Committee Potentials
using Plots, ACEpotentials, StatisticsPerform the fit
load some example training data
train, _, _ = ACEpotentials.example_dataset("Si_tiny")
data_keys = (energy_key = "dft_energy", force_key = "dft_force"); Downloading artifact: Si_tiny_dataset
Failure artifact: Si_tiny_dataset
Downloading artifact: Si_tiny_datasetcreate model
model = acemodel(elements = [:Si,], order = 3, totaldegree = 8);create solver, setting a nonzero committee size at present, the SVD factorization is required for committees
solver = ACEfit.BLR(committee_size=10, factorization=:svd);perform the fit
acefit!(model, train; solver=solver, data_keys...);┌───────────────┬──────────┬───────┬────┬─────┬─────┐
│ Type │ #Configs │ #Envs │ #E │ #F │ #V │
├───────────────┼──────────┼───────┼────┼─────┼─────┤
│ isolated_atom │ 1 │ 1 │ 1 │ 3 │ 0 │
│ dia │ 25 │ 50 │ 25 │ 150 │ 0 │
│ bt │ 25 │ 50 │ 25 │ 150 │ 0 │
│ liq │ 2 │ 128 │ 2 │ 384 │ 0 │
├───────────────┼──────────┼───────┼────┼─────┼─────┤
│ total │ 53 │ 229 │ 53 │ 687 │ 0 │
│ missing │ 0 │ 0 │ 0 │ 0 │ 318 │
└───────────────┴──────────┴───────┴────┴─────┴─────┘
[ Info: Assembling linear problem.
[ Info: - Creating feature matrix with size (740, 54).
[ Info: - Beginning assembly with processor count: 1.
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[ Info: - Assembly completed.
[ Info: Assembling full weight vector.
[ Info: Entering bayesian_linear_regression_svd
┌ Info: Computing SVD of (740, 54) matrix
│ BLAS.get_num_threads() = 2
│ BLAS.get_config() =
│ LinearAlgebra.BLAS.LBTConfig
│ Libraries:
└ └ [ILP64] libopenblas64_.so
[ Info: SVD completed after 3.363311666666667e-5 minutes
[ Info: Beginning to maximize marginal likelihood
Iter Function value Gradient norm
0 1.155681e+07 2.291558e+07
* time: 0.01537179946899414
1 1.323055e+04 3.211203e-05
* time: 0.7291429042816162
2 1.104783e+04 6.894847e-04
* time: 0.7293989658355713
3 1.085204e+04 9.054319e-04
* time: 0.7294869422912598
4 9.406472e+03 7.122083e-03
* time: 0.7295398712158203
5 8.339838e+03 3.316252e-02
* time: 0.7296218872070312
6 8.060072e+03 4.969367e-02
* time: 0.7296798229217529
7 5.440936e+03 1.552154e+00
* time: 0.7297999858856201
8 5.433681e+03 7.451985e-01
* time: 0.7299118041992188
9 5.424066e+03 2.007926e-01
* time: 0.7299599647521973
10 5.423534e+03 5.803090e-03
* time: 0.7300000190734863
11 5.423533e+03 2.580160e-03
* time: 0.7300448417663574
12 5.359344e+03 3.417668e+00
* time: 0.7301459312438965
13 5.214766e+03 2.719945e+00
* time: 0.730212926864624
14 5.169232e+03 1.635445e+00
* time: 0.7302780151367188
15 5.094924e+03 3.771349e-01
* time: 0.7303199768066406
16 5.016782e+03 4.912723e-01
* time: 0.7303848266601562
17 4.989165e+03 4.186593e-01
* time: 0.7304389476776123
18 4.925721e+03 1.872916e-01
* time: 0.7304809093475342
19 4.925709e+03 1.851066e-01
* time: 0.730543851852417
20 4.925294e+03 5.484493e-03
* time: 0.7305879592895508
21 4.925294e+03 2.085054e-05
* time: 0.7306318283081055
22 4.925294e+03 5.166931e-08
* time: 0.7306749820709229
23 4.925294e+03 3.177596e-13
* time: 0.7307188510894775
24 4.925294e+03 7.541391e-17
* time: 0.7307629585266113
┌ Info: Optimization complete
│ Results =
│ * Status: success
│
│ * Candidate solution
│ Final objective value: 4.925294e+03
│
│ * Found with
│ Algorithm: L-BFGS
│
│ * Convergence measures
│ |x - x'| = 3.79e-11 ≤ 1.0e-08
│ |x - x'|/|x'| = 2.11e-13 ≰ 0.0e+00
│ |f(x) - f(x')| = 9.09e-13 ≰ 0.0e+00
│ |f(x) - f(x')|/|f(x')| = 1.85e-16 ≰ 0.0e+00
│ |g(x)| = 7.54e-17 ≰ 0.0e+00
│
│ * Work counters
│ Seconds run: 1 (vs limit Inf)
│ Iterations: 24
│ f(x) calls: 143
│ ∇f(x) calls: 143
└ Inspect the total energies vs committee energies and error bars for a few perturbed structures. Note the training set is so small that we don't expect these committees to be particularly useful; this is only to illustrate how they might be used. Also note that the energy E is not in general the mean of co_E but it is the mean of the exact posterior distribution.
atoms = bulk(:Si, cubic=true) * 2; rattle = [0.03, 0.1, 0.3]
plot(; size = (300, 300), xlabel = "rattle", ylabel = "energy [eV]", ylims = (-10650, -10250),
xlims = (0.015, 0.6), xticks = (rattle, string.(rattle)), xscale = :log10)
for (i, rt) in enumerate(rattle)
rattle!(atoms, rt)
E, co_E = ACE1.co_energy(model.potential, atoms)
scatter!(rt*ones(10), co_E, c = 1, label=(i==1 ? "committee" : ""))
scatter!([rt,], [E,], yerror = [std(co_E),], c = 2, ms=6, label=(i==1 ? "mean" : ""))
end
plot!()
Committee forces are computed analogously. F is a vector of mean forces (i.e. a vector of 3-vectors), while co_F is a list of vectors of committe forces (i.e. a vector of vectors of 3-vectors).
F, co_F = ACE1.co_forces(model.potential, atoms)
@show typeof(F)
@show typeof(co_F);typeof(F) = Vector{StaticArraysCore.SVector{3, Float64}}
typeof(co_F) = StaticArraysCore.SVector{10, Vector{StaticArraysCore.SVector{3, Float64}}}The situation is analogous for committee virials
V, co_V = ACE1.co_virial(model.potential, atoms)
@show typeof(V)
@show typeof(co_V);typeof(V) = StaticArraysCore.SMatrix{3, 3, Float64, 9}
typeof(co_V) = StaticArraysCore.SVector{10, StaticArraysCore.SMatrix{3, 3, Float64, 9}}This page was generated using Literate.jl.