# NNP configuration: keywords

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The NNP settings file (usually named input.nn) contains the setup of neural networks and symmetry functions. Each line may contain a single keyword with no, one or multiple arguments. Keywords and arguments are separated by at least one whitespace. Lines or part of lines can be commented out with the symbol “#”, everything right of “#” will be ignored. The order of keywords is not important, most keywords may only appear once (exceptions: symfunction_short and atom_energy). Here is the list of available keywords (if no usage information is provided, then the keyword does not support any arguments).

## General NNP keywords

These keywords provide the basic setup for a neural network potential. Therefore, they are mandatory for most NNP applications and a minimal example setup file would contain at least:

number_of_elements 1
elements H
global_hidden_layers_short 2
global_nodes_short 10 10
global_activation_short t t l
cutoff_type 1
symfunction_short ...
...


These commands will set up a neural network potential for hydrogen atoms (2 hidden layers with 10 neurons each, hyperbolic tangent activation function) and the cosine cutoff function for all symmetry functions. Of course, further symmetry functions need to be specified by adding multiple lines starting with the symfunction_short keyword.

### number_of_elements

Defines the number of elements the neural network potential is designed for.

Usage:

number_of_elements <integer>

Examples:

number_of_elements 3

### elements

Usage:

elements <string(s)>

Examples:

elements O H Zn

This keyword defines all elements via a list of element symbols. The number of items provided has to be consistent with the argument of the number_of_elements keyword. The order of the items is not important, elements are automatically sorted according to their atomic number. The list nnp::ElementMap::knownElements contains a list of recognized element symbols.

### atom_energy

Usage:

atom_energy <string> <float>

Examples:

atom_energy O -74.94518524

Definition of atomic reference energy. Shifts the total potential energy by the given value for each atom of the specified type. The first argument is the element symbol, the second parameter is the shift energy.

### global_hidden_layers_short

Usage:

global_hidden_layers_short <integer>

Examples:

global_hidden_layers_short 3

Sets the number of hidden layers for neural networks of all elements.

### global_nodes_short

Usage:

global_nodes_short <integer(s)>

Examples:

global_nodes_short 15 10 5

Sets the number of neurons in the hidden layers of neural networks of all elements. The number of integer arguments has to be consistent with the argument of the global_hidden_layers_short keyword. Note: The number of input layer neurons is determined by the number of symmetry functions and there is always only a single output neuron.

### global_activation_short

Usage:

global_activation_short <chars>

Examples:

global_activation_short t t t l

Sets the activation function per layer for hidden layers and output layers of neural networks of all elements. The number of integer arguments has to be consistent with the argument of the global_hidden_layers_short keyword (i.e. number of hidden layers + 1). Activation functions are chosen via single characters from the following table (see also nnp::NeuralNetwork::ActivationFunction).

### normalize_nodes

Activates normalized neural network propagation, i.e. the weighted sum of connected neuron values is divided by the number of incoming connections before the activation function is applied. Thus, the default formula to calculate the neuron

$y^{k}_{i} = f_a \left( b^{k}_{i} + \sum_{j=1}^{n_l} a^{lk}_{ji} \, y^{l}_{j} \right),$

is modified according to:

$y^{k}_{i} = f_a \left( \frac{b^{k}_{i} + \sum_{j=1}^{n_l} a^{lk}_{ji} \, y^{l}_{j}}{n_l} \right).$

### cutoff_type

Usage:

cutoff_type <integer> <<float>>

Examples:

cutoff_type 2 0.5

cutoff_type 7

Defines the cutoff function type used for all symmetry functions. The first argument determines the functional form, see nnp::CutoffFunction::CutoffType for all available options. Use one of the following integer numbers to select the cutoff type. The second argument is optional and sets the parameter $$\alpha$$. If not provided, the default value is $$\alpha = 0.0$$.

