# LTAU-FF: Loss Trajectory Analysis for Uncertainty in Atomistic Force Fields

arXiv: https://arxiv.org/abs/2402.00853 · HTML: https://mlsanity.com/paper/2402.00853/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 80 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 30 of 46)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Dataset Cartography: Mapping and Diagnosing Datasets with Training Dynamics](https://mlsanity.com/paper/2009.10795/) (2020)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Exploring the Limits of Out-of-Distribution Detection](https://mlsanity.com/paper/2106.03004/) (2021)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [Identifying Mislabeled Data using the Area Under the Margin Ranking](https://mlsanity.com/paper/2001.10528/) (2020)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learning](https://mlsanity.com/paper/2012.10630/) (2020)
- [Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel](https://mlsanity.com/paper/2010.15110/) (2020)
- [Contrastive Training for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2007.05566/) (2020)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Estimating Example Difficulty Using Variance of Gradients](https://mlsanity.com/paper/2008.11600/) (2020)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)

## Built on by (most cited first, 4 of 4)

- [Knowing when to trust machine-learned interatomic potentials](https://mlsanity.com/paper/2605.00640/) (2026)
- [A Systematic Survey and Benchmark of Deep Learning for Molecular Property Prediction in the Foundation Model Era](https://mlsanity.com/paper/2604.16586/) (2026)
- [AdaptNTK: Adaptive Uncertainty Quantification and Active Learning for Neural Network Potentials](https://mlsanity.com/paper/2609.00488/) (2026)
- [Risk-Controlled DFT Selection for Machine-Learned Interatomic Potentials](https://mlsanity.com/paper/2610.19630/) (2026)

## Abstract (arXiv)

Model ensembles are effective tools for estimating prediction uncertainty in deep learning atomistic force fields. However, their widespread adoption is hindered by high computational costs and overconfident error estimates. In this work, we address these challenges by leveraging distributions of per-sample errors obtained during training and employing a distance-based similarity search in the model latent space. Our method, which we call LTAU, efficiently estimates the full probability distribution function (PDF) of errors for any test point using the logged training errors, achieving speeds that are 2--3 orders of magnitudes faster than typical ensemble methods and allowing it to be used for tasks where training or evaluating multiple models would be infeasible. We apply LTAU towards estimating parametric uncertainty in atomistic force fields (LTAU-FF), demonstrating that its improved ensemble diversity produces well-calibrated confidence intervals and predicts errors that correlate strongly with the true errors for data near the training domain. Furthermore, we show that the errors predicted by LTAU-FF can be used in practical applications for detecting out-of-domain data, tuning model performance, and predicting failure during simulations. We believe that LTAU will be a valuable tool for uncertainty quantification (UQ) in atomistic force fields and is a promising method that should be further explored in other domains of machine learning.