inverse-source-em 0.1.0

Unified forward models, surrogate models, and inverse EM pipelines.

Inverse Source EM

Deep Learning Methods for Electromagnetic Inverse Source Problems

Version: 0.9.0-beta

This repository provides a complete scientific machine learning framework for electromagnetic inverse source problems in cylindrical geometries. It combines:

• Physics-based analytical solvers (Helmholtz equation, TM polarization)
• Neural surrogate models for fast forward simulations
• Deep learning pipelines for classification and localization of internal sources
• Modular evaluation suites for reproducible benchmarking
• A clean, pip-installable Python package (inverse_source_em)

The project has been fully migrated from notebooks into a modern, modular, production-ready architecture.

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1. Abstract

We study an inverse source problem inside a dielectric cylinder, belonging to the broader class of inverse scattering problems. The goal is to recover the:

• number of internal line sources,
• positions (Cartesian or polar),
• strengths,

using only electric surface field measurements at a single frequency.

The forward problem is solved analytically using cylindrical harmonics and Bessel/Hankel special functions. The PhysicsTM class provides a stable, vectorized implementation of the TM-polarized Helmholtz equation.

On top of this, we build three machine learning pipelines:

1. Surrogate EM models for fast forward simulations
2. Classification models for predicting the number of sources (1–5)
3. Regression models for localizing 1, 2, or 3 internal sources

The surrogate models enable large-scale dataset generation with high accuracy. The regression pipelines incorporate geometric sampling, canonical ordering, structured losses, and permutation-invariant evaluation.

The results demonstrate high accuracy, strong noise robustness, and reliable generalization even in challenging geometries.

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2. Project Structure

inverse-source-em/
│
├── data/
│   ├── classification/
│   ├── regression_1src/
│   ├── regression_2src/
│   ├── regression_3src/
│   └── surrogate/
│
├── models/
│   ├── surrogate_Esurf.pth
│   ├── surrogate_Hsurf.pth
│   ├── classifier_1_to_5_resnet1d.pt
│   ├── regression_1src/
│   ├── regression_2src/
│   └── regression_3src/
│
├── scripts/
│   ├── make_1src_dataset.py
│   ├── make_2src_dataset.py
│   ├── make_3src_dataset.py
│   ├── make_classification_dataset.py
│   ├── make_surrogate_dataset.py
│   ├── train_1src_model.py
│   ├── train_2src_model.py
│   ├── train_3src_model.py
│   ├── train_classification_model.py
│   └── train_surrogate_models.py
│
├── evaluation/
│   ├── classification/
│   ├── regression_1src/
│   ├── regression_2src/
│   ├── regression_3src/
│   └── surrogates/
│
├── notebooks/
│   ├── regression_1src_evaluation.ipynb
│   ├── regression_2src_evaluation.ipynb
│   ├── regression_3src_evaluation.ipynb
│   ├── classification_evaluation.ipynb
│   └── physics_vs_surrogate.ipynb
│
├── src/inverse_source_em/
│   ├── surrogate/
│   ├── data/
│   ├── physics/
│   ├── training/
│   ├── evaluation/
│   └── utils/
│
├── pyproject.toml
├── requirements.txt
└── README.md

---

3. Surrogate Pipeline (Canonical & Frozen)

The surrogate pipeline is complete and frozen. It provides:

• SurrogateEM — unified EM surrogate model
• SurrogateMLP — configurable MLP surrogate
• SurrogateWrapper — PhysicsTM-compatible interface
• Sampling and dataset generation utilities

These models form the reference baseline for all inverse tasks.

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4. Classification Pipeline (Completed)

Predicts the number of internal sources (1–5) from surface field intensities.

Includes:

• Sampling (sampling_classification.py)
• Dataset generation (generator_classification.py)
• PyTorch dataset wrapper (dataset_classification.py)
• ResNet1D classifier (classification_model.py)
• Training script (train_classification_model.py)
• Evaluation suite (evaluation/classification/)

Baseline performance:

• Validation accuracy: ~0.984
• Test accuracy: ~0.985
• Strong robustness to additive noise

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5. Regression Pipelines

5.1 Single-Source Localization (1src)

• Predicts (x, y, I)
• Canonical sampling
• High accuracy and noise robustness
• Full evaluation suite

5.2 Two-Source Localization (2src)

• Predicts (x1, y1), (x2, y2)
• Fully permutation-invariant
• Strong performance across all geometry levels
• Full evaluation suite

5.3 Three-Source Localization (3src) — New in v0.9.0-beta

• Predicts (x1, y1), (x2, y2), (x3, y3)
• Canonical ordering
• Geometry-level sampling (Levels 1–8)
• Modular evaluation suite:
  • accuracy
  • error tables
  • noise robustness
  • stress tests
  • timing
  • run_all (CLI entrypoint)

Run the full evaluation:

python -m evaluation.regression_3src.run_all

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6. Installation

From source

git clone https://github.com/<username>/inverse-source-em.git
cd inverse-source-em
pip install -e .

Requirements

pip install -r requirements.txt

---

7. Usage Examples

Surrogate forward model

from inverse_source_em.surrogate import SurrogateEM, SurrogateWrapper
from inverse_source_em.physics import PhysicsTM

phys = PhysicsTM()
sur = SurrogateEM(
    path_E="models/surrogate_Esurf.pth",
    path_H="models/surrogate_Hsurf.pth",
    R=phys.R
)
wrap = SurrogateWrapper(sur)

E = wrap.Esurf(rho_s, phi_s, theta)

Classification inference

import torch
from inverse_source_em.training.classification_model import SourceCountResNet1D

model = SourceCountResNet1D(...)
model.load_state_dict(torch.load("models/classifier_1_to_5_resnet1d.pt"))
model.eval()

pred = model(X).argmax(dim=1)

---

8. Evaluation Suites

Each task has a complete evaluation suite under evaluation/:

• classification/
• regression_1src/
• regression_2src/
• regression_3src/
• surrogates/

Each suite includes:

• accuracy
• error tables
• noise robustness
• stress tests
• timing
• run_all (CLI entrypoint)

Run an evaluation:

python -m evaluation.regression_3src.run_all

---

9. Reproducibility

• Surrogate pipeline is canonical and frozen
• Deterministic dataset generation
• Fixed seeds in training scripts
• Versioned datasets and models
• Modular evaluation suites
• Clean separation of concerns (physics / surrogate / ML / evaluation)

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10. License

This project is licensed under the MIT License.

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11. Citation

If you use this project in academic work, please cite:

Papadopoulos, T. D.
Master Thesis in Applied Mathematics
Hellenic Open University

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12. Roadmap

• Surrogate pipeline (canonical)
• Classification pipeline
• Regression 1src
• Regression 2src
• Regression 3src
• Unified evaluation suites
• GitHub release v0.9.0-beta
• pip packaging
• Regression IV (variable number of sources)
• v1.0.0 stable release

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13. Acknowledgments

I would like to express my sincere gratitude to my supervisor, Professor Nikolaos Tsitsas, whose guidance, insight, and continuous support were instrumental throughout the development of this research.

I would also like to acknowledge the team behind Microsoft Copilot for developing an advanced AI assistant that greatly facilitated the organization, refinement, and documentation of this project.