Mackey–Glass delay equation: classical integrator vs PINN

Mackey–Glass (n = 10). Three-dimensional delay embedding (state vs two lagged values): fine RK4 reference (grey), classical method-of-steps trajectory (black), PINN prediction (purple). Same style of figure as the long-horizon windowed experiment in the article.

This repository contains code to reproduce the Mackey–Glass benchmark from the companion IEEE conference paper (physics-informed neural network vs method-of-steps classical solver on a scalar DDE with fixed delay).

After cloning, use the repository root (the directory that contains this README.rst) as your working directory for every command below.

Table of contents

• What is included
• Matching the published results
• Environment
• Single run (main experiment)
• Multi-seed run (optional)
• Configuration files (configs/)
• Run outputs
• License and contact

What is included

Programs

• run_mglass_comparison.py — Main experiment: adaptive RK45 method-of-steps trajectory, high-accuracy RK4 reference, PINN training with windowed time domains, metrics, and figures.
• run_mglass_multi_seed.py — Optional robustness study: repeats the main experiment for several pseudorandom seeds and aggregates uncertainty in metrics and learning curves.

Supporting files

• requirements.txt — Python stack including a CPU PyTorch build (suitable for reviewers without a CUDA install).
• requirements-rocm.txt — How to swap in AMD ROCm PyTorch after the base install; NVIDIA users should follow PyTorch Get Started instead.
• configs/ — YAML recipes for horizons, windowing, and training hyperparameters described in the article.
• images/ — Banner figure for this README (3D overlay for n = 10).
• results/ — Default location for run outputs.

Matching the published results

Use the configuration files and hyperparameters stated in the paper (including any supplement). After changing code or YAML, rerun the pipeline and replace downstream plots or tables so reported numbers stay consistent.

Clone

git clone https://github.com/ml3m/PINN-and-Method-of-Steps-Integration-for-the-Mackey-Glass-DDE.git
cd PINN-and-Method-of-Steps-Integration-for-the-Mackey-Glass-DDE

Environment

• Python 3.10+ (3.12 tested). Use a virtual environment.
• requirements.txt installs NumPy, SciPy, Matplotlib, PyYAML, and a CPU PyTorch wheel (training is slower than on GPU but runs on typical laptops).
• For CUDA or ROCm PyTorch, reinstall torch as in the PyTorch site or requirements-rocm.txt.

From the repository root:

python -m venv .venv
source .venv/bin/activate   # Windows: .venv\Scripts\activate
pip install -U pip
pip install -r requirements.txt

Single run (main experiment)

python -u run_mglass_comparison.py \
  --config configs/config_mackey_glass_t200_windowed.yaml \
  --n-values 10 \
  --output-dir results/t200_windowed_n10

Defaults if you omit --config / --output-dir:

• Config: configs/config_mackey_glass_t200_windowed.yaml
• Output directory: results/ under the repository root

Config and output paths are resolved against the current working directory, then against the directory that contains run_mglass_comparison.py.

Multi-seed run (optional)

Runs the main program once per seed, then builds aggregate CSV/JSON and overlay plots.

AMD ROCm (optional): some GPUs need a gfx workaround. If required for your hardware, set this in the shell before the Python command; otherwise omit it:

export HSA_OVERRIDE_GFX_VERSION=10.3.0

Run:

python -u run_mglass_multi_seed.py \
  --config configs/config_mackey_glass_t100_windowed.yaml \
  --base-output results/t100_windowed_multi_seed \
  --n-values 10 \
  --n-seeds 10 --seed-start 1000

Use --python /path/to/python3 if the child jobs must use a different interpreter than the orchestrator.

Configuration files (configs/)

Filenames keep historical tags; each file encodes horizon and training layout:

• config_mackey_glass.yaml — Baseline setup (see YAML header).
• config_mackey_glass_t20.yaml — Short horizon [0,20].
• config_mackey_glass_t200.yaml — Single-window horizon [0,200].
• config_mackey_glass_t200_windowed.yaml — Windowed [0,200] (figures in the IEEE paper).
• config_mackey_glass_t100_windowed.yaml — Windowed [0,100] (shorter benchmark).
• config_mackey_glass_smoke_multi_seed.yaml — Minimal settings for quick CI or smoke tests.

Use the configs/ directory in this repository when reproducing the paper.

Run outputs

Each run writes under --output-dir:

• mglass_run.pkl — Serialized trajectories, metrics, and metadata for tables or follow-on scripts.
• mackey_glass_n*_comparison.png — Primary side-by-side comparison figure.
• n*_*.png / .pdf — Heatmaps, time slices, embeddings, losses, tables.
• checkpoints_n*/*.pt — PINN checkpoints per time window (runs resume if these exist).

Generated content under results/ is excluded from git by default (results/.gitignore).

License and contact

Reuse and attribution follow the LICENSE file shipped here, if present. Questions about the Mackey–Glass experiments should go to the authors via the published paper or its supplement.