Tutorial: Minimization with AENET + minsearch

This tutorial explains how to find the optimal N-N bond distance of an N2 dimer by combining a machine learning potential built with AENET and the minsearch (Nelder-Mead method) algorithm in ODAT-SE.

The sample files are located in sample/aenet_minsearch/.

Prerequisites

AENET’s predict.x must be installed
A trained ANN potential file (N.5t-5t.ann) must be prepared (see Tutorial: AENET Training Pipeline)

File Structure

sample/aenet_minsearch/
├── input.toml             # ODAT-SE configuration file
├── predict.in             # AENET prediction settings
├── template.xsf           # Structure template
└── run_all.sh             # Execution script

Description of input.toml

[base]
dimension = 1
output_dir = "output"

Sets the dimension of the parameter space to 1 (N-N bond distance only).

[solver]
name = "aenet"

[solver.config]
aenet_exec_file = "predict.x"
aenet_ann_potential = "N.5t-5t.ann"

[solver.param]
string_list = ["value_01"]

Specifies AENET as the solver, along with the path to predict.x and the ANN potential file. string_list defines the placeholders in the template.

[algorithm]
name = "minsearch"
label_list = ["z"]

[algorithm.param]
min_list = [0.5]
max_list = [2.0]
initial_list = [1.25]

[algorithm.minimize]
initial_scale_list = [0.25]
xatol = 0.0001
fatol = 0.0001
maxiter = 100

Minsearch algorithm settings:

Parameter	Description
`min_list` / `max_list`	Search range: N-N distance 0.5 to 2.0 Angstrom
`initial_list`	Initial value: 1.25 Angstrom
`initial_scale_list`	Scale of the initial simplex: 0.25 Angstrom
`xatol`	Convergence threshold for parameters: 0.0001 Angstrom
`fatol`	Convergence threshold for function value: 0.0001 eV/atom
`maxiter`	Maximum number of iterations: 100

Template File

template.xsf is the structure template for the N2 dimer:

ATOMS
N             0.0000000000        0.0000000000        0.0000000000
N             0.0000000000        0.0000000000        value_01

value_01 is the N-N bond distance to be optimized by minsearch.

How to Run

Using the execution script:

cd sample/aenet_minsearch
sh run_all.sh

Or run directly:

odatse-aenet input.toml

The Nelder-Mead optimization converges in 13 iterations (26 function evaluations) and completes in about 1 second.

Output

The calculation results are generated in the output/ directory:

output/res.txt: Optimization result (optimal parameters and objective function value)
output/SimplexData.txt: Iteration history of the Nelder-Mead simplex

res.txt contains the optimized N-N bond distance and its corresponding energy (eV/atom).

Format of SimplexData.txt:

# step  z  fx

Each line represents the parameter values and function value at each step of the simplex.

Results

The Nelder-Mead optimization yields an optimal N-N bond distance of approximately 1.1 Angstrom.

_images/minsearch_convergence.png — Convergence of the N-N bond distance by the Nelder-Mead method. Top: N-N distance. Bottom: Energy (eV/atom).

To check the optimization result:

cat output/res.txt