# Global Universal Scaling and Ultra-Small Parameterization in Machine Learning Interatomic Potentials with Super-Linearity

arXiv: https://arxiv.org/abs/2502.07293 · HTML: https://mlsanity.com/paper/2502.07293/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 54 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 10 of 10)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics](https://mlsanity.com/paper/1712.03641/) (2017)
- [GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasets](https://mlsanity.com/paper/2204.02782/) (2022)
- [PIGNet: A physics-informed deep learning model toward generalized drug-target interaction predictions](https://mlsanity.com/paper/2008.12249/) (2020)
- [AdsorbML: A Leap in Efficiency for Adsorption Energy Calculations using Generalizable Machine Learning Potentials](https://mlsanity.com/paper/2211.16486/) (2022)
- [Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Science](https://mlsanity.com/paper/2305.14247/) (2023)
- [Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties](https://mlsanity.com/paper/2006.01247/) (2020)

## Abstract (arXiv)

Using machine learning (ML) to construct interatomic interactions and thus potential energy surface (PES) has become a common strategy for materials design and simulations. However, those current models of machine learning interatomic potential (MLIP) provide no relevant physical constrains, and thus may owe intrinsic out-of-domain difficulty which underlies the challenges of model generalizability and physical scalability. Here, by incorporating physics-informed Universal-Scaling law and nonlinearity-embedded interaction function, we develop a Super-linear MLIP with both Ultra-Small parameterization and greatly expanded expressive capability, named SUS2-MLIP. Due to the global scaling rooting in universal equation of state (UEOS), SUS2-MLIP not only has significantly-reduced parameters by decoupling the element space from coordinate space, but also naturally outcomes the out-of-domain difficulty and endows the potentials with inherent generalizability and scalability even with relatively small training dataset. The nonlinearity-enbeding transformation for interaction function expands the expressive capability and make the potentials super-linear. The SUS2-MLIP outperforms the state-of-the-art MLIP models with its exceptional computational efficiency especially for multiple-element materials and physical scalability in property prediction. This work not only presents a highly-efficient universal MLIP model but also sheds light on incorporating physical constraints into artificial-intelligence-aided materials simulation.