A Materials Foundation Model via Hybrid Invariant-Equivariant Architectures

Materials foundation models can predict energy, force, and stress of materials and enable a wide range of downstream discovery tasks. A key design choice involves the trade-off between invariant and equivariant architectures. Invariant models offer computational efficiency but may not perform well 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 foundation model that integrates both invariant and equivariant message passing layers. HIENet is designed to achieve superior 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.

@article{yan2025_2503.05771,
  title={ A Materials Foundation Model via Hybrid Invariant-Equivariant Architectures },
  author={ Keqiang Yan and Montgomery Bohde and Andrii Kryvenko and Ziyu Xiang and Kaiji Zhao and Siya Zhu and Saagar Kolachina and Doğuhan Sarıtürk and Jianwen Xie and Raymundo Arroyave and Xiaoning Qian and Xiaofeng Qian and Shuiwang Ji },
  journal={arXiv preprint arXiv:2503.05771},
  year={ 2025 }
}