Chebyshev parameters

[Siwen Wang]

Hi Dr. Artrith

Recently our group is trying to apply aenet to alloy systems by using Chebyshev descriptor. I read your "Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species" and there are two main variables: RDF(r) and ADF(theta). But in your TiO2 example, there are four constant numbers:

BASIS type=Chebyshev

radial_Rc = 8.0  radial_N = 16 angular_Rc = 6.5  angular_N = 4

Do radial_Rc and angular_Rc mean the cutoff of radius and angle? And do radial_N and angular_N mean the order of radius and angle? If so, how do you determine these parameters?

To make my question more clear, can I use the same setting for all other metals?

Thanks for your help and time

Siwen

[Nongnuch Artrith]

Dear Siwen,

Thank you for the questions and for your interest in aenet.

Using the Chebyshev descriptor, the RDF and ADF are expanded in a basis of Chebyshev polynomials.  'radial_N' is the expansion order, i.e., the number of polynomials minus 1, for the RDF expansion, and 'angular_N' is the expansion order for the ADF.  For both RDF and ADF only atoms within a certain cutoff range are considered, and these ranges can be different.  'radial_Rc' is the cutoff radius for the RDF expansion, and 'angular_Rc' is the cutoff for the ADF.

Generally, the higher the expansion orders, the more accurately are RDF/ADF represented.  But the computational cost also increases with the expansion order.  Similarly, the shorter the cutoff radii, the faster the descriptor evaluation.  But for some materials large cutoffs are needed.  

A cutoff of 8 Angstrom is already quite long and should be good for most materials.  The expansion orders should generally be tested for each training set, but you could start with the TiO2 parameters and see if they give you a good accuracy for your materials.  The radial (RDF) expansion is generally more important and computationally more efficient than the angular (ADF). Thus we often use higher expansion orders and greater cutoffs for the radial expansion.

Please let us know if you have any further questions. 

Best,
Nong

[Siwen Wang]

Hi Dr. Artrith

Thanks so much for your explanation. I'll try these parameters first

Siwen