---
tags:
- physics
- simulation
- FEM
- electromagnetics
- neural-operator
- scientific-computing
size_categories:
- 100K<n<1M
pretty_name: MaxwellBench
dataset_creators:
  - Bosch Center for Artificial Intelligence (BCAI)
viewer: false
---

# MaxwellBench

<p align="center">
  <img src=".huggingface/Bosch_logo.png" alt="Bosch Logo" width="200">
</p>

<p align="center">
  <em>Created by <a href="https://www.bosch-ai.com/">Bosch Center for Artificial Intelligence (BCAI)</a></em>
  <br>
  <strong>Paper:</strong> TBD <!-- Replace with the paper URL once published -->
</p>

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).

### Sample Visualizations

<table>
<tr>
<td align="center"><strong>Transformer_2D_UU</strong><br><img src=".huggingface/Transformer_2D_UU.png"></td>
<td align="center"><strong>Transformer_2D_PQ</strong><br><img src=".huggingface/Transformer_2D_PQ.png"></td>
</tr>
<tr>
<td align="center"><strong>Transformer_2D_L</strong><br><img src=".huggingface/Transformer_2D_L.png"></td>
<td align="center"><strong>Inductor_2D_I_gap</strong><br><img src=".huggingface/Inductor_2D_I_gap.png"></td>
</tr>
<tr>
<td align="center"><strong>Inductor_2D_EI_multi_gap</strong><br><img src=".huggingface/Inductor_2D_EI_multi_gap.png"></td>
<td align="center"><strong>Inductor_2D_EI_multi</strong><br><img src=".huggingface/Inductor_2D_EI_multi.png"></td>
</tr>
<tr>
<td align="center"><strong>Inductor_2D_EE_multi</strong><br><img src=".huggingface/Inductor_2D_EE_multi.png"></td>
<td align="center"><strong>Inductor_2D_UU</strong><br><img src=".huggingface/Inductor_2D_UU.png"></td>
</tr>
<tr>
<td align="center"><strong>Inductor_2D_Circular_Small_Gap</strong><br><img src=".huggingface/Inductor_2D_Circular_Small_Gap.png"></td>
<td align="center"><strong>Inductor_2D_Circular_Large</strong><br><img src=".huggingface/Inductor_2D_Circular_Large.png"></td>
</tr>
<tr>
<td align="center"><strong>Inductor_2D_Circular_Large_Gap</strong><br><img src=".huggingface/Inductor_2D_Circular_Large_Gap.png"></td>
<td align="center"><strong>Electromagnet_2D</strong><br><img src=".huggingface/Electromagnet_2D.png"></td>
</tr>
<tr>
<td align="center"><strong>ElectromagnetC_wire_2D</strong><br><img src=".huggingface/ElectromagnetC_wire_2D.png"></td>
<td align="center"><strong>ElectromagnetC_chunk_2D</strong><br><img src=".huggingface/ElectromagnetC_chunk_2D.png"></td>
</tr>
</table>


## 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.