MatRIS: Toward Reliable and Efficient Pretrained Machine Learning Interaction Potentials

TL;DR

This work presents MatRIS, an invariant MLIP that introduces attention-based modeling of three-body interactions and indicates that its carefully designed invariant models can match or exceed the accuracy of equivariant models at a fraction of the cost.

Abstract

Foundation MLIPs demonstrate broad applicability across diverse material systems and have emerged as a powerful and transformative paradigm in chemical and computational materials science. Equivariant MLIPs achieve state-of-the-art accuracy in a wide range of benchmarks by incorporating equivariant inductive bias. However, the reliance on tensor products and high-degree representations makes them computationally costly. This raises a fundamental question: as quantum mechanical-based datasets continue to expand, can we develop a more compact model to thoroughly exploit high-dimensional atomic interactions? In this work, we present MatRIS (\textbf{Mat}erials \textbf{R}epresentation and \textbf{I}nteraction \textbf{S}imulation), an invariant MLIP that introduces attention-based modeling of three-body interactions. MatRIS leverages a novel separable attention mechanism with linear complexity $O(N)$, enabling both scalability and expressiveness. MatRIS delivers accuracy comparable to that of leading equivariant models on a wide range of popular benchmarks (Matbench-Discovery, MatPES, MDR phonon, Molecular dataset, etc). Taking Matbench-Discovery as an example, MatRIS achieves an F1 score of up to 0.847 and attains comparable accuracy at a lower training cost. The work indicates that our carefully designed invariant models can match or exceed the accuracy of equivariant models at a fraction of the cost, shedding light on the development of accurate and efficient MLIPs.

Figures (9)

• Figure 1: Trade-offs between training time and F1 score of foundation MLIPs. Training times for eSEN and eqV2 are estimated on Nvidia-A100. Nequix koker2025trainingfoundationmodelmaterials was trained on JAX; all others on PyTorch. Larger marks indicate models with more parameters.
• Figure 2: Conversion from an Atom Graph to a Line Graph.
• Figure 3: Overview of MatRIS. The model architecture (a) consists of feature embedding (e), graph attention (b), refinement (c), and a readout block(f).
• Figure 4: (a) Summary of model performance on the MDR phonon benchmark. The evaluation metrics include $\omega_{max}$ (K), $S$ (J/K/mol), $F$ (kJ/mol), and $C_V$ (J/K/mol), where the reported values represent the MAE between the model predictions and the DFT results. (b) Predicted phonon dispersion obtained using MatRIS with a 0.01Å displacement. The DFT results are taken from the phononDB dataset.
• Figure 5: Efficiency-accuracy comparison.