# First example (Julia)

## Developing a new ACE1.jl model

This is a very tutorial to demonstrate how to use ACE1 and IPFitting to construct an ACE1 model for Si by fitting to an empirical potential.

Make sure to first read the installation notes. Now start by importing the required packages:

using ACE1pack
import Random
using LinearAlgebra: norm, Diagonal

### Step 1: specify the ACE basis

The ACE basis can be set up using the function rpi_basis, where the parameters have the following meaning:

• species: chemical species, for multiple species provide a list
• N : correlation order
• maxdeg: maximum polynomial degree
• D : specifies the notion of polynomial degree for which there is no canonical definition in the multivariate setting. Here we use SparsePSHDegree which specifies a general class of sparse basis sets; see its documentation for more details.
• r0 : an estimate on the nearest-neighbour distance for scaling, JuLIP.rnn() function returns element specific earest-neighbour distance
• rin, rcut : inner and outer cutoff radii
• pin : specifies the behaviour of the basis as the inner cutoff radius.
r0 = rnn(:Si)
basis = ace_basis(;
species = :Si,
N = 3,                        # correlation order = body-order - 1
maxdeg = 12,                  # polynomial degree
D = SparsePSHDegree(; wL=1.5, csp=1.0),
r0 = r0,                      # estimate for NN distance
rin = 0.65*r0, rcut = 5.0,    # domain for radial basis (cf documentation)
pin = 2)
@show length(basis)
211

### Step 2: Generate a training set

Normally one would generate a training set using DFT data, store it e.g. as an .xzy file, which can be loaded via IPFitting. Here, we will just general a random training set to show how it will be used.

• gen_dat() generates a single training configuration wrapped in an IPFitting.Dat structure. Each d::Dat contains the structure d.at, and energy value and a force vector to train against. These are stored in the dictionary d.D. Other observations can also be provided. The string "diax$n" is a configtype label given to each structure which is useful in seeing what the performance of the model is on different classes of structures. • train is then a list of 50 such training configurations. function gen_dat() sw = StillingerWeber() n = rand(2:4) at = rattle!(bulk(:Si, cubic=true) * n, 0.3) return Dat(at, "diax$n"; E = energy(sw, at), F = forces(sw, at) )
end

Random.seed!(0)
train = [ gen_dat() for _=1:50 ];
nothing #hide

### Step 3: Estimate Parameters

First we evaluate the basis on all training configurations. We do this by assembling an LsqDB which contains all information about the basis, the training data and also stores the values of the basis on the training data for later reuse e.g. to experiment with different parameter estimation algorithms, or parameters. Using the empty string "" as the filename means that the LsqDB will not be automatically stored to disk.

dB = LsqDB("", basis, train);
nothing #hide

To assemble the LSQ system we now need to specify weights. If we want to give the same energy and force weights to all configurations, we can just do the following. But e.g. we could give different weights to diax2, diax3, diax4 configs (more on this in other tutorials).

weights = Dict("default" => Dict("E" => 15.0, "F" => 1.0 , "V" => 1.0 ))
Dict{String, Dict{String, Float64}} with 1 entry:
"default" => Dict("V"=>1.0, "E"=>15.0, "F"=>1.0)

Now we can fit the potential using

IP, lsqinfo = lsqfit(dB; weights = weights, error_table = true,
solver = Dict("solver" => :qr));
nothing #hide

This assembles the weighted LSQ system, and retuns the potential IP as well as a dictionary lsqinfo with some general information about the potential and fitting process. E.g., to see the training errors we can use

rmse_table(lsqinfo["errors"])

Note that IP is a JuLIP.jl calculator and can be used to evaluate e.g. energy, forces, virial on new configurations.

### Step 4: Run some tests

At a minimum we should have a test set to check generalisations, but more typically we would now run extensive robustness tests. For this mini-tutorial we will just implement a very basic energy generalisation test.

test =  [ gen_dat() for _=1:20 ]
Etest = [ dat.D["E"]/length(dat.at) for dat in test ]
Emodel = [ energy(IP, dat.at)/length(dat.at) for dat in test ]
rmse_E = norm(Etest - Emodel) / sqrt(length(test))
@show rmse_E;    # rmse_E = 5.842000599246454e-5
nothing #hide