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---
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.