Accelerating Multicomponent Phase-Coexistence Calculations with Physics-informed Neural Networks

Install Instructions

Please install using the setup.py.

$ git clone https://github.com/webbtheosim/ml-ternary-phase.git
$ cd ml-ternary-phase
$ conda create --name phase python=3.8.16
$ conda activate phase
$ # or source activate phase
$ pip install -e .

Download Data and Results

Select a disk location for data storage and update the directory paths before running the program. Download the required data from Zenodo here.

• DATA_DIR: Stores data pickle files (approx. 400 MB).

# LOAD DATA
DATA_DIR = "your/custom/dir/"

filename = os.path.join(DATA_DIR, f"data_clean.pickle")
with open(filename, "rb") as handle:
    (x, y_c, y_r, phase_idx, num_phase, max_phase) = pickle.load(handle)

• x: Input x = (χ_AB, χ_BC, χ_AC, v_A, v_B, v_C, φ_A, φ_B) ∈ ℝ⁸.
• y_c: Output one-hot encoded classification vector y_c ∈ ℝ³.
• y_r: Output equilibrium composition and abundance vector y_r = (φ_A^α, φ_B^α, φ_A^β, φ_B^β, φ_A^γ, φ_B^γ, w^α, w^β, w^γ) ∈ ℝ⁹.
• phase_idx: A single integer indicating which unique phase system it belongs to.
• num_phase: A single integer indicates the number of equilibrium phases the input splits into.
• max_phase: A single integer indicates the maximum number of equilibrium phases the system splits into.

To train from scratch, only the DATA_DIR is required.

Optional training results can be downloaded here.

• TRAIN_RESULT_DIR: Stores training results in pickle format (approx. 5GB). These pickle files can be used to reproduce the post-ML optimization results. Download
• RESULT_DIR: Stores results in pickle format for analysis and plotting (approx. 229 MB). These are temporary files. In the notebook, if reload=False, the plots will be generated using these files. Download
• OPT_RESULT_DIR: Stores post-ML Newton-CG optimization results in pickle format (approx. 78 MB) . Each file represents the optimization of a single phase system, identified by a unique index. Download
• PICKLE_INNER_PATH: Stores training results of hyperparameter tuning (approx. 16 MB). These small files contain hyperparameter tuning results. If you want to start with only the outer loop of cross-validation, you can directly use these files and run run_outercv.py. If you'd prefer to perform hyperparameter tuning yourself, run run_innercv.py. Download

File Structure

Notebooks

The notebook folder contains Jupyter notebooks for reproducing figures and tables:

• result.ipynb: Visualizes all result figures from the paper.
• optimization.ipynb: Generates coexistence curves using ML predictions and post-ML Newton-CG optimization.

Machine Learning Core

The mlphase folder contains the core ML code:

• run_innercv.py: Performs hyperparameter tuning using 10% of the training data (inner loop of nested five-fold cross-validation).
• run_outercv.py: Conducts production run training using the best hyperparameter combinations (outer loop of nested five-fold cross-validation).
• run_opt.py: Executes post-ML Newton-CG optimization for coexistence curve predictions.
• analysis/: Scripts for calculating and evaluating accuracy metrics of model predictions.
• data/: Scripts for data splitting and loading.
• models/: Defines architecture and implementation of various machine learning models.
• plot/: Scripts for creating visual representations of data, including figures for analysis and publication.

Data Generation

The hull_creation folder contains code for convex hull data generation.

Results

• result_pickle/: Contains temporary files used for figure preparation.
• result_csv/: Contains temporary files used for table creation.

Note: To generate your own results, set reload=True in the notebooks.

Job Submission

The submit folder contains job submission scripts for High-Performance Computing environments:

• innercv.submit: Neural network hyperparameter tuning.
• outercv.submit: Neural network production run training.
• post_opt.submit: Post-ML optimization.