Wavelet Scattering Regression of Quantum Chemical Energies

By Matthew J. Hirn, Stéphane Mallat, Nicolas Poilvert. 2016

101 citations recorded by the source corpus.

We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. Similarly to density functional theory (DFT), the molecule is represented by an electronic density function. A multiscale invariant dictionary is calculated with wavelet scattering invariants. It cascades a first wavelet transform which separates scales, with a second wavelet transform which computes interactions across scales. Sparse scattering regressions give state of the art results over two databases of organic planar molecules. On these databases, the regression error is of the order of the error produced by DFT codes, but at a fraction of the computational cost.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Materials Chemistry, Computational Chemistry & Drug Discovery, Signal Processing

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Citations in the corpus

SchNet: A continuous-filter convolutional neural network for modeling quantum interactions (2017, background): “Commonly, this can be solved by a re-sampling approach defining a representation on a grid [7, 27, 28].”
SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks (2020, neutral): “TASK α ∆ε εHOMO εLUMO μ Cν UNITS bohr(3) meV meV meV D cal/mol K WaveScatt [11] .”
Cormorant: Covariant Molecular Neural Networks (2019, background): “…community has formed around trying to use machine learning to learn more descriptive force ﬁelds directly from DFT computations [Behler and Parrinello, 2007, Bartók et al., 2010, Rupp et al., 2012, Shapeev, 2015, Chmiela et al., 2016, Zhang et al., 2018, Schütt et al., 2017, Hirn et al., 2017].”
N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials (2018, background): “…networks framework of Mallat and coworkers, which, at least in the limit of an inﬁnite number of neural network layers, provides a representation of functions that is both globally invariant with respect to symmetries and Lipschitz with respect to warpings (Mallat, 2012; Hirn et al., 2017).”
Extended Physics-informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition based Deep Learning Framework for Nonlinear Partial Differential Equations (2020, background): “The initial values of ν,α in the two subdomains are [2, 6]e−3, [1.”
Deep learning of vortex-induced vibrations (2018, background): “[33], as well as the contemporary works of Kondor [34, 35], Hirn [36], and Mallat [37].”
Machine Learning a General-Purpose Interatomic Potential for Silicon (2018, unknown): “Using a multiscale description to capture these is an alternative approach [225].”
Solid Harmonic Wavelet Scattering: Predicting Quantum Molecular Energy from Invariant Descriptors of 3D Electronic Densities (2017, background): “A rotation invariant scattering transform has been proposed to regress quantum energies of planar molecules [9].”
Solid Harmonic Wavelet Scattering for Predictions of Molecule Properties (2018, methodology): “The power q = 1 scales linearly with the number of electronic particles represented by the density ρ , while q = 2 encodes pairwise interactions, which are related to electrostatic Coulomb interactions in 26 .”