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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')

  1. J. Behler and M. Parrinello. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett., April 2007. doi:10.1103/physrevlett.98.146401. ↩↩

  2. J. Behler. Constructing high-dimensional neural network potentials: A tutorial review. Int. J. Quantum Chem., 115:1032–1050, August 2015. doi:10.1002/qua.24890. ↩↩

  3. 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. ↩