2.2. Getting Started: Lennard-Jones Potential for Argon¶

The parameters are shown on the Parameters tab.

All the parameters in a parameter interface have names. For Lennard-Jones, there are only two parameters: eps and rmin.

Every parameter has a value and an allowed range of values. Above, the value for eps is shown to be 0.0003, and the allowed range to between 1e-5 and 0.01. This means that the eps variable will only be varied between \(10^{-5}\) and \(10^{-2}\) during the parametrization.

Similarly, the initial value for rmin is set to 4.0, and the allowed range is between 1.0 and 8.0.

The Active attribute of the parameters is set checked, meaning that they will be optimized. To not optimize a parameter, untick the Active checkbox.

The Val % column indicates how close to the Min or Max that the current value is. It is calculated as 100*(value-min)/(max-min). For example, for rmin, it is 100*(4.0-1.0)/(8.0-1.0) = 42.9. It has no effect on the parametrization; it only lets you quickly see if the value is close to the Min or Max.

The Jobs panel contains three entries. They have the JobIDs Ar32_frame001, Ar32_frame002, and Ar32_frame003.

Select one of the jobs in the table.

This updates the molecule area to the left to show the structure.

You can customize how the molecule is shown just like in AMSinput, AMSmovie, etc. For example, select View → Periodic → Repeat Unit Cells to see some periodic images.

Select View → Periodic → Repeat Unit cells again to only view one periodic image.

The Jobs panel has four columns:

• JobID: The name of the job. You can rename a job directly in the table by first selecting the row, and then clicking on the job id.
• Detail: Some information about the job. SinglePoint + gradients means that a single point calculation on the structure is performed, also calculating the gradients (forces). Double-click in the Detail column for a job to see and edit the details. You can also toggle the Info panel in the bottom half.
• Reference Engine: This column can contain details about the reference calculation, and is described more in the tutorials Import training data (GUI) and Calculate reference values with ParAMS.
• ParAMS Engine: This column can contain details about job-specific engine settings. It is described in the tutorial GFN1-xTB: Lithium fluoride

The Training Set panel contains five entries: two of type Energy and three of type Forces.

The first Energy entry has the Detail Ar32_frame001-Ar32_frame002. This means that for every iteration during the parametrization, the current Lennard-Jones parameters will be used to calculate the energy of the job Ar32_frame001 minus the energy of the job Ar32_frame002. The number should ideally be as close as possible to the reference value, which is given as 0.204 eV in the Value column. The greater the deviation from the reference value, the more this entry will contribute to the loss function.

Double-click in the Detail column for the first entry to see some more details.

This brings up a dialog where you can change

• What is calculated (the Energy text box). For example, energy("Ar32_frame001") extracts the energy of the Ar32_frame001 job. You can combine an arbitrary number of such energies with normal arithmetic operations (+, -, /, *). For details, see the Import training data (GUI) tutorial.
• Sigma: A number signifying an “acceptable prediction error”. Here, it is given as 0.0544 eV, which is the default value for energies. A smaller sigma will make the training set entry more important (contribute more to the loss function). For beginning ParAMS users, we do not recommend to modify Sigma, but instead to modify the Weight.
• Weight: A number signifying how important the training set entry is. A larger weight will make the training set entry more important (contribute more to the loss function). The default weight is 1.0.

• Unit: The unit that Sigma and the reference value are expressed in. Here, it is set to eV. See how to set preferred units.
• Value: The reference value (expressed in the unit above).

Click OK. This brings you back to the Training Set panel.

The W column contains the Weight of the training set entry. You can edit it directly in the table.

The Value column contains the reference value.

The Prediction column contains the predicted value (for the “best” parameter set) for running or finished parametrizations. It is now empty.

The Loss contribution column contains the how much an entry contributes to the loss function (in percent) for running or finished parametrizations. It is now empty.

Many different quantities can be extracted from a job. The third entry is of type Forces for the job Ar32_frame001. The reference data are the atomic forces (32 × 3 force components) from the job Ar32_frame001. The Value column gives a summary: [-0.3844, 0.3482] (32×3), meaning that the most negative force component is -0.3844 eV/Å, and the most positive force component is +0.3482 eV/Å.

To see all force components, either double-click in the Details column or switch to the Info panel at the bottom.

Open the Settings panel in the bottom half.

There are three lines:

• optimizer: Scipy(method='Nelder-Mead')
• parallel: ParallelLevels(parametervectors=1, jobs=1, processes=1)
• timeout: 120

Optimizer: The optimizer variable is an Optimizer. For simple optimization problems like Lennard-Jones, the Nelder-Mead method from scipy can be used. For more complicated problems, like ReaxFF optimization, a more advanced optimizer like the CMAOptimizer is recommended (see for example the ReaxFF: Gaseous H₂O tutorial).

