NBodyIPs.jl

Implementation Notes

As I am rewriting / redesigning some aspects of this package, I will slowly update some thoughts here about how NBodyIPs works internally.

hash

In NBodyIPs there is a dummy-type BASIS defined. This is primarily used to dispatch the hash function as follows: Each basis function implements

hash(::BASIS, V::T) = ...

which returns a hash key that describes only the basis function V but disregards its parameters. For example, OneBody(1.234) has a hash that includes the type information as well as the value 1.234 while

hash(::BASIS, V::OneBody) = hash(OneBody)

i.e. this ignores the parameter E0 = 1.234.

These basis-hashs are used to group and combine the basis functions to allow for faster assembly.

Reference potential

The lsqfit function allows the kw argument Vref which can be an arbitrary AbstractCalculator that can be used as a reference potential from which to start the fit. I.e. the final fit will be Vref + Vfit. If the kwarg E0 is provided, then Vref = OneBody(E0) is used as default. Providing both E0 and Vref means that E0 will be ignored.

Descriptors

The two main descriptors in NBodyIPs are BondAngleDesc and BondLengthDesc. Eacha are defined via a space transform and a cutoff function. Please see inline documentation for these.

Cutoff functions

• CosCut
• CosCut2s
• PolyCut
• PolyCutSym
• PolyCut2sA

Space transforms

• ExpTransform : x = exp(- A*(r/rnb - 1)
• PolyTransform : x = (r0/r)^p
• IdTransform : x = r
• CoulombTransform : x = 1/r
• MorseTransform : c = exp(-r)
• AnalyticTransform: this used to be called SpaceTransform, use only for experimenting. If a good new transform can be found then it can be implemented into NBodyIPs as a separate type.

Regularisation

Regularisers

More on Descriptors and Basis sets

Bond-length descriptor

Bond-angle descriptor

Environment-dependent N-Body potentials