GAP

This is an implementation of the sparse Gaussian Approximation Potential (GAP) [1] using Smooth Overlap of Atomic Positions (SOAP) [2] implemented in featomic.

The GAP model in metatrain can only train on CPU, but evaluation is also supported on GPU.

Installation

To install the package, you can run the following command in the root directory of the repository:

pip install metatrain[gap]

This will install the package with the GAP dependencies.

Default Hyperparameters

The default hyperparameters for the GAP model are:

architecture:
  name: gap

  model:
    soap:
      cutoff:
        radius: 5.0
        smoothing: 
          type: ShiftedCosine
          width: 1.0
      density:
        type: Gaussian
        center_atom_weight: 1.0
        width: 0.3
        scaling:
          type: Willatt2018
          rate: 1.0
          scale: 2.0
          exponent: 7.0
      basis:
        type: TensorProduct
        max_angular: 6
        radial:
          type: Gto
          max_radial: 7
    krr:
      degree: 2
      num_sparse_points: 500
    zbl: false

  training:
    regularizer: 0.001
    regularizer_forces: null

Tuning Hyperparameters

The default hyperparameters above will work well in most cases, but they may not be optimal for your specific dataset. In general, the most important hyperparameters to tune are (in decreasing order of importance):

• cutoff: This should be set to a value after which most of the interactions between atoms is expected to be negligible.

• num_sparse_points: Number of sparse points to use during the training, it select the number of actual samples to use during the training. The selection is done with the Further Point Sampling (FPS) algorithm. The optimal number of sparse points depends on the system. Increasing it might impreve the accuracy, but it also increase the memory and time required for training.

• regularizer: Value of the regularizer for the energy. It should be tuned depending on the specific dataset. If it is too small might lead to overfitting, if it is too big might lead to bad accuracy.

• regularizer_forces: Value of the regularizer for the forces. It has a similar effect as regularizer. By default is set equal to regularizer. It might be changed to have better accuracy.

• max_radial, max_angular: These hyperparameters control the size and depth of the SOAP descriptors, in particular the total number of radial and angular channels. In general, increasing these hyperparameters might lead to better accuracy, especially on larger datasets, at the cost of increased training and evaluation time.

• radial_scaling hyperparameters: These hyperparameters control the radial scaling of the SOAP descriptor. In general, the default values should work well, but they might need to be adjusted for specific datasets.

• degree: degree of the kernel. For now, only 2 is allowed.

Architecture Hyperparameters

param name:

gap

model

soap

param cutoff:

Spherical cutoff (Å) to use for atomic environments. Default 5.0

param max_radial:

Number of radial basis function to use. Default 8

param max_angular:

Number of angular basis function to use also denoted by the maximum degree of spherical harmonics. Default 6

param atomic_gaussian_width:

Width of the atom-centered gaussian creating the atomic density. Default 0.3

param center_atom_weight:

Weight of the central atom contribution to the features. If 1.0 the center atom contribution is weighted the same as any other contribution. If 0.0 the central atom does not contribute to the features at all. Default 1.0

param cutoff_function:

cutoff function used to smooth the behavior around the cutoff radius. The supported cutoff function are

• Step: Step function, 1 if r < cutoff and 0 if r >= cutoff. This cutoff function takes no additional parameters and can set as in .yaml file:

  cutoff_function:
    Step:
  

• ShiftedCosine (Default value): Shifted cosine switching function f(r) = 1/2 * (1 + cos(π (r- cutoff + width) / width )). This cutoff function takes the width` as additional parameter and can set as in options.yaml file as:

  cutoff_function:
    ShiftedCosine:
      width: 1.0
  

param radial_scaling:

Radial scaling can be used to reduce the importance of neighbor atoms further away from the center, usually improving the performance of the model. The supported radial scaling functions are

• None: No radial scaling.

  radial_scaling:
    None:
  

• Willatt2018 (Default value): Use a long-range algebraic decay and smooth behavior at \(r \rightarrow 0\): as introduced by Willatt et al.[3] as f(r) = rate / (rate + (r / scale) ^ exponent) This radial scaling function can be set in the options.yaml file as.

  radial_scaling:
    Willatt2018:
      rate: 1.0
      scale: 2.0
      exponent: 7.0
  

Note

Currently, we only support a Gaussian type orbitals (GTO) as radial basis functions and radial integrals.

krr

param degree:

degree of the polynomial kernel. Default 2

param num_sparse_points:

number of pseudo points to select (by farthest point sampling). Default 500

training:

param regularizer:

value of the energy regularizer. Default 0.001

param regularizer_forces:

value of the forces regularizer. Default null

References

[1]

Albert P. Bartók, Risi Kondor, and Gábor Csányi. On representing chemical environments. Phys. Rev. B, 87(18):184115, May 2013. doi:10.1103/PhysRevB.87.184115.

[2]

Albert P. Bartók, Mike C. Payne, Risi Kondor, and Gábor Csányi. Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons. Phys. Rev. Lett., 104(13):136403, April 2010. doi:10.1103/PhysRevLett.104.136403.

[3]

Michael J. Willatt, Félix Musil, and Michele Ceriotti. Feature optimization for atomistic machine learning yields a data-driven construction of the periodic table of the elements. Phys. Chem. Chem. Phys., 20(47):29661–29668, December 2018. doi:10.1039/C8CP05921G.