain |
+| `Inductor_2D_Circular_Large_Gap` | Inductor (circular large core, with gaps) | x, y | Frequency-domain |
+| `ElectromagnetC_chunk_2D` | Electromagnet (C core, chunk coil) | x, y | Stationary |
+
+> ⚠️ **Note:** The `Electromagnet_2D` subset is **not publicly released** as it is closely related to a real business use case. It is listed here for completeness but is excluded from the public download. The public release contains 13 subsets (143,000 samples total).
+
+## Data Format
+
+Each sample is stored as an HDF5 file `Data_{i}.h5`. Inside the file, a top-level group is named after the subset (e.g., `Transformer_2D_UU`). The group contains the following structure:
+
+### Attributes
+
+| Attribute | Description | Values |
+|---|---|---|
+| `Type` | Simulation type | `"Stationary"` or `"Frequency domain"` |
+| `Coordinate` | Coordinate system | `"x, y"` or `"r, z"` |
+
+### Fields (Mesh & Geometry)
+
+Located under `<subset_name>/Fields/`:
+
+| Key | Shape | Description |
+|---|---|---|
+| `Nodes` | `(N_n, 3)` | Node coordinates and type: `[p0, p1, node_type]`. `p0, p1` are spatial coordinates; `node_type` indicates boundary/interior. |
+| `Nodes_connectivity` | `(N_conn, 2)` | Edge connectivity (node index pairs). |
+| `Body_elements` | `(N_b, 3)` | Triangular element connectivity (3 node indices per element). |
+| `Body_areas` | `(N_b, 1)` | Area of each triangular element. |
+| `Edge_elements` | `(N_e, 2)` | Edge element connectivity (2 node indices per edge). |
+| `Edge_lengths` | `(N_e, 1)` | Length of each edge element. |
+
+### Materials
+
+**Body materials** (`<subset_name>/Materials_body/`): Each named material subgroup contains:
+- An index array mapping body elements to this material.
+- `BH` attribute: B-H curve as a `(K, 2)` array of `[H, B]` pairs (nonlinear permeability).
+- `sigma` attribute: Electrical conductivity (S/m).
+
+**Edge materials** (`<subset_name>/Materials_edge/`): Each named material subgroup contains an index array mapping edge elements to this material (used to identify material interfaces).
+
+### Sources
+
+Located under `<subset_name>/Sources/`: Each named source subgroup contains:
+- An index array mapping body elements to this source.
+- `magnitude` attribute: Current density magnitude (A/m²).
+- `frequency` attribute: Excitation frequency (Hz). Zero for stationary problems.
+- `phase` attribute: Phase angle (rad).
+
+### Boundaries
+
+Located under `<subset_name>/Boundaries/`: Each named boundary subgroup contains:
+- An index array mapping edge elements to this boundary.
+- `normal` attribute: `(2,)` outward normal vector.
+- `type` attribute: Boundary condition type — `"Mag_insulation"` or `"Axial_sym"`.
+
+### Physics (Target Output)
+
+Located under `<subset_name>/Physics/`: The solved magnetic flux density field on body elements.
+
+**Stationary problems:**
+
+| Key | Shape | Description |
+|---|---|---|
+| `realBx_elem` / `realBr_elem` | `(N_b, 1)` | Real part of B in x/r direction |
+| `realBy_elem` / `realBz_elem` | `(N_b, 1)` | Real part of B in y/z direction |
+
+**Frequency-domain problems** (additional imaginary components):
+
+| Key | Shape | Description |
+|---|---|---|
+| `realBx_elem` / `realBr_elem` | `(N_b, 1)` | Real part of B in x/r direction |
+| `imagBx_elem` / `imagBr_elem` | `(N_b, 1)` | Imaginary part of B in x/r direction |
+| `realBy_elem` / `realBz_elem` | `(N_b, 1)` | Real part of B in y/z direction |
+| `imagBy_elem` / `imagBz_elem` | `(N_b, 1)` | Imaginary part of B in y/z direction |
+
+## Directory Structure
+
+```
+MaxwellBench/
+├── Transformer_2D_UU/
+│   ├── train/
+│   │   ├── Data_0.h5
+│   │   ├── Data_1.h5
+│   │   └── ...           # 10000 files
+│   └── val/
+│       ├── Data_0.h5
+│       └── ...           # 1000 files
+├── Transformer_2D_PQ/
+│   ├── train/
+│   └── val/
+├── Inductor_2D_I_gap/
+│   ├── train/
+│   └── val/
+└── ...                   # same structure for all subsets
+```
+
+## Quick Start
+
+```python
+import h5py
+
+subset = "Transformer_2D_UU"
+with h5py.File(f"MaxwellBench/{subset}/train/Data_0.h5", "r") as f:
+    sim = f[subset]
+
+    # Metadata
+    sim_type = sim.attrs["Type"]          # "Stationary" or "Frequency domain"
+    coord = sim.attrs["Coordinate"]       # "x, y" or "r, z"
+
+    # Mesh
+    nodes = sim["Fields"]["Nodes"][:]              # (N_n, 3)
+    connectivity = sim["Fields"]["Nodes_connectivity"][:]  # (N_conn, 2)
+    elements = sim["Fields"]["Body_elements"][:]   # (N_b, 3)
+    areas = sim["Fields"]["Body_areas"][:]         # (N_b, 1)
+
+    # Target B field
+    Bx = sim["Physics"]["realBx_elem"][:]          # (N_b, 1)
+    By = sim["Physics"]["realBy_elem"][:]          # (N_b, 1)
+```
+A github repo with dataloader, model, and distributed training pipeline will be published in the future.
+
+## Intended Use
+
+MaxwellBench is designed to:
+- Train and benchmark **neural operators** for electromagnetic field prediction.
+- Evaluate **generalization** across device topologies, coordinate systems, and simulation regimes.
+- Support research on **foundation models** for scientific computing / PDE solving.
+
+## Citation
+
+If you use MaxwellBench in your work, please cite:
+
+> Paper forthcoming. Citation details will be updated upon publication.