# Wavelet Scattering Regression of Quantum Chemical Energies

arXiv: https://arxiv.org/abs/1605.04654 · HTML: https://mlsanity.com/paper/1605.04654/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2016.

## Built on by (most cited first, 8 of 8)

- [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)
- [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)
- [Accurate Prediction of Free Solvation Energy of Organic Molecules via Graph Attention Network and Message Passing Neural Network from Pairwise Atomistic Interactions](https://mlsanity.com/paper/2105.02048/) (2021)
- [DeepChem Equivariant: SE(3)-Equivariant Support in an Open-Source Molecular Machine Learning Library](https://mlsanity.com/paper/2510.16897/) (2025)
- [Bayesian Scattering: A Principled Baseline for Uncertainty on Image Data](https://mlsanity.com/paper/2603.20908/) (2026)

## Abstract (arXiv)

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.