cerebral

Tool for creating multi-output deep ensemble neural-networks for alloy property modelling.

See our paper Machine-learning improves understanding of glass formation in metallic systems for discussion of the model, it's architecture, and performance.

Installation

The cerebral package can be installed from pypi using pip:

pip install cerebral

Cerebral makes heavy use of the metallurgy package to manipulate and approximate properties of alloys. Cerebral can be used with the evomatic package to perform alloy searching.

Usage

Cerebral can be used to create multi-input mult-output deep neural networks for the modelling of arbitrary alloy properties.

The following example shows configuration of cerebral to predict the "price" property of an alloy, based on atomic percentages alone. Cerebral is configured to load data for this problem from the tests directory - this data is for demonstration and testing only, it is synthetically created by the metallurgy package for the Cu-Zr binary alloy system.

import cerebral as cb

cb.setup(
    {
        "targets": [{"name": "price"}],
        "input_features": [
            "percentages"
        ],
        "data": {"files": ["tests/CuZr_prices.csv"]},
    }
)

data = cb.features.load_data()

>>> data
     composition      price  Cu_percentage  Zr_percentage
0          Cu100   6.000000          1.000          0.000
1    Cu99.9Zr0.1   6.044626          0.999          0.001
2    Cu99.7Zr0.3   6.133763          0.997          0.003
3    Cu99.6Zr0.4   6.178273          0.996          0.004
4    Cu99.4Zr0.6   6.267177          0.994          0.006
..           ...        ...            ...            ...
662  Zr99.4Cu0.6  36.969779          0.006          0.994
663  Zr99.5Cu0.5  36.991515          0.005          0.995
664  Zr99.7Cu0.3  37.034949          0.003          0.997
665  Zr99.8Cu0.2  37.056646          0.002          0.998
666        Zr100  37.100000          0.000          1.000

Once a DataFrame of alloy compositions, input features, and prediction targets is available, it can be used to train a model. The following example takes the DataFrame created above, and trains a neural network to reproduce the target features (for a maximum of 200 training epochs). The neural network model produced is a standard Keras / TensorFlow model.

model, history, train_data, test_data = cb.models.train_model(
    data, max_epochs=200
)

>>> model
<keras.engine.functional.Functional object at 0x7f1810feac80>

>>> history.history["loss"]
[22.522766767894105, 21.966949822959215, ...] 

Once a model has been created, cerebral provides automation for evaluating its performance by comparison against the training and test datasets. Since the pricing data is based on a very simple linear mixture, the model is able to learn quite well the relationship between percentages of Cu and Zr and the price.

(
    train_predictions,
    train_errors,
    test_predictions,
    test_errors,
    metrics,
) = cb.models.evaluate_model(
    model,
    train_data["dataset"],
    train_data["labels"],
    test_ds=test_data["dataset"],
    test_labels=test_data["labels"],
    train_compositions=train_data["compositions"],
    test_compositions=test_data["compositions"],
)

>>> metrics
{
  'price': {
    'train': {
      'R_sq': 0.9994298579318788, 
      'RMSE': 0.21407108083268242, 
      'MAE': 0.16591635524599488
    }, 
    'test': {
      'R_sq': 0.9994089218056131,
      'RMSE': 0.21349478924250365, 
      'MAE': 0.1721696906690461
    }
  }
}

Futher, the model can be used to generate predictions for arbitrary alloys, as long as the required input features are supplied. Here, we see that the simple example model predicts price value for pure copper which is in the vicinity of the value originally calculated by linear mixture:

>>> cb.models.predict(model, "Cu100")["price"]
{'price': array([6.60157898])}

>>> mg.calculate("Cu100", "price")
6.0

Documentation

Documentation is available here.