# Solid Harmonic Wavelet Scattering for Predictions of Molecule Properties

arXiv: https://arxiv.org/abs/1805.00571 · HTML: https://mlsanity.com/paper/1805.00571/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2018.

## Built on by (most cited first, 12 of 12)

- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)
- [Parametric Scattering Networks](https://mlsanity.com/paper/2107.09539/) (2021)
- [Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms](https://mlsanity.com/paper/2104.11244/) (2021)
- [Tackling the Accuracy-Interpretability Trade-off in a Hierarchy of Machine Learning Models for the Prediction of Extreme Heatwaves](https://mlsanity.com/paper/2410.00984/) (2024)
- [Wavelets Beat Monkeys at Adversarial Robustness](https://mlsanity.com/paper/2304.09403/) (2023)
- [Energy Propagation in Scattering Convolution Networks Can Be Arbitrarily Slow](https://mlsanity.com/paper/2406.05121/) (2024)
- [The Maximal Overlap Discrete Wavelet Scattering Transform and Its Application in Classification Tasks](https://mlsanity.com/paper/2506.12039/) (2025)
- [Machine Learning Time Propagators for Time-Dependent Density Functional Theory Simulations](https://mlsanity.com/paper/2508.16554/) (2025)
- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [Bayesian Scattering: A Principled Baseline for Uncertainty on Image Data](https://mlsanity.com/paper/2603.20908/) (2026)
- [Notes on Fourier-Bessel wavelets](https://mlsanity.com/paper/2609.26537/) (2026)
- [Transversal Pooling Neural Networks](https://mlsanity.com/paper/2609.36237/) (2026)

## Abstract (arXiv)

We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which we compute invariant "solid harmonic scattering coefficients" that account for different types of interactions at different scales. Multi-linear regressions of various physical properties of molecules are computed from these invariant coefficients. Numerical experiments show that these regressions have near state of the art performance, even with relatively few training examples. Predictions over small sets of scattering coefficients can reach a DFT precision while being interpretable.