# Model-free quantification of completeness, uncertainties, and outliers in atomistic machine learning using information theory

arXiv: https://arxiv.org/abs/2404.12367 · HTML: https://mlsanity.com/paper/2404.12367/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 68 references that are in the map.
- First posted on arXiv 18 Apr 2024.

## Builds on (most cited first, 12 of 12)

- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles](https://mlsanity.com/paper/2305.01754/) (2023)
- [Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks](https://mlsanity.com/paper/2101.11588/) (2021)
- [Fast Uncertainty Estimates in Deep Learning Interatomic Potentials](https://mlsanity.com/paper/2211.09866/) (2022)
- [Automated discovery of a robust interatomic potential for aluminum](https://mlsanity.com/paper/2003.04934/) (2020)
- [Data efficiency and extrapolation trends in neural network interatomic potentials](https://mlsanity.com/paper/2302.05823/) (2023)
- [Inorganic synthesis-structure maps in zeolites with machine learning and crystallographic distances](https://mlsanity.com/paper/2307.10935/) (2023)

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

- [A Generative Diffusion Model for Amorphous Materials](https://mlsanity.com/paper/2507.05024/) (2025)
- [Unsupervised Atomic Data Mining via Multi-Kernel Graph Autoencoders for Machine Learning Force Fields](https://mlsanity.com/paper/2509.12358/) (2025)
- [Model Accuracy and Data Heterogeneity Shape Uncertainty Quantification in Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2508.03405/) (2025)
- [Maximizing Efficiency of Dataset Compression for Machine Learning Potentials With Information Theory](https://mlsanity.com/paper/2511.10561/) (2025)
- [Comparing the latent features of universal machine-learning interatomic potentials](https://mlsanity.com/paper/2512.05717/) (2025)
- [Contrast transfer functions help quantify neural network out-of-distribution generalization in HRTEM](https://mlsanity.com/paper/2512.09067/) (2025)
- [A Critical Examination of Active Learning Workflows in Materials Science](https://mlsanity.com/paper/2601.05946/) (2026)
- [Inverse design of bespoke interatomic potentials via active learning by information-matching](https://mlsanity.com/paper/2606.08148/) (2026)
- [Full-data accuracy with fewer labels for training and fine-tuning machine-learning force fields](https://mlsanity.com/paper/2607.14486/) (2026)
- [Misalignment of Low-Loss Regions Causes Grokking](https://mlsanity.com/paper/2610.00620/) (2026)

## Abstract (arXiv)

An accurate description of information is relevant for a range of problems in atomistic machine learning (ML), such as crafting training sets, performing uncertainty quantification (UQ), or extracting physical insights from large datasets. However, atomistic ML often relies on unsupervised learning or model predictions to analyze information contents from simulation or training data. Here, we introduce a theoretical framework that provides a rigorous, model-free tool to quantify information contents in atomistic simulations. We demonstrate that the information entropy of a distribution of atom-centered environments explains known heuristics in ML potential developments, from training set sizes to dataset optimality. Using this tool, we propose a model-free UQ method that reliably predicts epistemic uncertainty and detects out-of-distribution samples, including rare events in systems such as nucleation. This method provides a general tool for data-driven atomistic modeling and combines efforts in ML, simulations, and physical explainability.