Learning Materials Interatomic Potentials via Hybrid Invariant-Equivariant Architectures

ICLR 2026 Conference Submission19103 Authors

Keywords: Machine-Learning Interatomic Potentials, Materials, Equivariance, GNNs

Abstract: Machine learning interatomic potentials (MLIPs) can predict energy, force, and stress of materials and enable a wide range of downstream discovery tasks. A key design choice in MLIPs involves the trade-off between invariant and equivariant architectures. Invariant models offer computational efficiency but may not perform as well, especially when predicting high-order outputs. In contrast, equivariant models can capture high-order symmetries, but are computationally expensive. In this work, we propose HIENet, a hybrid invariant-equivariant materials interatomic potential model that integrates both invariant and equivariant message passing layers. Furthermore, we show that HIENet provably satisfies key physical constraints. HIENet achieves state-of-the-art performance with considerable computational speedups over prior models. Experimental results on both common benchmarks and downstream materials discovery tasks demonstrate the efficiency and effectiveness of HIENet. Finally, additional ablations further demonstrate that our hybrid invariant-equivariant approach scales well across model sizes and works with different equivariant model architectures, providing powerful insights into future MLIP designs.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 19103