Parallellization: The parallel variable is a ParallelLevels, specifying how to parallelize the parameter optimization. Here, it is explicitly set to run in serial. If you remove the option by clicking the button, that will instead try to use an optimal parallelization strategy for your machine.

Timeout: The timeout variable gives the maximum number of seconds that the parametrization is allowed to run. If the parametrization takes longer than two minutes (120 seconds), it will stop. If you remove the option by clicking the button, then there is no time limit.

There are also a few more options. Click the yellow Settings drop-down to add other options. Their meaning can be found in the ParAMS Main Script documentation.

The best (optimized) parameters are shown on the Parameters tab in the bottom half of the window. They get automatically updated as the optimization progresses.

You can also find them in the file lennardjones.results/optimization/training_set_results/best/lj_parameters.txt (or lennardjones.results/optimization/training_set_results/best/parameter_interface.yaml):

Engine LennardJones
    Eps 0.00019604583935927278
    RMin 3.653807860077536
EndEngine

Go to the Graphs panel. There are three curves shown:

• The loss function vs. evaluation number
• The RMSE (root mean squared error) of energy predictions vs. evaluation number
• A scatter plot of predicted vs. reference energies

There are many different types of graphs that you can plot. To plot a correlation plot between the predicted and reference forces:

In the drop-down that currently says Energy, choose Forces

Click on one of the plotted points

This selects the corresponding Job in the table above

In the 3D area the atom for the force component you clicked is selected

The black diagonal line is the line y = x. In this case, the predicted forces are very close to the reference forces! Let’s compare to the initially predicted forces, i.e. let’s compare the optimized parameters eps = 0.000196 and rmin = 3.6538 (from evaluation 144) to the initial parameters eps = 0.0003 and rmin = 4.0 (from evaluation 0):

In the Data From dropdown above the correlation plot, tick Training(initial): forces.

This adds a set of green datapoints with the initial predictions.

There is a third drop-down where you can choose whether to plot the Best or Latest training data. In this example, both correspond to evaluation 144. In general, the latest evaluation doesn’t have to be the best. This is especially true for other optimizers like the CMA optimizer (recommended for ReaxFF).

Go to the Graphs panel.

The left-most plot shows the evolution of the loss function with evaluation number. The goal of the parametrization is to minimize the loss function.

By default, the loss function value is saved every 10 evaluations or whenever it decreases.

You can also choose between the RMSE and MAE (mean absolute error) for energies and forces (and other predicted properties):

In the drop-down that says Stats: Energy, choose Stats → Forces

This plots the RMSE of the forces vs. evaluation number

In the drop-down that says RMSE, choose MAE

This plots the MAE of the forces vs. evaluation number

By default, the RMSE and MAE are saved every 10 evaluations or whenever the loss function decreases.

In the bottom table, switch to the Graphs panel.

In one of the drop-downs, choose Active Parameters: eps.

This plots the value of the eps parameter vs. evaluation number

The parameters are by default saved every 500 evaluations, or whenever the loss function decreases.

You can similarly plot the rmin parameter.

Mouse-over the graph to see the value of the parameter at that iteration.

The best parameter values are shown on the Parameters tab.

Switch to the Training Set panel in the upper table.

The Prediction column contains the predicted values (for the best evaluation, i.e., the one with the lowest loss function value). For the forces, only a summary of the minimum and maximum value is given. To see all predicted, values select one of the Forces entries and go to the Info panel at the bottom and scroll down.

You can also view the predicted values in a different way:

Switch to the Results panel in the bottom table

In the drop-down, select Training best: energy

This shows the file lennardjones.results/optimization/training_set_results/best/scatter_plots/energy.txt

This shows a good agreement between the predicted and reference values for the relative energies in the training set.

In the drop-down, select Training best: forces

This shows the file lennardjones.results/optimization/training_set_results/best/scatter_plots/forces.txt

energy.txt and forces.txt are the files that are plotted when making Correlation plots.

There is one file for every extractor in the training set.

In the top table, switch to the Training Set panel.

The last column contains the Loss Contribution. For each training set entry, it gives the fraction that the entry contributes to the loss function value.

Here, for example, the two Energy entries only contribute 0.96% to the loss function, and the three Forces entries contribute 99.04%. If you notice that some entries have a large contribution to the loss function, and that this prevents the optimization from progressing, you may consider decreasing the weight of those entries.

In the bottom table, switch to the Results panel.

In the drop-down, select Training best: stats

This shows the file lennardjones.results/optimization/training_set_results/best/stats.txt