Note

Click here to download the full example code

# Train a Stillinger-Weber potential#

In this tutorial, we train a Stillinger-Weber (SW) potential for silicon that is archived on OpenKIM.

Before getting started to train the SW model, let’s first make sure it is installed.

If you haven’t already, follow Installation to install `kim-api`

and
`kimpy`

, and `openkim-models`

.

Then do `$ kim-api-collections-management list`

, and make sure
`SW_StillingerWeber_1985_Si__MO_405512056662_006`

is listed in one of the
collections.

Note

If you see `SW_StillingerWeber_1985_Si__MO_405512056662_005`

(note the last
three digits), you need to change `model = KIMModel(model_name="SW_StillingerWeber_1985_Si__MO_405512056662_006")`

to the corresponding model name in your installation.

We are going to create potentials for diamond silicon, and fit the potentials to a
training set of energies and forces consisting of compressed and stretched diamond
silicon structures, as well as configurations drawn from molecular dynamics trajectories
at different temperatures.
Download the training set `Si_training_set.tar.gz`

.
(It will be automatically downloaded if not present.)
The data is stored in # **extended xyz** format, and see Dataset for more
information of this format.

Warning

The `Si_training_set`

is just a toy data set for the purpose to demonstrate how to
use KLIFF to train potentials. It should not be used to train any potential for real
simulations.

Let’s first import the modules that will be used in this example.

```
from kliff.calculators import Calculator
from kliff.dataset import Dataset
from kliff.dataset.weight import Weight
from kliff.loss import Loss
from kliff.models import KIMModel
from kliff.utils import download_dataset
```

## Model#

We first create a KIM model for the SW potential, and print out all the available
parameters that can be optimized (we call this `model parameters`

).

```
model = KIMModel(model_name="SW_StillingerWeber_1985_Si__MO_405512056662_006")
model.echo_model_params()
```

```
#================================================================================
# Available parameters to optimize.
# Parameters in `original` space.
# Model: SW_StillingerWeber_1985_Si__MO_405512056662_006
#================================================================================
name: A
value: [15.28484792]
size: 1
name: B
value: [0.60222456]
size: 1
name: p
value: [4.]
size: 1
name: q
value: [0.]
size: 1
name: sigma
value: [2.0951]
size: 1
name: gamma
value: [2.51412]
size: 1
name: cutoff
value: [3.77118]
size: 1
name: lambda
value: [45.5322]
size: 1
name: costheta0
value: [-0.33333333]
size: 1
'#================================================================================\n# Available parameters to optimize.\n# Parameters in `original` space.\n# Model: SW_StillingerWeber_1985_Si__MO_405512056662_006\n#================================================================================\n\nname: A\nvalue: [15.28484792]\nsize: 1\n\nname: B\nvalue: [0.60222456]\nsize: 1\n\nname: p\nvalue: [4.]\nsize: 1\n\nname: q\nvalue: [0.]\nsize: 1\n\nname: sigma\nvalue: [2.0951]\nsize: 1\n\nname: gamma\nvalue: [2.51412]\nsize: 1\n\nname: cutoff\nvalue: [3.77118]\nsize: 1\n\nname: lambda\nvalue: [45.5322]\nsize: 1\n\nname: costheta0\nvalue: [-0.33333333]\nsize: 1\n\n'
```

The output is generated by the last line, and it tells us the `name`

, `value`

,
`size`

, `data type`

and a `description`

of each parameter.

Note

You can provide a `path`

argument to the method `echo_model_params(path)`

to
write the available parameters information to a file indicated by `path`

.

Note

The available parameters information can also by obtained using the **kliff**
Command Line Tool:
`$ kliff model --echo-params SW_StillingerWeber_1985_Si__MO_405512056662_006`

Now that we know what parameters are available for fitting, we can optimize all or a subset of them to reproduce the training set.

```
model.set_opt_params(
A=[[5.0, 1.0, 20]], B=[["default"]], sigma=[[2.0951, "fix"]], gamma=[[1.5]]
)
model.echo_opt_params()
```

```
#================================================================================
# Model parameters that are optimized.
# Note that the parameters are in the transformed space if
# `params_transform` is provided when instantiating the model.
#================================================================================
A 1
5.0000000000000000e+00 1.0000000000000000e+00 2.0000000000000000e+01
B 1
6.0222455840000000e-01
sigma 1
2.0951000000000000e+00 fix
gamma 1
1.5000000000000000e+00
'#================================================================================\n# Model parameters that are optimized.\n# Note that the parameters are in the transformed space if \n# `params_transform` is provided when instantiating the model.\n#================================================================================\n\nA 1\n 5.0000000000000000e+00 1.0000000000000000e+00 2.0000000000000000e+01 \n\nB 1\n 6.0222455840000000e-01 \n\nsigma 1\n 2.0951000000000000e+00 fix \n\ngamma 1\n 1.5000000000000000e+00 \n\n'
```

Here, we tell KLIFF to fit four parameters `B`

, `gamma`

, `sigma`

, and `A`

of the
SW model. The information for each fitting parameter should be provided as a list of
list, where the size of the outer list should be equal to the `size`

of the parameter
given by `model.echo_model_params()`

. For each inner list, you can provide either one,
two, or three items.

One item. You can use a numerical value (e.g.

