MaxwellBench

Created by Bosch Center for Artificial Intelligence (BCAI)
Paper: TBD

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

Transformer_2D_UU	Transformer_2D_PQ
Transformer_2D_L	Inductor_2D_I_gap
Inductor_2D_EI_multi_gap	Inductor_2D_EI_multi
Inductor_2D_EE_multi	Inductor_2D_UU
Inductor_2D_Circular_Small_Gap	Inductor_2D_Circular_Large
Inductor_2D_Circular_Large_Gap	Electromagnet_2D
ElectromagnetC_wire_2D	ElectromagnetC_chunk_2D

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

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.