Weight-Parameterization in Continuous Time Deep Neural Networks for Surrogate Modeling

Manuscript, code, and data for:

@article{RossoRuthottoSargsyan,
  title         = {Weight-Parameterization in Continuous Time Deep Neural Networks for Surrogate Modeling},
  author        = {Haley Rosso and Lars Ruthotto and Khachik Sargsyan},
  year          = {2025},
  eprint        = {2507.22045},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG},
  url           = {https://arxiv.org/abs/2507.22045}
}

Contents

main.tex       manuscript
matlab/        discretize-then-optimize experiments (ResNet, Hamiltonian network)
python/        optimize-then-discretize experiments (neural ODE) and the figure and table generators
data/          ELM and CDR datasets, dataset loaders, train/validation/test splits
results/       run ledgers, sweep manifests, curve data
tables/        generated tabular bodies, included by main.tex
figures/       generated figures, included by main.tex

Requirements: MATLAB R2022a or newer with the Symbolic Math Toolbox, Python 3.13 with python/requirements.txt, and a LaTeX distribution with latexmk.

Build

make test      # MATLAB and Python unit tests
make figures   # compile the figure sources to PDF
make tables    # regenerate tables/*.tex from results/
make paper     # main.pdf

make tables, make figures and make paper read the committed ledgers in results/ and do not retrain.

Reproduce the experiments

Each sweep takes hours to days and writes to results/raw/<sweepId>/, which is not committed.

cd matlab/experiments && ./runNamedSweep.sh runPaperSweep paper 20
cd python && ./run_node_sweep.sh <sweepId>

results/README.md lists the sweeps behind each table and figure and the format of the ledgers. matlab/README.md and python/README.md describe the two pipelines.

Data

• data/NNERDS.mat (ELM) and data/CDR_Data.mat (CDR) are included.
• DCR_Data.mat (64 MB) is hosted at 10.5281/zenodo.21537966. data/setupDCR.m downloads it on first use. Batch jobs cannot answer its prompt, so run setupDCR once interactively, or place the file in data/, before launching a sweep.
• data/splits.mat holds the train/validation/test index permutations used by both pipelines.

License

MIT, see LICENSE. matlab/meganet/ is forked from Meganet and keeps its own license.