19 research outputs found
SchNet: A continuous-filter convolutional neural network for modeling quantum interactions
Deep learning has the potential to revolutionize quantum chemistry as it is
ideally suited to learn representations for structured data and speed up the
exploration of chemical space. While convolutional neural networks have proven
to be the first choice for images, audio and video data, the atoms in molecules
are not restricted to a grid. Instead, their precise locations contain
essential physical information, that would get lost if discretized. Thus, we
propose to use continuous-filter convolutional layers to be able to model local
correlations without requiring the data to lie on a grid. We apply those layers
in SchNet: a novel deep learning architecture modeling quantum interactions in
molecules. We obtain a joint model for the total energy and interatomic forces
that follows fundamental quantum-chemical principles. This includes
rotationally invariant energy predictions and a smooth, differentiable
potential energy surface. Our architecture achieves state-of-the-art
performance for benchmarks of equilibrium molecules and molecular dynamics
trajectories. Finally, we introduce a more challenging benchmark with chemical
and structural variations that suggests the path for further work
Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds
The Euclidean scattering transform was introduced nearly a decade ago to
improve the mathematical understanding of convolutional neural networks.
Inspired by recent interest in geometric deep learning, which aims to
generalize convolutional neural networks to manifold and graph-structured
domains, we define a geometric scattering transform on manifolds. Similar to
the Euclidean scattering transform, the geometric scattering transform is based
on a cascade of wavelet filters and pointwise nonlinearities. It is invariant
to local isometries and stable to certain types of diffeomorphisms. Empirical
results demonstrate its utility on several geometric learning tasks. Our
results generalize the deformation stability and local translation invariance
of Euclidean scattering, and demonstrate the importance of linking the used
filter structures to the underlying geometry of the data.Comment: 35 pages; 3 figures; 2 tables; v3: Revisions based on reviewer
comment
Generalizing Geometric Nonwindowed Scattering Transforms on Compact Riemannian Manifolds
Let be a compact, smooth, -dimensional Riemannian manifold
without boundary. In this paper, we generalize nonwindowed geometric scattering
transforms, which we formulate as norms of a
cascade of geometric wavelet transforms and modulus operators. We then provide
weighted measures for these operators, prove that these operators are
well-defined under specific conditions on the manifold, invariant to the action
of isometries, and stable to diffeomorphisms for -bandlimited
functions.Comment: Initial draft. Comments welcome