Potential sign mismatch between the reference formula the implementation of the forces and stresses

[mtaillefumier]

Summary

I am currently working on a deterministic version of this set of functions, prod_force_{a,r}_gpu which is related to the issue #3270. I compared both implementations to the equations found in the PRL paper https://journals.aps.org/prl/supplemental/10.1103/PhysRevLett.120.143001.

After looking at both the CPU and GPU implementation of the forces, I found a possible inconsistency between the code (both on CPU and GPU) and the formula found in the supplementary material. Let me take the CPU variant as all terms are in the same function

the line

deepmd-kit/source/lib/src/prod_force.cc

Line 45 in f8a0b31

force[i_idx_nall * 3 + 0] -= net_deriv[i_idx * ndescrpt + aa] *

has -= which agrees with the formula in the paper but the line after

deepmd-kit/source/lib/src/prod_force.cc

Line 61 in f8a0b31

force[kk * nall * 3 + j_idx * 3 + 0] +=

which describes the "non-local" part of the atomic forces contains a += operation in contradiction with the the second part of the formula for the forces.

All terms in the original article contain a minus sign. The code contains -= and +=.
the net_deriv which corresponds to the gradient of the energy is calculated here

deepmd-kit/deepmd/descriptor/loc_frame.py

Line 342 in f8a0b31

[net_deriv] = tf.gradients(atom_ener, self.descrpt)

.

Why is there a sign change between the article and the implementation ?

DeePMD-kit Version

all

Backend and its version

CPU and GPU

Python Version, CUDA Version, GCC Version, LAMMPS Version, etc

No response

Details

see summary

[mtaillefumier]

@asedova

[njzjz]

The equation in the paper contains a typo. $D_{jk}^\alpha$ in the first term should be $D_{ik}^\alpha$:

In the formula $\nabla R_i D_{jk}^\alpha$, when $k$ is $i$, it is equal to $-\nabla R_j D_{jk}^\alpha$, which introduces a sign change.

[mtaillefumier]

thank you very much. It was not obvious from the formula and the code combined.