# Enhancing Reconstruction Capability of Wavelet Transform Amorphous Radial Distribution Function via Machine Learning Assisted Parameter Tuning

arXiv: https://arxiv.org/abs/2512.17245 · HTML: https://mlsanity.com/paper/2512.17245/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 37 references that are in the map.
- First posted on arXiv 19 Dec 2025.

## Builds on (most cited first, 1 of 1)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)

## Abstract (arXiv)

Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for analyzing amorphous structures, reliably reconstructing the first and second Radial Distribution Function (RDF) peaks and overall curve trends in both binary (Ge 0.25 Se 0.75) and ternary Ag x(Ge 0.25 Se 0.75)100-x (x = 5, 10, 15, 20, 25) systems. Despite these strengths, WT-RDF shows limitations in amplitude accuracy, which affects quantitative analyses such as coordination numbers. The shortcoming arises from improper parameter (a, b, Kf, C, and Lambda)) selection, as the parameters intrinsically represent atomic interactions within amorphous materials. This study addresses the issue by optimizing WT-RDF parameters using a machine learning approach via learnable parameter optimization, parameter bounding, and selective loss, producing the enhanced WT-RDF+ framework. WT-RDF+ improves the precision of peak reconstructions and outperforms benchmark Machine Learning (ML) models, including Radial Basis Function (RBF) and Long Short-term Memory (LSTM), when trained on only 25% of the binary dataset. Specifically, the machine learning benchmarks are defined as regressors with radial distance r input and G(r) output taken from Ab Initio Molecular Dynamics (AIMD) RDF simulation, not the reduced structure factor SR(q) to G(r) inversions. These results demonstrate that WT-RDF+ is a robust and reliable model for RDF reconstruction of Ge-Se and Ag-Ge-Se family.