NeuralCAE Experiments

Physical AI exploration by a CAE engineer: MeshGraphNet, FNO, PyG experiments, and NPM (Neural Percolation Model) validation.

中文版 README

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NPM Framework Study Series

#	Title	Status	Link
#1	Predicting Emergence Order	Published	Zenodo (DOI: 10.5281/zenodo.19440042)
#2	Physical Interpretation of Critical Exponent	Planned	—
#3	Emergence Curve Across Critical Threshold	Planned	—
#4	Operationalizing Data Quality Parameter	Planned	—

NPM main framework: Zenodo (DOI: 10.5281/zenodo.19209722)

Validation Data & Code (validation/)

• scripts/ — NPM fitting, Brier Score computation
• results/ — MMLU evaluation results for 9 models (Pythia 70M–12B + Phi-2)
• figures/ — Accuracy vs Brier Score scatter plots (CN/EN)

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MeshGraphNets Experiments with PhysicsNeMo

API validation, training pipeline reproduction, and documentation issue reporting for MeshGraphNet models under the NVIDIA PhysicsNeMo framework.

Based on DeepMind's 2021 MeshGraphNets paper, using the model implementation provided by NVIDIA PhysicsNeMo.

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Environment

Package	Purpose
PyTorch	Deep learning framework
PyTorch Geometric (PyG)	Graph neural network backend (recommended)
DGL	Graph neural network backend (required by older PhysicsNeMo)
PhysicsNeMo	NVIDIA physics simulation AI framework, provides MeshGraphNet models
h5py	Reading HDF5 format CFD simulation data
TensorFlow 1.x	Data preprocessing only (triangles_to_edges function)
torch_scatter	PyG message passing dependency
matplotlib	Visualization and animation generation

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Directory Structure

NeuralCAE-experiments/
├── 01-meshgraphnets.py          # PhysicsNeMo API test (DGL backend)
├── 01-meshgraphnets-3.py        # PhysicsNeMo API test (PyG backend) + bug report
├── 01-MeshGraphNets_PyG.py      # Full training pipeline (PyG, based on DeepMind paper)
├── 02-pyg.py                    # DGL vs PyG graph creation comparison
├── validation/                  # NPM validation experiments
│   ├── scripts/                 # NPM fitting & Brier Score scripts
│   ├── results/                 # MMLU evaluation results (9 models)
│   └── figures/                 # Scatter plots (CN/EN)
├── datasets/                    # Datasets (excluded by .gitignore)
├── best_models/                 # Training outputs
├── animations/                  # Velocity field prediction animations (GIF)
├── 2d_loss_plots/               # Loss curve plots (PDF)
└── .gitignore

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Scripts

1. 01-meshgraphnets.py — API Test (DGL Backend)

Tests PhysicsNeMo MeshGraphNet models using DGL graph format:

• MeshGraphNet: Base model, 100-node toy graph forward pass
• MeshGraphKAN: KAN (Kolmogorov-Arnold Networks) variant, num_harmonics=5
• BiStrideMeshGraphNet: Multi-scale variant, requires BistrideMultiLayerGraphDataset

2. 01-meshgraphnets-3.py — API Test (PyG Backend) + Bug Report

Tests all 4 model variants using PyG Data objects, with documentation issue reports (see Findings section).

3. 02-pyg.py — DGL vs PyG Graph Creation

Compares graph creation approaches between DGL and PyG for the same 3-node directed graph.

4. 01-MeshGraphNets_PyG.py — Full Training Pipeline

Complete MeshGraphNet training pipeline based on the DeepMind paper, implemented with PyG:

Module	Function
Data Loading	Reads CFD simulation data from valid.h5, builds PyG graphs
ProcessorLayer	Custom MessagePassing layer (edge MLP → node MLP, with residual connections)
MeshGraphNet	Encoder-Processor-Decoder architecture (multi-layer ProcessorLayer)
train() / test()	Training loop + acceleration loss + velocity validation RMSE
visualize()	Generates Ground Truth / Prediction / Error animations via matplotlib

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Experiments

num_layers	batch_size	hidden_dim	epochs	lr	weight_decay	shuffle	train/test	Note
10	16	10	5000	0.001	5e-4	False	45/10	Control group
10	16	10	5000	0.001	5e-4	True	45/10	Shuffle comparison
10	16	10	5000	0.001	5e-4	True	85/15	Increased data
10	16	30	5000	0.001	5e-4	True	420/80	Largest scale

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Findings

Three issues found in NVIDIA PhysicsNeMo official documentation during API testing:

Bug 1: Input type error. Documentation passes edge_index (Tensor), but the model requires a PyG Data object.

Bug 2: HybridMeshGraphNet edge structure. Documentation does not mention that mesh edges and world edges must be merged into a single graph.

Bug 3: BiStrideMeshGraphNet example unusable. The simple example in the documentation cannot run. The model requires BistrideMultiLayerGraphDataset preprocessing to generate correct multi-scale graph structures.

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Usage

# API test (PyG backend, recommended)
python 01-meshgraphnets-3.py

# Full training pipeline (requires datasets/valid.h5)
python 01-MeshGraphNets_PyG.py

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Data

Dataset files are large (~4.9GB total) and not included in the repository.

File	Size	Description
valid.h5	1.2 GB	Raw CFD simulation data (HDF5)
meshgraphnets_miniset5traj_vis.pt	1.3 GB	5 trajectories, full timesteps
meshgraphnets_miniset100traj25ts_vis.pt	1.1 GB	100 trajectories, 25 timesteps
meshgraphnets_miniset30traj5ts_vis.pt	59 MB	30 trajectories, 5 timesteps (lightweight)
test_processed_set.pt	1.8 MB	2 trajectories, 2 timesteps (toy example)

Data source: DeepMind MeshGraphNets cylinder flow dataset.

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License: MIT | Author: Tiexin Ding | NeuralCAE | All work conducted in personal time.