Towards Robust Surrogate Models: Benchmarking Machine Learning on Phase Field Modeling of Brittle Fracture

Dataset for benchmarking ML surrogate models on phase-field modeling of fracture. This repository provides script for downloading the datasets, training the baseline models and ensemble learning methods that was discussed in the paper.

Prerequisites

Install the project in editable mode:

pip install -e .

Downloading Datasets

You can download the dataset by providing the boundary condition using --case, energy decompositoin method using --decomp and data download method using --method to the download_data.py script. We suggest using the indie option for download method which is the default option. After downloading the data the file names are padded with 0s.

Arguments

• --case: The case type (required)
  • Options: tension or shear or lite
• --decomp: The energy decomposition method (required). If you want to download the lite version of the dataset you should instead choose from 1c, 2c, and 3c
  • Options: spect, vol, or star, 1c, 2c, 3c
• --method: Download method (default on indie)
  • Options: indie, curl or ez

Examples

# Download tension spectral data
python download_data.py --case tension --decomp spect --method indie

To download the lite version of the dataset with 2 cracks:

python download_data.py --case lite --decomp 2c --method indie

Datasets

Download phase-field evolution datasets from Harvard Dataverse:

Available Datasets

Case	Decomposition	DOI
tension	spect	doi:10.7910/DVN/YLQGUO
tension	vol	doi:10.7910/DVN/G5DLI7
tension	star	doi:10.7910/DVN/9URYI1
shear	spect	doi:10.7910/DVN/KZDRUE
shear	vol	doi:10.7910/DVN/OCVQJ1
shear	star	doi:10.7910/DVN/APUKE5

PFM-Fracture Lite

Case	Decomposition	Resolution	#Initial Cracks	DOI
tension	vol	128	1	doi:10.7910/DVN/J9QVSD
tension	vol	128	2	doi:10.7910/DVN/DTKMZK
tension	vol	128	3	doi:10.7910/DVN/NRZZRC
tension	vol	fullres	1	doi:10.7910/DVN/HKXBMO
tension	vol	fullres	2	doi:10.7910/DVN/GIHUIZ
tension	vol	fullres	3	doi:10.7910/DVN/NMAMIO

Output Structure

The downloaded datasets are stored in the data directory with the following structure:

data/
├── tension/
|  ├── spect/
|  ├── vol/
|  └── star/
├── shear/
|  ├── spect/
|  ├── vol/
|  └── star/
|      └── 17882.hdf5
|      └── 19030.hdf5
|      └── ...

Accessing the data

You can have access to the data of each data sample in this way:

#Import the necessary packages
import h5py
import numpy as np
file_path = "2519.hdf5"
with h5py.File(file_path, "r") as f:
  # The key is the seed used to generate the initial crack
  print(f.keys())
  #>> <KeysViewHDF5 ['00002519']># Now you can access the data using the key
  print(f['00002519'].keys())#>> <KeysViewHDF5 ['data', 'force_disp_x', 'force_disp_y', 'grid','init']>
  print(f['00002519']['data'].shape)
  #>> (3, 101, 128, 128)# The first dimension is the number of fields (damage, displacement x,displacement y)
  # The second dimension is the number of steps# The third and fourth dimensions are the spatial dimensions

Using the pretrained models

You can also download the pretrained models and the compressed predictions from here to reproduce the results in the paper.

