Electrochemical Interfaces at Constant Potential: Data-Efficient Transfer Learning for Machine-Learning-Based Molecular Dynamics

TL;DR

The paper tackles the high cost of simulating electrified metal/water interfaces at constant potential with explicit solvent. It introduces TRECI, a transfer-learning-based, data-efficient workflow that builds ML-FFs capable of ab initio accuracy in electronically grand-canonical MD by combining general-purpose and domain-specific descriptors with multi-head readouts and DEAL-based active learning. TRECI enables MD across a wide potential range $V$ (e.g., $-0.5\, ext{V}$ to $-2.0\, ext{V}$ vs SHE) using around 1000 labelled configurations and allows the use of high-level functionals (e.g., meta-GGA SCAN) and rigorous electrification schemes (double-reference). Applied to Cu(111)/water, TRECI uncovers bias-dependent solvent restructuring, including formation of distinct interfacial regions and dipole reorientation, with new phenomena (region III) not accessible to conventional AIMD. The approach is modular and broadly applicable to diverse electrochemical interfaces, significantly reducing data and labelling costs for quantitative electrochemical modelling.

Abstract

Simulating electrified metal/water interfaces with explicit solvent under constant potential is essential for understanding electrochemical processes, yet remains prohibitively expensive with ab initio methods. We present TRECI, a data-efficient workflow for constructing machine learning force-fields (ML-FFs) that achieve ab initio-level accuracy in electronically grand-canonical molecular dynamics. By leveraging transfer learning from general-purpose and domain-specific models, TRECI enables stable and accurate simulations across a wide potential range using a reduced number of reference configurations. This efficiency allows the use of high-level meta-GGA functionals and rigorous surface-electrification schemes. Applied to Cu(111)/water, models trained on just one thousand configurations yield accurate molecular dynamics simulations, capturing bias-dependent solvent restructuring effects not previously reported. TRECI offers a general strategy for characterising diverse materials and interfacial chemistries, significantly lowering the cost of realistic constant-potential simulations and expanding access to quantitative electrochemical modelling.

Figures (8)

• Figure 1: General scheme of TRECI for electronically grand-canonical machine learning force-fields: the pillars of the methods are a high-quality dataset at multiple applied bias values, a data-efficient ML architecture via transfer learning and an effective active learning approach.
• Figure 2: TRECI strategy for the training of the constant potential ML-FFs via transfer learning: the node features of a pre-trained general-purpose or domain-specific GNNs are used as descriptors for a multi-head Franken model. Each readout block implements a large-scale kernel regression model targeting an applied bias value. Kernel functions are approximated by means of Random Fourier Features (RF)
• Figure 3: Evolution of the learning process for TRECI models at representative target biases during the active learning. (a) Stability range of the different descriptors (Franken-MP0 vs Franken-PZC ): coloured bars show the iterations at which the ML-FFs are stable; dark colours identify the descriptors employed for the sampling at the different iterations. (b) Force RMSE for Franken-MP0 and Franken-PZC . Solid lines identify the descriptors employed for the sampling. The accuracy is not reported when the models are not stable. (c) Peak value of the oxygen density in the different interfacial regions.
• Figure 4: Properties of interfacial water. (a) Density profile in the solvent region vs the distance z with respect to the surface zsurf, at different values of external potential. Arrows emphasise trends moving towards more negative potentials. (b) Summary of the oxygen peak density height in the interfacial regions vs the applied potential. VDOS spectra for hydrogen atoms in region I (c) and region II (d). From low to high frequencies, it is possible to identify the peaks associated with the H-bond bending ($\approx$ 40 $\div$ 50 cm-1), the libration (150 $\div$ 700 cm-1), the H-O-H bending ($\approx$ 1200 cm-1), the O-H symmetric and asymmetric stretching (2300 $\div$ 2800 cm-1) le_theoretical_2018jin_temperature_2024. Spectra are computed using the deuterium mass for the hydrogen species. Frames of the MD trajectory in which specific molecules are emphasised to show the typical water orientation in regions I and II at PZC (e) and at $-2.00$ V vs SHE (f). O and H atoms of emphasised molecules are depicted in red and white, respectively.
• Figure S1: Comparison of the RMSE error on force prediction at V = -0.50 V and -2.00 vs SHE, using different descriptors (Franken-MP0 vs Franken-PZC) for different training set sizes and numbers of random features.