The Behler-Parrinello Neural Network
Introduction
Behler-Parrinello Neural Network1 (BPNN) is an ANN architecture developed by Jörg Behler and Micheler Parrinello. It features the description of atomic environments with the so called symmetry functions (SFs) and the usage of element specific neural network for atomic energies.
Note
The symmetry functions (SFs) are defined according to the Behler's tutorial review on neural network potentials in 2015.2 Note that the naming of symmetry functions is different in the original paper. 1
Parameters
| Parameter | Default | Description |
|---|---|---|
| sf_spec | symmetry function specification | |
| nn_spec | neural network specification | |
| rc | cutoff radius | |
| act | 'tanh' |
actication function |
| cutoff_type | 'f1' |
'f1' or 'f2' 3 |
| fp_range | [] |
speficies the range of atomic fingerprints, see below |
| fp_scale | False |
scales the atomic fingerprints according to fp_range |
| preprocess | False |
run in preprocess mode |
| use_jacobian | True |
compute Jacobians of fps w.r.t coordiniates to speed up force training |
| out_units | 1 | dimension of outputs |
| out_pool | False |
min, max or sum, pool atomic outputs to give global predictions |
Example sf_spec
[{'type':'G2', 'i': 1, 'j': 8,
'Rs': [1.,2.], 'eta': [0.1,0.2]},
{'type':'G2', 'i': 8, 'j': 1,
'Rs': [1.,2.], 'eta': [0.1,0.2]},
{'type':'G4', 'i': 8, 'j': 8,
'lambd':[0.5,1], 'zeta': [1.,2.], 'eta': [0.1,0.2]}]
Preprocessing the SFs
The computation of angular BP symmetry functions is costly, especially when training a BPNN potential with force labels. The process can be greatly accelerated by caching the SFs and the derivative of those SFs with respect to the input coordinates.
# Write a preprocessed
from pinn.io import write_tfrecord
ds = ... # load dataset here
bpnn = BPNN(**network_params)
write_tfrecord('ds_pre.yml', ds.map(bpnn.preprocess))
It's worth noting that the SFs can occupy large disk space. To work around this, you can cache the pre-computed SFs in memory or (when that's not feasible) in a scratch file with TensorFlow's dataset API.
# Caching the dataset in memory
ds_cached = ds.map(bpnn.preprocess).cache()
# Or in a local scratch file
ds_cached = ds.map(bpnn.preprocess).cache('/tmp/scratch')
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1 J. Behler, and M. Parrinello, “Generalized neural-network representation of high-dimensional potential-energy surfaces,” Phys. Rev. Lett. 98, (2007). ↩↩
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1 J. Behler, “Constructing high-dimensional neural network potentials: A tutorial review,” Int. J. Quantum Chem. 115, 1032–1050 (2015). ↩↩
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The f2 cutoff function is scaled by a factor of \(\mathrm{tanh}(1)^{-3}\) as compared to the original form in 2, so that the function asymptotically equals 1 when \(r_{ij}\) approaches \(0\). ↩