Training the baseline models

UNet

You can find the code for training the UNet model in src/models/UNet/:

Files:

• unet.py – network architecture and loss functions (Dice, Focal, Combined)
• utils.py – Dataset handler class
• train.py – full training loop with validation and Weights & Biases logging

Training parameters:

Parameter	Default	Description
--seed	0	Random seed
--res	128	Resolution of the input data
--epochs	100	Number of training epochs
--batch_size	16	Batch size
--learning_rate	0.0001	Initial learning rate
--decay_rate	1	Decay rate for the learning rate
--decay_step	50	Decay step for the learning rate
--in_channels	1	Number of input channels
--alpha	0.5	Weight for Dice loss
--beta	0.5	Weight for Focal loss
--threshold	0.4	Threshold for binarization
--data_dir	data/tension/spect	Path to the dataset

Example:

python src/models/unet/train.py \
  --data_dir data/tension/spect \
  --epochs 200 \
  --batch_size 8 \
  --learning_rate 5e-5

FNO

You can find the code for training the FNO model in src/models/FNO/: Files:

• fno.py - Network definition with spectral convolution blocks
• utils.py - Dataset handler for sequence data
• train.py - Autoregressive training loop with checkpointing

Training parameters:

Parameter	Default	Description
--initial_step	10	Input timesteps for the network
--training_type	autoregressive	Training type
--t_train	101	Total timesteps to predict
--model_update	10	How often to update the model
--data_dir	data/tension/spect	Path to the dataset
--epochs	1001	Training epochs
--batch_size	4	Batch size
--learning_rate	1e-3	Initial learning rate
--scheduler_step	100	Steps for learning rate scheduler
--scheduler_gamma	0.5	Gamma for learning rate scheduler
--res	128	Resolution of the input data
--seed	1	Random seed
--num_channels	1	Number of channels
--modes	12	Fourier modes per dimension
--width	20	Network channel width
--use_wandb	True	Enable wandb logging
--wandb_project	test-gh	Wandb project name
--wandb_entity	None	Wandb entity name
--continue_training	False	Continue training from checkpoint

Example:

python src/models/FNO/train.py \
  --data_dir data/tension/spect \
  --epochs 500 \
  --batch_size 4 \
  --learning_rate 1e-3

DRM

You can find the code to reproduce the results in the PINN section of the paper in the src/DRM directory, you have to run the src/DRM/paper_pattern/main.py code with the network architecture.

python src/models/DRM/paper_pattern/main.py 6 100 0 TrainableReLU 3.0 volumetric

Evaluating the models

You can evaluate the models by running the evaluate.py script for each model. It will save the predictions and dice scores in a dictionary in a pickle file.

Arguments:

• You can provide the threshold values for the prediciton and ground truth as the arguments to the evaluate.py scripts.

Parameter	Default	Description
--model_path	None	Path to the trained model checkpoint
--data_dir	None	Path to the dataset directory
--out_dir	None	Output directory for predictions
--ds_size	-1	Dataset size limit (-1 for all)
--threshold_pred	0.5	Threshold for predictions
--threshold_gt	0.5	Threshold for ground truth

Example:

python src/models/FNO/evaluate.py \
  --model_path src/models/FNO/results/wandb_project/models/FNO_tension_miehe_c64x64_3_300.pt \
  --data_dir data/tension/spect \
  --out_dir src/models/FNO/results/test_gh/preds
  --threshold_pred 0.5 \
  --threshold_gt 0.5

Example:

python src/models/UNet/evaluate.py \
  --model_path src/models/UNet/results/wandb_project/models/UNet_tension_spect_3.pkl \
  --data_dir data/tension/spect \
  --out_dir src/models/UNet/results/test_gh/preds
  --threshold_pred 0.5 \
  --threshold_gt 0.5

Ensembling the models

You can ensemble the models by running the ensembling.py script.

Arguments:

• You can provide the parameters needed for the ensembling methods using the ensembling_config.yml file.

Parameter	Default	Description
--model	None	Model type (FNO or UNet)
--config	None	Path to the ensembling config file

Citation

If you use this code or the datasets in your research, please cite:

@article{hamdi2026robust,
title = {Towards robust surrogate models: Benchmarking machine learning approaches to expediting phase field simulations of brittle fracture},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {449},
pages = {118526},
year = {2026},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2025.118526},
url = {https://www.sciencedirect.com/science/article/pii/S0045782525007984},
author = {Erfan Hamdi and Emma Lejeune}
}