2288 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
capable of automatically selecting configurations in many
different applications exist (Smith et al. 2018), strategies
to lighten the training cost are still in their infancy. Yet, a
machine learning force field (MLFF) (Ryosuke et al. 2019)
model can be iteratively trained by generating new data
points from CMD trajectories. In our work, we follow a
ALFF (active learning force field) procedure based on the
connection between construction, training, and validation
of the data set, see Figure 3. The whole process involving all
three steps is repeated iteratively until a converged data set
and potential has been obtained.
In particular, we use both the High Dimensional Neural
Network Potential (HDNNPs) (Behler and Parrinello
2007) and Smooth Overlap of Atomic Position (SOAP)
(Bartók et al. 2013) methods in order to develop scalable
and accurate models to investigate the adsorption of col-
lectors upon mineral surfaces. In HDNNP, the NN repre-
senting the total energy is replaced by a set of atomic NNs.
Each NN then provides the contribution Ei of an atom to
the total energy of the system. As depicted in Figure 4(a),
during the feed-forward propagation cartesian inputs are
modified in order to obtain symmetric functions which are
invariant by rotation, permutation and translation. In the
back-propagation (Figure 4(b)), weights (i.e., the connec-
tions between nodes) are optimized after evaluation of the
cost function related to the total energy E.
SOAP model employs a rotation- and permutation-
invariant environment descriptor to directly construct the
kernel as well as the power spectrum of a spherical harmon-
ics. Atomic Cluster Expansion (ACE) (Drautz, R. 2019)
reformulates and significantly extends the SOAP framework
to obtain a complete set of invariant polynomials where
the angular component is described by spherical harmonics
expansion of the atomic density. This formulation removes
the steep scaling of the evaluation of the site energy with
the number of neighbors, resulting in highly efficient inter-
atomic potentials for materials. Eventually, ACE descriptor
is employed in a gaussian process regression.
Figure 3. ALFF scheme. (a) The ML descriptor for the substrate/water interface is tuned by monitoring (b) the root mean
square error (RMSE) values of training and test sets. (c) The presence of holes in the data set is checked by predicting energies
and forces and selecting additional reference structures on the fly to reduce the regions of the configuration space that are not
well sampled
capable of automatically selecting configurations in many
different applications exist (Smith et al. 2018), strategies
to lighten the training cost are still in their infancy. Yet, a
machine learning force field (MLFF) (Ryosuke et al. 2019)
model can be iteratively trained by generating new data
points from CMD trajectories. In our work, we follow a
ALFF (active learning force field) procedure based on the
connection between construction, training, and validation
of the data set, see Figure 3. The whole process involving all
three steps is repeated iteratively until a converged data set
and potential has been obtained.
In particular, we use both the High Dimensional Neural
Network Potential (HDNNPs) (Behler and Parrinello
2007) and Smooth Overlap of Atomic Position (SOAP)
(Bartók et al. 2013) methods in order to develop scalable
and accurate models to investigate the adsorption of col-
lectors upon mineral surfaces. In HDNNP, the NN repre-
senting the total energy is replaced by a set of atomic NNs.
Each NN then provides the contribution Ei of an atom to
the total energy of the system. As depicted in Figure 4(a),
during the feed-forward propagation cartesian inputs are
modified in order to obtain symmetric functions which are
invariant by rotation, permutation and translation. In the
back-propagation (Figure 4(b)), weights (i.e., the connec-
tions between nodes) are optimized after evaluation of the
cost function related to the total energy E.
SOAP model employs a rotation- and permutation-
invariant environment descriptor to directly construct the
kernel as well as the power spectrum of a spherical harmon-
ics. Atomic Cluster Expansion (ACE) (Drautz, R. 2019)
reformulates and significantly extends the SOAP framework
to obtain a complete set of invariant polynomials where
the angular component is described by spherical harmonics
expansion of the atomic density. This formulation removes
the steep scaling of the evaluation of the site energy with
the number of neighbors, resulting in highly efficient inter-
atomic potentials for materials. Eventually, ACE descriptor
is employed in a gaussian process regression.
Figure 3. ALFF scheme. (a) The ML descriptor for the substrate/water interface is tuned by monitoring (b) the root mean
square error (RMSE) values of training and test sets. (c) The presence of holes in the data set is checked by predicting energies
and forces and selecting additional reference structures on the fly to reduce the regions of the configuration space that are not
well sampled