Training of cluster expansions

Here, we will explore some more advanced concepts regarding the training of a cluster expansion. Specifically we will consider

1. Selecting cutoffs

2. Selecting an optimization algorithm and hyper-parameters

3. Ensemble training

Note here that steps 1 and 2 are to some degree dependent on each other, i.e., the optimal cutoffs may depend on what optimization algorithm you use. But here, for simplicity, we will consider them in succession.

We consider the Ag-Pd system with the same training structures as used in the tutorial.

Note also when doing cross-validation with small datasets one always ends up with some amount of noise, e.g., in the resulting RMSEs.

Contents

• Selecting cutoffs
  • Setup
  • Scan pair cutoff
  • Plot results of pair cutoff scan
  • Third-order cutoff
  • Fourth-order cutoff
• Hyper-parameter scans
  • Preparations
  • ARDR: Hyperparameter scan
  • RFE: Hyperparameter scan
  • LASSO: Hyperparameter scan
  • Adaptive-LASSO: Hyperparameter scan
  • Plot results
• EnsembleOptimizer
  • Uncertainty predictions for structures