Update README.md

**Additional Information:**

Dipole moment i.e. local polarization P_u of each unit cell calculated using:

<img src="figs/smc-eq.png" alt="drawing" width="600"/>

where $`V_u`$ is the volume of the unit cell, $`Z_{Ti}^*`$, $`Z_{Ba}^*`$, $`Z_{O}^*`$ are the charges of the Ti, Ba and O atoms obtained using the Electron Equilibration Method (EEM) approach in ReaxFF, and $`r_{Ti} (t)`$,$`r_{Ba,i} (t)`$,$`r_{O,i} (t)`$ are the positions of the Ti, Ba and O atoms of each unit cell at time $`t`$ [1].

<img src="figs/smc_fig1.png" alt="drawing" width="600"/> 

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<bold> Fig. (A) shows a unit cell of the BaTiO3 (top), following Ti atoms motion resulted in the UP and DOWN polarization, (red arrow) points out the UP and DOWN polarization in a sectional view of BaTiO3 at equilibrium state(bottom).[2] </bold>

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<img src="figs/smc_fig2.png" alt="drawing" width="600"/>

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<bold> Fig. (B) shows, hysteric response to the applied electric field, results ordered arrangement of BaTiO3 [2] </bold>

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Ti atoms' motion shown in fig. (A) determines the unit cell's local polarization for a given system. Based on the local polarization order from fig (A), blue and orange regions are two different symmetric order arrangements at equilibration. States that exist at equilibration are called 'static' states. The system may possess an infinite number of orders in the equilibrium state with no applied electric field. The interface may have different 'static' states that can hard to analyze with traditional methods (as shown in fig. A). With the help of data provided in SUBSET A, we are interested to know the existence of different order parameters-'static states' for the given systems. 

States exist with an applied electric field called dynamic states. The ordered dynamics of the BaTiO3 system differed by adding defects and applying directional electric field with non-zero magnitude value that results in the hysteresis loop in fig. (B). Data in SUBSET B, we provided four sets of configuration each has applied a non-zero magnitude of an electric field with defects and no-defects. Earlier studies used methods such as DMD (Dynamic mode decomposition) method [3], VAE (Variational autoencoders), and TICA (time-lagged independent component analysis)[4] to separate the 'static' or 'dynamic' states from sequential data.

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**Datasets:**

We uploaded a two class of datasets a) system equilibrated at constant temperature (no electric field) b) system applied with a varying electric field.

 Dataset (a) contains 4 sub datasets with varying concentration of defects

|        |                 | 2pBaOv (with defect)  | VTKFILES, LOCAL_DIPOLE_FILES |

One can visualize the dynamics of the given dataset by using VTKFILES using paraview software. 

LOCAL_DIPOLE_FILES snippet below contains co-ordinate of Ti atoms and dipole moment for each snapshot. 

Below we have showed the 

LOCAL_DIPOLE_FILES snippet shown below, contains co-ordinate of Ti atoms and dipole moment (Local polarization) for each snapshot. 

```

# TIMESTEP 250000 0.000000  0.000000  0.000000 162.462759 81.229598 120.800000 

 2.079  2.043 20.809       0.00505805      -0.00416993      -0.00028926  

. #TIMESTEP <timestep> <xlow> <ylow> <zlow> <xhigh> <yhigh> <zhigh>

. <x>,<y><z> <Px> <Py> <Pz>

```

Dipole moment i.e. local polarization P_u of each unit cell calculated using:

<img src="figs/smc-eq.png" alt="drawing" width="600"/>

where $`V_u`$ is the volume of the unit cell, $`Z_{Ti}^*`$, $`Z_{Ba}^*`$, $`Z_{O}^*`$ are the charges of the Ti, Ba and O atoms obtained using the Electron Equilibration Method (EEM) approach in ReaxFF, and $`r_{Ti} (t)`$,$`r_{Ba,i} (t)`$,$`r_{O,i} (t)`$ are the positions of the Ti, Ba and O atoms of each unit cell at time $`t`$ [1].

<img src="figs/smc_fig1.png" alt="drawing" width="600"/> 

<br>

<bold> Fig. (A) shows a unit cell of the BaTiO3 (top), following Ti atoms motion resulted in the UP and DOWN polarization, (red arrow) points out the UP and DOWN polarization in a sectional view of BaTiO3 at equilibrium state(bottom).[2] </bold>

<br>

<img src="figs/smc_fig2.png" alt="drawing" width="600"/>

<br>

<bold> Fig. (B) shows, hysteric response to the applied electric field, results ordered arrangement of BaTiO3 [2] </bold>

<br>

<br>

<br>

Motion of Ti atoms shown in Fig. (A) determines the local polarization of the unit cell in a given system. System may possess an infinite number of orders in the equilibrium state with no applied electric field. With the help of dynamics data provided in SUBSET A we are interested to know the order parameter of the given system. Ordered dynamics of BaTiO3 system differed by application of directional electric field with non-zero magnitude value that results in the hysteresis loop as shown in the Fig. (B). Data in SUBSET B we provided a 4 sets of configuration each has applied a non-zero magnitude of electric field. Earlier studies used methods such as DMD (Dynamic mode decomposition) method [3], VAE (Variational autoencoders) and TICA (time-lagged independent component analysis)[4] to separate out the dynamics from sequential data.

<br> </br>

**The challenge questions are:**

1)	Can we map the molecular dynamics onto a convolutional graph dynamical network[5]?

2)	Can we then identify both ‘static’ polarization states (i.e. regions with polarization that doesn’t change with time) as well as ‘dynamic’ polarization states (i.e. regions with dynamic change in polarization)?

3) Is it possible to use above mentioned methods (DMD,TICA or VAE) to identify both ‘static’/'dynamic' polarization states?

4) Can we cluster the different states as shown in fig. (A)?

**Notes**

1)	ML algorithms to be implemented in one of the following languages: Python, C/C++, Julia.