Final project for the course Generative Neural Networks for the Sciences at Heidelberg University.

This project studies Mechanistic Neural Networks (MNNs) for scientific machine learning, with a focus on:

• equation identifiability
• robustness under noise and sparsity
• representation learning and generalization
• regularization effects on Lorenz equation discovery

The work is based on the paper and official codebase of Mechanistic Neural Networks, and extends the original setup with additional analyses on identifiability and regularization.

Mechanistic Neural Networks (MNNs) aim to bridge neural network flexibility and mechanistic interpretability by learning explicit ODE-based representations rather than purely latent mappings.

In this project, we reproduce key parts of the original MNN framework and then investigate several research questions:

1. Identifiability and robustness
   How reliably can MNNs recover the true governing equations under noisy, sparse, or partially observed conditions?

2. Representation learning and generalization
   How does mechanistic structure affect interpretability, out-of-distribution behavior, and long-horizon forecasting compared to more standard neural architectures?

3. Lorenz regularization case study
   Does sparsity-based regularization, such as (L_1) and Elastic Net penalties, improve identifiability in Lorenz equation discovery?

This repository contains:

• baseline reproduction of the original MNN implementation
• identifiability experiments on damped sine systems
• architecture and generalization experiments on damped sine and two-body systems
• Lorenz equation discovery experiments
• uncertainty and robustness extensions
• final report and supporting figures

GNN-Final/
├── figs/                     # figures used in the report
├── results/                  # generated experiment outputs
├── report_gnn.tex            # main LaTeX report
├── references.bib           # bibliography
├── acronyms.tex             # acronym definitions
├── glossary.tex             # glossary
├── hsluthesis.cls           # thesis/report style
├── hsluthesisterms.sty      # additional style file
└── ...