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 3.343613333333334e-5 minutes
[ Info: Beginning to maximize marginal likelihood
Iter Function value Gradient norm
0 1.155681e+07 2.291558e+07
* time: 0.015307903289794922
1 1.323055e+04 3.211203e-05
* time: 0.8638138771057129
2 1.104783e+04 6.894847e-04
* time: 0.864084005355835
3 1.085204e+04 9.054319e-04
* time: 0.8641810417175293
4 9.406472e+03 7.122083e-03
* time: 0.8642370700836182
5 8.339838e+03 3.316252e-02
* time: 0.8643250465393066
6 8.060072e+03 4.969368e-02
* time: 0.8643879890441895
7 5.440921e+03 1.551345e+00
* time: 0.864508867263794
8 5.433645e+03 7.441536e-01
* time: 0.8646199703216553
9 5.424063e+03 2.001076e-01
* time: 0.864670991897583
10 5.423534e+03 5.746550e-03
* time: 0.8647139072418213
11 5.423533e+03 2.605396e-03
* time: 0.8647639751434326
12 5.367192e+03 3.472664e+00
* time: 0.8648710250854492
13 5.297705e+03 2.489120e+00
* time: 0.8649449348449707
14 5.275075e+03 5.514594e-01
* time: 0.8649890422821045
15 5.255304e+03 2.075148e-01
* time: 0.865062952041626
16 5.160334e+03 1.326801e-01
* time: 0.8651199340820312
17 5.141369e+03 1.112467e-01
* time: 0.8651750087738037
18 5.100246e+03 2.168017e-02
* time: 0.8652310371398926
19 5.049360e+03 3.610391e-02
* time: 0.8652749061584473
20 5.006103e+03 6.247583e-02
* time: 0.8653428554534912
21 4.995258e+03 5.149655e-02
* time: 0.865386962890625
22 4.984123e+03 9.519155e-02
* time: 0.8654310703277588
23 4.964259e+03 1.507008e+00
* time: 0.8654999732971191
24 4.963605e+03 3.289420e-01
* time: 0.8655569553375244
25 4.937312e+03 1.106698e+00
* time: 0.8656010627746582
26 4.935445e+03 9.423114e-01
* time: 0.8656809329986572
27 4.926953e+03 2.032554e-01
* time: 0.8657388687133789
28 4.925570e+03 5.163711e-02
* time: 0.8657879829406738
29 4.925349e+03 2.696016e-02
* time: 0.8658318519592285
30 4.925294e+03 2.793348e-03
* time: 0.8658759593963623
31 4.925294e+03 5.575531e-04
* time: 0.8659238815307617
32 4.925294e+03 4.144730e-07
* time: 0.8659729957580566
33 4.925294e+03 6.542649e-10
* time: 0.8660180568695068
34 4.925294e+03 6.225166e-16
* time: 0.8660628795623779
35 4.925294e+03 6.225166e-16
* time: 0.8661189079284668
┌ Info: Optimization complete
│ Results =
│ * Status: success
│
│ * Candidate solution
│ Final objective value: 4.925294e+03
│
│ * Found with
│ Algorithm: L-BFGS
│
│ * Convergence measures
│ |x - x'| = 7.11e-15 ≤ 1.0e-08
│ |x - x'|/|x'| = 3.96e-17 ≰ 0.0e+00
│ |f(x) - f(x')| = 0.00e+00 ≤ 0.0e+00
│ |f(x) - f(x')|/|f(x')| = 0.00e+00 ≤ 0.0e+00
│ |g(x)| = 6.23e-16 ≰ 0.0e+00
│
│ * Work counters
│ Seconds run: 1 (vs limit Inf)
│ Iterations: 35
│ f(x) calls: 185
│ ∇f(x) calls: 185
└ 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.