Assignment 4: Finding Materials with High Hardness

Perform Bayesian optimization with featurization and a contextual variable to maximize hardness as a function of material composition.

The Assignment

Some data representations cannot be directly used for optimization due to a lack of continuity or differentiability. In such cases, it is necessary to transform the data into a form that can be more easily understood by machine learning models. This process is called featurization and is very common in the materials, chemistry, and biological informatics fields. In this assignment, you will use Ax to help select a material composition with a high hardness based on a list of potential candidates. This differs from previous assignments in that candidate data is discrete and will be fed to the optimization model manually.

Thankfully you won't be starting from scratch! An intern spent some time looking through the literature and found hardness data as a function of composition and stored it in a CSV file called train.csv. Unfortunately, much of the data was captured using different hardness testers, so the applied loads used in the literature tests are differnet. Your machine is set to a load of 0.98 kgf, which wasn't used in any of the literature data. You suspect that by including the load as a feature, the model will be able to account for this discrepancy. You have devised a list of potential candidate materials and stored them in a CSV file called candidate.csv. These will be used the candidates you select from at each optimization iteration.

Your goal is to use Honegumi and your knowledge of the Ax API to develop an optimization script to help find a composition that maximizes the yield strength of a developed alloy. Your experimental budget is limited to 25 experiments. A synthetic objective function has been provided that will serve as a proxy for real experimental measurements.

TASK A: Featurize the data using the featurize_data function.

Featurize the the training set and the candidate set using the provided function. Store the results in the variables X_train, y_train, and X_candidates. Note that as the candidate data hasn't be evaluated, the harndness values are all set to 0.

The featurize_data() function takes in a dataframe with material compositions and properties and returns a dataframe with the features, X, and a dataframe with the property values y.

TASK B: Use Honegumi to set up the optimization problem and attach the training data.

Honegumi will help with the general framework, but you will need to make several changes to the typical structure to allow discrete candidates to be passed and evaluated. We provide a few helpful tips below for making these modifications.

1. As solutions are drawn from a discrete list, a typical Sobol generation strategy at the start will not work. You will need to use a custom generation strategy that immediately starts with a GP model - we reccommend BOTORCH_MODULAR for this.

2. The parameter names are fixed to the columns of the featurized DataFrame. We will assume that all of the generated candidates are feasible and can set arbitratiy large bounds for the ranges on these parameters to avoid Ax throwing an error.

3. The training data will need to be attached to the optimization problem using the attach_trial method. This will serve as the initial training set for the optimization.

TASK C: Build the optimization loop and and evaluate 25 candidates.

Now you will build an optimization loop that passes the candidate features to the trained model, returns the acquisition function for each, and selects a candidate to evaluate. Reminder that passing custom parameter evaluations to the model requires one to create an ObservationFeatures object. For evaluations, you will use the provided measure_hardness function.

Some pseudocode for getting acquisition function values from manually passed data is provided below to help you construct the manual optimization loop.

ax_client.fit_model()
model = ax_client.generation_strategy.model 
obs_feat = ObservationFeatures({"feat":val})
acqf_value = model.evaluate_acquisition_function(obs_feat)

TASK D: Report the optimal composition and associated hardness.

Now that you have completed the optimization, identify the chemical composition of the optimial parameters parameter combination and assign it to a variable named optimal_composition. Assign the optimal hardness to a variable named max_hardness.

TASK E: Report the most important feature and its correlation for predicting hardness.

Identify the most important feature for predicting hardness and assign it to a variable named most_important. Then indicate whether it is positively (1) or negatively (-1) correlated with hardness and assign it to a variable named correlation.

TASK F: How many materials have a hardness greater than 43?

There are often secondary constraints in an optimization problem and having several options to choose from can be helpful. Determine how many materials have a hardness greater than 43 and assign the result to a variable named n_hard_materials.

Setup command

See postCreateCommand from devcontainer.json.

Run command

pytest

Notes

• pip's install path is not included in the PATH var by default, so without installing via sudo -H, pytest would be inaccessible.