Doubts related to NNPs

[Sudarsan m pai]

Respected Ma‘am,

My name is Sudarsan Manjunatha Pai.I am a 3rd semester Computational materials science student from the Technische Universität Bergakademie, Freiberg.

As part of the personal programming project,I intend to construct artificial neural network potentials from scratch based on your research article named ‘An implementation of artificial neural-network potentials for atomistic

materials simulations: Performance for TiO2‘.I have conducted my background research on the topic but have a few doubts.

a)I would like to know why the long range interactions were omitted by considering the condensed phases of TiO2.Wouldn‘t the structural energy calculated using DFT for the reference calculations contain this electrostatic energy contribution?

As this project emphasises more on the programming part,I was suggested to show that the resulting potential from the neural network could be used in a 2D molecular dynamics simulation using programming.

b)I understood that individual atomic NNs will provide the individual atomic energy contribution.But for an MD simulation,as the inputs are the positions of atoms and the inter-atomic energy function,I wanted to how I could find the inter-atomic energies of atoms from their individual energy values.

It would be really helpful if you could share your thoughts. 

Looking forward to your valuable insights.

Thanks in advance,

Sudarsan Manjunatha Pai,

Master student,Computational materials science

TU Bergakademie Freiberg,

Germany

[troydl...@gmail.com]

Hi,

I think I could help you here.

a)I would like to know why the long range interactions were omitted by considering the condensed phases of TiO2.Wouldn‘t the structural energy calculated using DFT for the reference calculations contain this electrostatic energy contribution?

Yes it wouldn't explicitly include long range interactions, but the thing is even with a short range potential you can still get a pretty good approximation.  Especially since those tend to be the dominant contributions where as the long range contributions tend to be smaller in scope.  The neural networks also have a habit of sort of "averaging out" the long range component which includes some of it implicitly.

There are Neural Net models that have long range contributions explicitly defined as well I might add. 

b)I understood that individual atomic NNs will provide the individual atomic energy contribution.But for an MD simulation,as the inputs are the positions of atoms and the inter-atomic energy function,I wanted to how I could find the inter-atomic energies of atoms from their individual energy values.

Those are the inter-atomic energies.  The energy of a single atom is based on its local environment or in other words it is based on its interaction with other atoms. It may look a bit different from standard pair-wise potentials, but that is what they are.

-Troy Loeffler

Center for Nanoscale Materials

Argonne National Lab

[Sudarsan m pai]

Hi all,

I have few more doubts related to the NNPs.

a)Should the unit cell be repeated before considering the cutoff sphere for symmetry functions?(I have this doubt because the xsf files contains co-ordinates of periodic structures,and I think that the atoms in the neighbouring unit cells can also come inside the cutoff sphere for a particular atom and contribute towards its structural fingerprint.)

b)By going through one of the questions in this group,I came to know that the reference energy commented in the xsf is not the structural energy,but the cohesive energy.So can I compare this cohesive energy with the sum of outputs of the atomic NNs (ΣEi) to get the cost function(RMSE or MAE)?

(In other words,is the cohesive energy and the E_ref same ?)

Any insights would be appreciated.

Thanks and regards,

Sudarsan M Pai

Computational Materials Science,3rd Sem

TU Bergakademie Freiberg

Germany

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[troydl...@gmail.com]

Hi,

a)Should the unit cell be repeated before considering the cutoff sphere for symmetry functions?(I have this doubt because the xsf files contains co-ordinates of periodic structures,and I think that the atoms in the neighbouring unit cells can also come inside the cutoff sphere for a particular atom and contribute towards its structural fingerprint.)

I can't remember if AENet itself uses a ghost atom system, but if you are in doubt it never hurts to expand the box size within reason. You train time shouldn't increase by that much if you scale up the box size to say 30-100 atoms instead of 4-6.  So long as your boxes are at least 2x the cutoff it takes care of the first problem which is incorrect energies for a periodic system. 

However, in my experience I will also say if your boxes are small enough that you're worried about that you might run into another problem which is finite size effects.  That is when you have periodic boxes that are too small it's mathematically impossible to create certain atom arrangements.  Larger systems have more statistical diversity than smaller systems which is highly important for training a neural network. To give you a simple example, a box with 1 atom and a fixed box length the distance between the atom and its periodic image can never change.

If your training set only deals with small box configurations very often when you go to apply your neural network to a real system you'll find it falls apart because you never trained it against configurations you will experience in the larger real system. 

b)By going through one of the questions in this group,I came to know that the reference energy commented in the xsf is not the structural energy,but the cohesive energy.So can I compare this cohesive energy with the sum of outputs of the atomic NNs (ΣEi) to get the cost function(RMSE or MAE)?

(In other words,is the cohesive energy and the E_ref same ?)

As far as the XSF, the answer is it's both.  It depends on how you define it in your input. 

The reference in the XSF file is by default the total energy of the system, but you can also define it as the cohesive energy with a bit of magic in the input scripts. In the AENet input scripts you'll find a place you can specify the isolated atom DFT energies for each atom type in your system. 

If you set the isolated atom energies of all atoms to 0, then the total energy in the file will be the cohesive energy.

 E_coh = E_total - N_atom1*E_atom1 - N_atom2*E_atom2....

If E_atom1= E_atom2 = .... = 0 then

  E_coh = E_total 

This is how you would define it if you are training a neural network against a classical forcefield where the isolated atoms are defined to be 0 by convention. That's a consequence of the cohesive energy equation.

So it's possible to either put the cohesive energy or the total energy in the XSF files so long as the isolated atom energies in the input file match. Though when training against DFT or other quantum methods it's a bit better in my opinion to supply the total structure energies and the isolated atom energies in case you have to re-compute the structural energies or isolated atom energies for whatever reason.  

AENet will compute and return the cohesive energy along with the total energy prediction.  As far as the cost function is concerned it should be identical for cohesive and total energy if they both the AENet and DFT Reference use the same isolated atom reference since the isolated atom energies will drop out of the equation when you subtract it.

-Troy Loeffler

 Center for Nanoscale Materials

 Argonne National Lab.