# Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials

arXiv: https://arxiv.org/abs/2606.04100 · HTML: https://mlsanity.com/paper/2606.04100/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 65 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 29 of 29)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019)
- [SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials](https://mlsanity.com/paper/2209.10702/) (2022)
- [Isambard-AI: a leadership class supercomputer optimised specifically for Artificial Intelligence](https://mlsanity.com/paper/2410.11199/) (2024)
- [A Stein variational Newton method](https://mlsanity.com/paper/1806.03085/) (2018)
- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [Support points](https://mlsanity.com/paper/1609.01811/) (2016)
- [Stein Variational Gradient Descent With Matrix-Valued Kernels](https://mlsanity.com/paper/1910.12794/) (2019)
- [A Coreset Selection of Coreset Selection Literature: Introduction and Recent Advances](https://mlsanity.com/paper/2505.17799/) (2025)
- [Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks](https://mlsanity.com/paper/2101.11588/) (2021)
- [Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models](https://mlsanity.com/paper/2506.17139/) (2025)
- [Stochastic Gradient MCMC with Repulsive Forces](https://mlsanity.com/paper/1812.00071/) (2018)
- [Bayesian experimental design using regularized determinantal point processes](https://mlsanity.com/paper/1906.04133/) (2019)
- [Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials](https://mlsanity.com/paper/2312.01416/) (2023)
- [Compress Then Test: Powerful Kernel Testing in Near-linear Time](https://mlsanity.com/paper/2301.05974/) (2023)
- [A stochastic version of Stein Variational Gradient Descent for efficient sampling](https://mlsanity.com/paper/1902.03394/) (2019)
- [Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materials](https://mlsanity.com/paper/2410.01464/) (2024)
- [Stein Self-Repulsive Dynamics: Benefits From Past Samples](https://mlsanity.com/paper/2002.09070/) (2020)
- [Multilevel Stein variational gradient descent with applications to Bayesian inverse problems](https://mlsanity.com/paper/2104.01945/) (2021)
- [Projected support points: a new method for high-dimensional data reduction](https://mlsanity.com/paper/1708.06897/) (2017)
- [Metadynamics for Training Neural Network Model Chemistries: a Competitive Assessment](https://mlsanity.com/paper/1712.07240/) (2017)
- [Data Curation for Machine Learning Interatomic Potentials by Determinantal Point Processes](https://mlsanity.com/paper/2603.22160/) (2026)
- [ESCORT: Efficient Stein-variational and Sliced Consistency-Optimized Temporal Belief Representation for POMDPs](https://mlsanity.com/paper/2510.21107/) (2025)

## Abstract (arXiv)

Machine learning interatomic potentials (MLIPs) enable efficient and accurate atomistic simulations but depend critically on the quality and diversity of the training data. We introduce Stein kernelized molecular dynamics (SKMD), an enhanced sampling method that uses interacting particle dynamics to acquire informative training configurations for the active learning and fine-tuning of MLIPs. SKMD corresponds to a stochastic variant of Stein variational gradient descent that is adapted for molecular dynamics by incorporating asynchronous particle updates and a kernel of global atomic descriptors, which provides a symmetry-aware measure of configurational similarity. Unlike other enhanced samplers used in molecular dynamics, SKMD preserves the Boltzmann distribution as the asymptotic distribution of the dynamics. This property enforces a balance between the exploration of diverse configurations and attraction toward high-probability regions of the energy landscape. We further propose an approach to efficient online data acquisition using an adaptive stopping criterion that selects non-redundant training data over the course of simulation. We demonstrate SKMD for the active learning of a neural network model of the M"uller-Brown potential and the fine-tuning of a MACE interatomic potential for alanine dipeptide. Compared to active learning baselines, our method achieves higher model accuracy in fewer training iterations with the same number of acquired training samples.