# AdaptNTK: Adaptive Uncertainty Quantification and Active Learning for Neural Network Potentials

arXiv: https://arxiv.org/abs/2609.00488 · HTML: https://mlsanity.com/paper/2609.00488/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 22 of 22)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Less is more: sampling chemical space with active learning](https://mlsanity.com/paper/1801.09319/) (2018)
- [A Framework and Benchmark for Deep Batch Active Learning for Regression](https://mlsanity.com/paper/2203.09410/) (2022)
- [Transition1x -- a Dataset for Building Generalizable Reactive Machine Learning Potentials](https://mlsanity.com/paper/2207.12858/) (2022)
- [Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles](https://mlsanity.com/paper/2305.01754/) (2023)
- [Fast Uncertainty Estimates in Deep Learning Interatomic Potentials](https://mlsanity.com/paper/2211.09866/) (2022)
- [Uncertainty Quantification with the Empirical Neural Tangent Kernel](https://mlsanity.com/paper/2502.02870/) (2025)
- [A prediction rigidity formalism for low-cost uncertainties in trained neural networks](https://mlsanity.com/paper/2403.02251/) (2024)
- [BLIPs: Bayesian Learned Interatomic Potentials](https://mlsanity.com/paper/2508.14022/) (2025)
- [LTAU-FF: Loss Trajectory Analysis for Uncertainty in Atomistic Force Fields](https://mlsanity.com/paper/2402.00853/) (2024)
- [Pretrained Model Representations as Acquisition Signals for Active Learning of MLIPs](https://mlsanity.com/paper/2605.03964/) (2026)
- [Force-Aware Neural Tangent Kernels for Scalable and Robust Active Learning of MLIPs](https://mlsanity.com/paper/2605.13788/) (2026)

## Abstract (arXiv)

Machine learning interatomic potentials bridge the gap between quantum chemical precision and classical computational speed, enabling molecular dynamics simulations with first-principles accuracy. Their reliability is often improved through active learning, which iteratively expands the training set by identifying uncertain, out-of-distribution configurations. Existing uncertainty-quantification methods often involve a trade-off between computational cost and reliability, and generally cannot account for redundancy as an acquisition batch is assembled. Here, we introduce AdaptNTK, a single-model framework that measures uncertainty as a regularized Mahalanobis distance in empirical neural tangent kernel (NTK) feature space. With the NTK features fixed during acquisition, the uncertainty depends on the acquired configurations but not their reference labels. This allows the uncertainty to be updated recursively after each selection without retraining, reducing redundancy within an acquisition batch. On held-out rMD17 data, AdaptNTK achieves the highest mean correlations with force errors (Spearman 0.68, Pearson 0.71) and matches a three-member ensemble in error retention. In active learning experiments, AdaptNTK achieves the lowest force errors across rMD17 and Transition-1X, with particularly strong performance on transition-state configurations in Transition-1X. AdaptNTK provides a 2.6-fold speedup per Transition-1X cycle relative to the ensemble, providing efficient single-model uncertainty estimation with sequential updates for data-efficient active learning.