Minimalist machine-learned interatomic potentials can predict complex structural behaviors accurately

TL;DR

This work questions the prevailing view that reliable interatomic potentials require large, meticulously curated datasets. It tests minimalist MLIPs—kernel GAP-SOAP and E(3)-equivariant Allegro nets—trained with tiny, on-the-fly datasets derived from known phases, across BaTiO$_3$, BiFeO$_3$, PbZrO$_3$, and HfO$_2$. The models interpolate well to DFT data and, crucially, extrapolate to predict non-trivial phenomena such as vortex-antivortex textures, polarization switching paths, and near-degenerate low-energy polymorphs, often with quantitative accuracy. These findings suggest that simple, low-cost potentials can serve as effective tools for discovering and predicting emergent behavior in complex ferroelectrics, potentially broadening the practical scope of MLIPs and guiding future explorations in domain-generalization and interpretability.

Abstract

The past decade has witnessed a spectacular development of machine-learned interatomic potentials (MLIPs), to the extent that they are already the approach of choice for most atomistic simulation studies not requiring an explicit treatment of electrons. Typical MLIP usage guidelines emphasize the need for exhaustive training sets and warn against applying the models to situations not considered in the corresponding training space. This restricts the scope of MLIPs to interpolative calculations, essentially denying the possibility of using them to discover new phenomena in a serendipitous way. While there are reasons to be cautious, here we adopt a more sanguine view and challenge the predictive power of two representative and widely available MLIP approaches. We work with minimalist training sets that rely on little prior knowledge of the investigated materials. We show that the resulting models -- for which we adopt modest/default choices of the defining hyperparameters -- are very successful in predicting non-trivial structural effects (competing polymorphs, energy barriers for structural transformations, occurrence of non-trivial topologies) in a way that is qualitatively and quasi-quantitatively correct. Our results thus suggest an expanded scope of modern MLIP approaches, evidencing that somewhat trivial -- and easy to compute -- models can be an effective tool for the discovery of novel and complex physical phenomena.

Figures (5)

• Figure 1: Configuration space explored in the training of BiFeO$_3$ and HfO$_2$. The top panels show histograms for the main perovskite distortions: antiphase ($R$) and in-phase ($M$) octahedral tilts, as well as the polarization ($P$). The histograms are derived from the MD trajectories corresponding to the on-the-fly training starting from the ferroelectric ground state ($R3c$ polymorphs); they show that the material fluctuates around the ground state configuration, characterized by $R_{x}=R_{y}=R_{z}\neq 0$, $P_{x}=P_{y}=P_{z}\neq 0$, and $M_{x}=M_{y}=M_{z}=0$ (values indicated by dashed black lines). The bottom panel shows simulated diffraction patterns for configurations visited during the HfO$_2$ training, corresponding to the MD run that started from the tetragonal polymorph. By comparison with reference data (colored) for important HfO$_2$ phases, we can appreciate that the material evolved spontaneously toward low-symmetry polymorphs during the MD run, visiting the oIII ferroelectric phase in particular.
• Figure 2: Histograms for the errors made by our minimalist MLIPs in reproducing the DFT energies, forces, and stresses corresponding to structures typical of the explored configuration space (see text). Each distribution is normalized to 1. We use different bin sizes for clarity.
• Figure 3: Phonon bands for high-symmetry reference phases (see text). In black, solid lines, the DFT result. In red, long dashed lines, the VASP MLIP prediction. In green, short dashed lines the Allegro MLIP prediction.
• Figure 4: Vortex-antivortex electric dipole patterns mimicking experimental observations in BaTiO$_3$ moiré bilayers (see text). The arrows denote in-plane local polarization components (see text), while the color map corresponds to the out-of-plane component.
• Figure 5: Ferroelectric switching path for BiFeO$_3$ (see text). Shown are, as a function of structure along the path, the energy vs polarization (a), polarization components (b), and antiphase tilt components (c).