# Scattering Spectra Models for Physics

arXiv: https://arxiv.org/abs/2306.17210 · HTML: https://mlsanity.com/paper/2306.17210/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 74 references that are in the map.
- First posted on arXiv 29 Jun 2023.

## Builds on (most cited first, 6 of 6)

- [Adaptive wavelet distillation from neural networks through interpretations](https://mlsanity.com/paper/2107.09145/) (2021)
- [Maximum Entropy Models from Phase Harmonic Covariances](https://mlsanity.com/paper/1911.10017/) (2019)
- [Non-Gaussian information from weak lensing data via deep learning](https://mlsanity.com/paper/1802.01212/) (2018)
- [Scale Dependencies and Self-Similar Models with Wavelet Scattering Spectra](https://mlsanity.com/paper/2204.10177/) (2022)
- [How to quantify fields or textures? A guide to the scattering transform](https://mlsanity.com/paper/2112.01288/) (2021)
- [Unearthing InSights into Mars: Unsupervised Source Separation with Limited Data](https://mlsanity.com/paper/2301.11981/) (2023)

## Built on by (most cited first, 10 of 10)

- [Wavelet Diffusion Neural Operator](https://mlsanity.com/paper/2412.04833/) (2024)
- [Hierarchic Flows to Estimate and Sample High-dimensional Probabilities](https://mlsanity.com/paper/2405.03468/) (2024)
- [One Wave To Explain Them All: A Unifying Perspective On Feature Attribution](https://mlsanity.com/paper/2410.01482/) (2024)
- [Separation Capacity of Scattering Networks](https://mlsanity.com/paper/2606.30822/) (2026)
- [MGD: Moment Guided Diffusion for Maximum Entropy Generation](https://mlsanity.com/paper/2602.17211/) (2026)
- [Competing with AI Scientists: Agent-Driven Approach to Astrophysics Research](https://mlsanity.com/paper/2604.09621/) (2026)
- [Mean-Field Microcanonical Gradient Descent](https://mlsanity.com/paper/2403.08362/) (2024)
- [Denoising: from classical methods to deep CNNs](https://mlsanity.com/paper/2404.16617/) (2024)
- [Neural Contrast Expansion for Explainable Structure-Property Prediction and Random Microstructure Design](https://mlsanity.com/paper/2508.16857/) (2025)
- [Generative Modeling via Kernelized Stochastic Interpolants](https://mlsanity.com/paper/2602.20070/) (2026)

## Abstract (arXiv)

Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a point-wise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multi-scale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to 4th order. These scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.