ANN (Artificial Neural Network) function for plumed

This is the repository for plumed ANN function (annfunc) module. It implements ANN class, which is a subclass of Function class. ANN class takes multi-dimensional arrays as inputs for a fully-connected feedforward neural network with specified neural network weights and generates corresponding outputs. The ANN outputs can be used as collective variables, inputs for other collective variables, or inputs for data analysis tools.

Dependency

• plumed

Installation

TODO: currently we are working on a pull request for plumed. Once it is merged, you may directly install this module from there.

Usage

It is used in a similar way to other plumed functions. To define an ANN function object, we need to define following keywords:

• ARG (string array): input variable names for the fully-connected feedforward neural network

• NUM_LAYERS (int): number of layers for the neural network

• NUM_NODES (int array): number of nodes in all layers of the neural network

• ACTIVATIONS (string array): types of activation functions of layers, currently we have implemented "Linear", "Tanh", "Circular" layers, it should be straightforward to add other types as well

• WEIGHTS (numbered keyword, double array): this is a numbered keyword, WEIGHTS0 represents flattened weight array connecting layer 0 and layer 1, WEIGHTS1 represents flattened weight array connecting layer 1 and layer 2, ... An example is given in the next section.

• BIASES (numbered keyword, double array): this is a numbered keyword, BIASES0 represents bias array for layer 1, BIASES1 represents bias array for layer 2, ...

Assuming we have an ANN function object named ann, we use ann.node-0, ann.node-1, ... to access component 0, 1, ... of its outputs (used as collective variables, inputs for other collective variables, or data analysis tools).

Examples

Assume we have an ANN with numbers of nodes being [2, 3, 1], and weights connecting layer 0 and 1 are

[[1,2],
[3,4],
[5,6]]

weights connecting layer 1 and 2 are

[[7,8,9]]

Bias for layer 1 and 2 are

[10, 11, 12]

and

[13]

respectively.

All activation functions are Tanh.

Then if input variables are l_0_out_0, l_0_out_1, the corresponding ANN function object can be defined using following plumed script:

ann: ANN ARG=l_0_out_0,l_0_out_1 NUM_LAYERS=3 NUM_NODES=2,3,1 ACTIVATIONS=Tanh,Tanh  WEIGHTS0=1,2,3,4,5,6 WEIGHTS1=7,8,9  BIASES0=10,11,12 BIASES1=13

This plumed script can be generated with function Plumed_helper.get_ANN_expression() in this repository. Following is the Python code using this function to generate the script above:

from plumed_helper import Plumed_helper
ANN_weights = [np.array([1,2,3,4,5,6]), np.array([7,8,9])]
ANN_bias = [np.array([10, 11, 12]), np.array([13])]
Plumed_helper.get_ANN_expression('ANN', node_num=[2, 3, 1], 
                                 ANN_weights=ANN_weights, ANN_bias=ANN_bias,
                                 activation_list=['Tanh', 'Tanh'])

Contact

For any questions, feel free to contact weichen9@illinois.edu or open a github issue.