This repository is an in-progress project, so I will regularly edit it. My purpose is to collect articles and reproduce their way of tackling this problem, so stay tuned!

neural network potentials

When we take advantage of a neural network to construct a potential energy surface (how atoms see their neighbors! and interact with them), we should consider the physical system symmetries. We already know that we should take translation, rotation, permutation, and reflection symmetry into account for a problem such as potential energy. People already did different works for tackling these symmetry things. Still, the problem is already out there (and that is the reason why we every day see a lot of creative ways of representing molecular configurations for machine learning).

image method

We will start with the image representation of an atomistic environment, implemented in the Ryczko et al article [1]. in order to convert atomistic systems to image, one can use this code:

#converting atomistic systems to images, here we just created on point (with positions x and y)

import numpy as np

a = 5
num = 2
pos_x = np.random.rand(num)
pos_y = np.random.rand(num)

#number of pixeles in image
grid = 256
points = np.linspace(0, a, grid)


X, Y = np.meshgrid(points, points)
image = np.zeros((grid, grid))

for p_x,p_y in zip(pos_x,pos_y):

    dx1 = X - p_x
    dy1 = Y - p_y

    dr1 = np.sqrt(dx1** 2 + dy1**2)

    image = image + np.exp(- (dr1**2 / (2 * (0.2 **2))))

and the result will be something like this image:

Suppose that we had converted our atomistic environment to an image (in our case, a 2D image of graphene), and we already had a sufficient amount of that data. We can then feed those images to the neural network (in our case, Convolutional Neural Network or only CNN). We here take advantage of Keras (with TensorFlow backend). The NN model will be like the following:

def model_paper():
  model = Sequential()

  model.add(Conv2D(input_shape=(256,256,1),filters=64,kernel_size=(3,3),strides=(2,2),padding="same", activation="relu"))

  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1,padding="same", activation="relu"))
  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1 ,padding="same", activation="relu"))

  model.add(Conv2D(filters=64,kernel_size=(3,3),strides=(2,2),padding="same", activation="relu"))

  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1,padding="same", activation="relu"))
  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1 ,padding="same", activation="relu"))

  model.add(Conv2D(filters=64,kernel_size=(3,3),strides=(2,2),padding="same", activation="relu"))

  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1,padding="same", activation="relu"))
  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1 ,padding="same", activation="relu"))

  model.add(Conv2D(filters=64,kernel_size=(3,3),strides=(2,2),padding="same", activation="relu"))

  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1,padding="same", activation="relu"))
  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1 ,padding="same", activation="relu"))

  model.add(Conv2D(filters=64,kernel_size=(3,3),strides=(2,2),padding="same", activation="relu"))

  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1,padding="same", activation="relu"))
  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1 ,padding="same", activation="relu"))

  model.add(Conv2D(filters=64,kernel_size=(3,3),strides=(2,2),padding="same", activation="relu"))

  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1,padding="same", activation="relu"))
  model.add(Conv2D(filters=16,kernel_size=(4,4),strides= 1 ,padding="same", activation="relu"))

  model.add(Conv2D(filters=64,kernel_size=(3,3),strides=(2,2),padding="same", activation="relu"))

  model.add(Flatten())
  model.add(Dense(units=1024,activation="relu"))

  model.add(Dense(units = 1, activation="linear"))

  return model

References

[1] in Ryczko K, Mills K, Luchak I, Homenick C, Tamblyn I. Convolutional neural networks for atomistic systems. Computational Materials Science. 2018 Jun 15;149:134-42.