Enhanced Representation-Based Sampling for the Efficient Generation of Datasets for Machine-Learned Interatomic Potentials

TL;DR

ERBS addresses the need for diverse, informative training data for MLIPs by deriving low-dimensional collective variables from the mean descriptor via PCA and applying an OPES-explore bias to promote exploration along high-variance directions of descriptor space. It is paired with Gaussian Moment Neural Networks and shallow ensembles to deliver accurate predictions with uncertainty estimates, enabling efficient active learning. Across alanine dipeptide, liquid water, and BMIM+BF4-, ERBS improves FES reconstruction, accelerates diffusion-coefficient convergence, and outperforms uncertainty-driven sampling in challenging liquids. The framework is representation-agnostic and scalable, offering a practical path to rapid dataset construction for MLIPs and potential extensions to atomistic foundation models and solid-state systems.

Abstract

In this work, we present Enhanced Representation-Based Sampling (ERBS), a novel enhanced sampling method designed to generate structurally diverse training datasets for machine-learned interatomic potentials. ERBS automatically identifies collective variables by dimensionality reduction of atomic descriptors and applies a bias potential inspired by the On-the-Fly Probability Enhanced Sampling framework. We highlight the ability of Gaussian moment descriptors to capture collective molecular motions and explore the impact of biasing parameters using alanine dipeptide as a benchmark system. We show that free energy surfaces can be reconstructed with high fidelity using only short biased trajectories as training data. Further, we apply the method to the iterative construction of a liquid water dataset and compare the quality of simulated self-diffusion coefficients for models trained with molecular dynamics and ERBS data. Further, we active-learn models for liquid water with and without enhanced sampling and compare the quality of simulated self-diffusion coefficients. The self-diffusion coefficients closely match those simulated with a reference model at a significantly reduced dataset size. Finally, we compare the sampling behaviour of enhanced sampling methods by benchmarking the mean squared displacements of \ce{BMIM+BF4-} trajectories simulated with uncertainty-driven dynamics and ERBS and find that the latter significantly increases the exploration of configurational space.

Figures (14)

• Figure 1: (a) Illustration of an active learning cycle: Starting from seed data, models are iteratively trained and used to sample candidate configurations. From these candidates, the most informative ones are selected for DFT calculations. (b) Sampling stability improves and predicted uncertainties decrease over active learning iterations. (c) Workflow for constructing the ERBS potential: high-dimensional atomic descriptors $\mathbf{s'}$ are aggregated and reduced to collective variables $\mathbf{s}$ via dimensionality reduction. The bias potential flattens the sampled distribution $P$.
• Figure 2: a--c) Coverage vs parameter choices, d) $\Phi-\Psi$-space coverage of alanine dipeptide over time using molecular dynamics and the enhanced sampling method.
• Figure 3: Cross-validation of force MAEs. The x-axis indicates the training dataset used to generate each model. The colored bars within each group represent the model's performance on the four distinct validation datasets, as defined in the legend.
• Figure 4: (a) Free energy surface (FES) of alanine dipeptide computed with the reference force field. (b–d) Signed errors ($\Delta$FES = FES$_{\text{MLIP}}$ - FES$_{\text{Reference}}$) between the reference and the FES computed with models trained on data from (b) MD-1200 K, (c) ERBS A, and (d) ERBS B. Blue regions indicate lower predicted free energies relative to the reference, while red regions indicate overestimation. The red cross and green stars indicate the location of the Global free energy minimum of the reference force field and trained MLIPs, respectively.
• Figure 5: a) Force mean absolute errors with respect to the literature water dataset across active learning iterations for the models created with MD and ERBS-based active learning. b) Diffusion coefficients of water simulated using models from successive active learning iterations, compared to the value obtained with the model trained on the literature dataset.