### scale_symmetry_functions_sigma

Combining these keywords determines how the symmetry functions are scaled before they are used as input for the neural network. See nnp::SymFnc::ScalingType and the following table for allowed combinations:

Keywords present

Scaling type

None

nnp::SymFnc::ST_NONE

scale_symmetry_functions

nnp::SymFnc::ST_SCALE

center_symmetry_functions

nnp::SymFnc::ST_CENTER

scale_symmetry_functions + center_symmetry_functions

nnp::SymFnc::ST_SCALECENTER

scale_symmetry_functions_sigma

nnp::SymFnc::ST_SCALESIGMA

### scale_max_short

Usage:

scale_min_short <float>

scale_max_short <float>

Examples:

scale_min_short 0.0

scale_max_short 1.0

Set minimum $$S_{\min}$$ and maximum $$S_{\max}$$ for symmetry function scaling. See nnp::SymmetryFunction::ScalingType.

### symfunction_short

Usage:

symfunction_short <string> <integer> ...

Examples:

symfunction_short H 2 H 0.01 0.0 12.0

symfunction_short H 3 O H 0.2 -1.0 4.0 12.0

symfunction_short O 9 H H 0.1  1.0 8.0 16.0

symfunction_short H 12 0.01 0.0 12.0

symfunction_short O 13 0.1 0.2 1.0 8.0 16.0

Defines a symmetry function for a specific element. The first argument is the element symbol, the second sets the the type. The remaining parameters depend on the symmetry function type, follow the links in the right column of the table and look for the detailed description of the class.

## Training-specific keywords

The following keywords are solely used for training with nnp-train. All other tools and interfaces will ignore these keywords.

### selection_mode

Usage:

selection_mode <integer> <<pairs of integers>>

Examples:

selection_mode 0

selection_mode 2 15 1 20 2

Sets the scheme to select energy and force candidates during training (first integer argument, mandatory). If only one argument is given the chosen mode is used for the entire training. The optional pairs of integers allow to switch the selection mode during training. The first integer of each pair determines the epoch when to switch while the second denotes the selection mode to switch to. Hence, the above example means: Start the training with selection mode 2, then after 15 epochs switch to mode 1 and finally at epoch 20 switch back to mode 2 until training is completed. There are three selection modes implemented:

• 0: Random selection

Select training candidates randomly.

• 1: Sort by RMSE

At the beginning of each epoch all training candidates are sorted according to their current RMSE. Throughout the epoch this list is then processed sequentially in order of descending RMSE, i.e. from highest to lowest error. This selection scheme can be helpful to decrease the error of outlier forces when used in conjunction with the optional selection mode switching (see above).

• 2: Random selection with threshold

Select training candidates randomly but use the choice only for training if the current error is above a threshold. Otherwise, select another candidate. The threshold can be set for energies and forces separately with the keywords short_energy_error_threshold and short_force_error_threshold and is expressed in terms of the last epochs RMSE, e.g. short_energy_error_threshold 1.5 means a threshold of $$1.5 \times RMSE$$. Training candidates are selected randomly until the threshold condition is fulfilled or a the number of trial choices (keyword rmse_threshold_trials) is exceeded. If even in the latter case no candidate above the threshold is found, the candidate with the highest error so far is used. This selection scheme is a variation of the adaptive process described by Blank and Brown 1 and is described here 2.

### main_error_metric

Usage:

main_error_metric <string>

Examples:

main_error_metric RMSEpa

main_error_metric MAE

Selects the error metric to display on the screen during training. Four variants are available:

• RMSEpa: RMSE of energies per atom, RMSE of forces.

• RMSE: RMSE of energies, RMSE of forces.

• MAEpa: MAE of energies per atom, MAE of forces.

• MAE: MAE of energies, MAE of forces.

If this keyword is omitted the default value is RMSEpa. The keyword does not influence the output in the learning-curve.out file. There, all error metrics are written.

1

Blank, T. B.; Brown, S. D. Adaptive, Global, Extended Kalman Filters for Training Feedforward Neural Networks. J. Chemom. 1994, 8 (6), 391–407. https://doi.org/10.1002/cem.1180080605

2

Singraber, A.; Morawietz, T.; Behler, J.; Dellago, C. Parallel Multistream Training of High-Dimensional Neural Network Potentials. J. Chem. Theory Comput. 2019, 15 (5), 3075–3092. https://doi.org/10.1021/acs.jctc.8b01092