`gamma`

) to provide an initial guess of the parameter. Alternatively, the string`'default'`

can be provided to use the default value in the model (e.g.`B`

).Two items. The first item should be a numerical value and the second item should be the string

`'fix'`

(e.g.`sigma`

), which tells KLIFF to use the value for the parameter, but do not optimize it.Three items. The first item can be a numerical value or the string

`'default'`

, having the same meanings as the one item case. In the second and third items, you can list the lower and upper bounds for the parameters, respectively. A bound could be provided as a numerical values or`None`

. The latter indicates no bound is applied.

The call of `model.echo_opt_params()`

prints out the fitting parameters that we
require KLIFF to optimize. The number `1`

after the name of each parameter indicates
the size of the parameter.

Note

The parameters that are not included as a fitting parameter are fixed to the default values in the model during the optimization.

## Training set#

KLIFF has a `Dataset`

to deal with the training data (and possibly
test data). Additionally, we define the `energy_weight`

and `forces_weight`

corresponding to each configuration using `Weight`

. In
this example, we set `energy_weight`

to `1.0`

and `forces_weight`

to `0.1`

.
For the silicon training set, we can read and process the files by:

```
dataset_path = download_dataset(dataset_name="Si_training_set")
weight = Weight(energy_weight=1.0, forces_weight=0.1)
tset = Dataset(dataset_path, weight)
configs = tset.get_configs()
```

```
2022-10-06 23:44:01.093 | INFO | kliff.dataset.dataset:_read:398 - 1000 configurations read from /Users/mjwen.admin/Packages/kliff/examples/Si_training_set
```

The `configs`

in the last line is a list of `Configuration`

.
Each configuration is an internal representation of a processed **extended xyz** file,
hosting the species, coordinates, energy, forces, and other related information of a
system of atoms.

## Calculator#

`Calculator`

is the central agent that exchanges information
and orchestrate the operation of the fitting process. It calls the model to compute the
energy and forces and provide this information to the Loss function (discussed below)
to compute the loss. It also grabs the parameters from the optimizer and update the
parameters stored in the model so that the up-to-date parameters are used the next time
the model is evaluated to compute the energy and forces. The calculator can be created
by:

```
calc = Calculator(model)
_ = calc.create(configs)
```

```
2022-10-06 23:44:01.499 | INFO | kliff.calculators.calculator:create:107 - Create calculator for 1000 configurations.
```

where `calc.create(configs)`

does some initializations for each
configuration in the training set, such as creating the neighbor list.

## Loss function#

KLIFF uses a loss function to quantify the difference between the training set data and
potential predictions and uses minimization algorithms to reduce the loss as much as
possible. KLIFF provides a large number of minimization algorithms by interacting with
SciPy. For physics-motivated potentials, any algorithm listed on
scipy.optimize.minimize and scipy.optimize.least_squares can be used. In the
following code snippet, we create a loss of energy and forces and use `2`

processors
to calculate the loss. The `L-BFGS-B`

minimization algorithm is applied to minimize
the loss, and the minimization is allowed to run for a max number of 100 iterations.

```
steps = 100
loss = Loss(calc, nprocs=2)
loss.minimize(method="L-BFGS-B", options={"disp": True, "maxiter": steps})
```

```
2022-10-06 23:44:01.500 | INFO | kliff.loss:minimize:290 - Start minimization using method: L-BFGS-B.
2022-10-06 23:44:01.501 | INFO | kliff.loss:_scipy_optimize:406 - Running in multiprocessing mode with 2 processes.
2022-10-06 23:44:36.663 | INFO | kliff.loss:minimize:292 - Finish minimization using method: L-BFGS-B.
fun: 0.6940780132865667
hess_inv: <3x3 LbfgsInvHessProduct with dtype=float64>
jac: array([ 8.88178346e-07, -3.50830474e-06, 7.77156122e-08])
message: 'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL'
nfev: 184
nit: 37
njev: 46
status: 0
success: True
x: array([14.93863457, 0.58740273, 2.20146129])
```

The minimization stops after running for 27 steps. After the minimization, we’d better save the model, which can be loaded later for the purpose to do a retraining or evaluations. If satisfied with the fitted model, you can also write it as a KIM model that can be used with LAMMPS, GULP, ASE, etc. via the kim-api.

```
model.echo_opt_params()
model.save("kliff_model.yaml")
model.write_kim_model()
# model.load("kliff_model.yaml")
```

```
#================================================================================
# Model parameters that are optimized.
# Note that the parameters are in the transformed space if
# `params_transform` is provided when instantiating the model.
#================================================================================
A 1
1.4938634567965085e+01 1.0000000000000000e+00 2.0000000000000000e+01
B 1
5.8740272891468026e-01
sigma 1
2.0951000000000000e+00 fix
gamma 1
2.2014612879744848e+00
2022-10-06 23:44:36.670 | INFO | kliff.models.kim:write_kim_model:695 - KLIFF trained model write to `/Users/mjwen.admin/Packages/kliff/examples/SW_StillingerWeber_1985_Si__MO_405512056662_006_kliff_trained`
```

The first line of the above code generates the output. A comparison with the original
parameters before carrying out the minimization shows that we recover the original
parameters quite reasonably. The second line saves the fitted model to a file named
`kliff_model.pkl`

on the disk, and the third line writes out a KIM potential named
`SW_StillingerWeber_1985_Si__MO_405512056662_006_kliff_trained`

.

See also

For information about how to load a saved model, see Frequently Used Modules.

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