Learning Electromagnetic Fields Based on Finite Element Basis Functions

This repository implements the methodology from the paper “Learning Electromagnetic Fields Based on Finite Element Basis Functions”. It combines Isogeometric Analysis (IGA), Proper Orthogonal Decomposition (POD), and Deep Neural Networks (DNNs) to efficiently predict electromagnetic fields in a parametric model of a Permanent Magnet Synchronous Machine (PMSM). Instead of learning field values directly, the network predicts coefficients in a reduced POD basis derived from high-fidelity IGA simulations, ensuring physical consistency and enabling rapid evaluation of quantities of interest such as torque. Two surrogate models are provided:

• Airgap field surrogate for torque-focused applications.
• Full field surrogate for detailed rotor, stator, and airgap predictions.

Related Publication

If you use this code, please cite:

10.1109/TMAG.2025.3629546

Requirements

• Python 3.11+
• MATLAB R2024b (tested until R2026a) with MATLAB Curve Fitting Toolbox

Install Python dependencies:

pip install -r requirements.txt

Python dependencies:

pandas 2.3.3
torch 2.8.0
numpy 2.3.4
matplotlib 3.10.6

No other packages need to be downloaded at this point. To provide a fully working snapshot, we already include here the code snapshots for the packages:

• GeoPDEs: [https://rafavzqz.github.io/geopdes/]
• NURBS toolbox: [https://de.mathworks.com/matlabcentral/fileexchange/26390-nurbs-toolbox-by-d-m-spink]

We acknowledge these toolboxes and also reused parts of the code published here.

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Usage

To reproduce the full pipeline:

1. Data Generation (MATLAB)

Run:

matlab -batch "computeSamples(isgap)"

Where isgap is:

• true for airgap field
• false for full field

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2. POD Computation (Python)

python perform_pod.py true

Replace true with false for full field.

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3. Train Neural Network

python train_net.py true

Replace true with false for full field.

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4. Analyze Predictions

python analyze_net.py true false

Arguments:

• first: true for airgap field, false for full field
• second: false to use your trained network

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5. Compute Errors (MATLAB)

Run:

matlab -batch "computeErrors(isgap, paper)"

Arguments:

• isgap: true for airgap field, false for full field
• paper: false to use your generated predictions

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Output Files

• Directories: sol_XX_training, sol_XX_testing, sol_XX_validation
• Torch model: model_XX.pt
• Predictions: Predictions_XX_XX
• Error tables: Error_XX_XX.csv

Important: The mean, standard deviation, and maximum values of the computed error tables may differ slightly from those in the paper because of numerical errors during data generation, projection matrix computation, and training, as well as minor hyperparameter differences.

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Reproducing Paper Results

Download the training, testing, and validation data as well as the two files MatrixK_full.csv and MatrixK_gap.csv from Zenodo and put them into the main folder:

Run:

python analyze_net.py true true

Then:

matlab -batch "computeErrors(true, true)"