Deep learning based domain knowledge integration for small datasets: illustrative applications in materials informatics

This software is an application for the domain knowledge-aware convolutional neural networks (DKACNN) on small dataset. The efficacy of the proposed approach is tested on two materials science datasets with different types of inputs and outputs, for which domain knowledge-aware convolutional neural networks (CNNs) are developed.

To use this software, what the algorithm requires as input are a numpy array. For homogenization dataset, the shape of data point is (x, 51, 51, 51) where x is the number of microscale volume elements (MVEs) and the dimension of microstructure should be three-dimensional (i.e. 51x51x51). For crystal plasticity dataset, the shape of data point is (x, 224, 224) where x is the number of strain profile images/crops and the size of strain profile image/crop is 224x224. The software will take the row data and corresponding two-point correlation funcion (i.e. integerated domain knowledge with same size as row data, which can be computed using PyMKS software) as input, and train the predictive models. The detailed drscription about data preprocessing and model can be found in the published paper given below.

Requirements

• Python 3.6.3
• Numpy 1.18.1
• Sklearn 0.20.0
• Keras 2.3.1
• Pickle 4.0
• TensorFlow 2.1.0
• h5py 2.9.0

Files

1. homogenization.py: The CNN has two branches where one branch takes the original 3D microstructure image as input and the other brach takes the corresponding two-point autocorrelation as input. Finally the two branches are concatenated togetogher to make the final prediction for effective elastic stiffness. After training, the trained model will be saved in 'my_model.h5' file.
2. crystalPlasticity.py: The CNN has two branches where one branch takes the original 2D microstructure image as input and the other brach takes the corresponding two-point autocorrelation as input. Finally the two branches are concatenated togetogher to make the final prediction for initial deformation level. After training, the trained model will be saved in 'my_model.hdf5' file.
3. homogenization_data.pkl: Example data for homogenization dataset, includeing 10 51x51x51 3D microstrctures.
4. crystal_plasticity_data.pkl: Example data for crystal plasticity dataset, including 10 224x224 strain profiles.

How to run it

1. Run commend below, which trains the CNN model for homogenization dataset and save the trained model in 'my_model.hdf5' file.

   python homogenization.py
   

2. Run commend below, which trains the CNN model for crystal plasticity dataset and save the trained model in 'my_model.hdf5' file.

   python crystalPlasticity.py
   

Acknowledgement

This work was performed under the following financial assistance award 70NANB14H012 from U.S. Department of Commerce, National Institute of Standards and Technology as part of the Center for Hierarchical Materials Design (CHiMaD). Partial support is also acknowledged from the following grants: NSF award CCF-1409601; DOE awards DE-SC0007456, DE-SC0014330; AFOSR award FA9550-12-1-0458, and Northwestern Data Science Initiative.

Related Publications

Z. Yang, R. Al-Bahrani, A. Reid, S. Papanikolaou, S. Kalidindi, W.-keng Liao, A. Choudhary, and A. Agrawal, “Deep learning based domain knowledge integration for small datasets: Illustrative applications in materials informatics,” in Proceedings of International Joint Conference on Neural Networks (IJCNN), 2019, pp. 1–8.

Contact

Zijiang Yang zyz293@ece.northwestern.edu; Ankit Agrawal ankitag@ece.northwestern.edu