# Mixture of Experts Framework in Machine Learning Interatomic Potentials for Atomistic Simulations

arXiv: https://arxiv.org/abs/2604.26143 · HTML: https://mlsanity.com/paper/2604.26143/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 8 of 8)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [High-performance training and inference for deep equivariant interatomic potentials](https://mlsanity.com/paper/2504.16068/) (2025)
- [Mixture of Diverse Size Experts](https://mlsanity.com/paper/2409.12210/) (2024)
- [Efficient and Accurate Spatial Mixing of Machine Learned Interatomic Potentials for Materials Science](https://mlsanity.com/paper/2502.19081/) (2025)
- [Mixture of experts architectures for machine learning interatomic potentials](https://mlsanity.com/paper/2603.07977/) (2026)

## Built on by (most cited first, 2 of 2)

- [Distilling latent electrostatics from foundation machine learning interatomic potentials](https://mlsanity.com/paper/2606.15001/) (2026)
- [BranchIP: Learning Adaptive Equivariant Computation for Interatomic Potentials](https://mlsanity.com/paper/2610.02013/) (2026)

## Abstract (arXiv)

First-principles atomistic simulations are essential for understanding complex material phenomena but are fundamentally limited by their computational cost. While Machine Learning Interatomic Potentials (MLIPs) have drastically improved cost for a given accuracy, their inference cost remains a bottleneck for massive systems or long timescales. To address this, we introduce a multifidelity "Mixture-of-Experts" framework based on the E(3)-equivariant Allegro architecture. Our method spatially partitions the simulation domain into a chemically complex region (e.g., reactive interfaces) and a simple region (e.g., bulk lattice), assigning models of varying capacity to each. Among the challenges in such static domain decomposition, the mechanical mismatch between models at the interface is particularly critical, as it can generate artificial stress fields and instability. We address this challenge with a co-training strategy in which the loss function includes agreement constraints -- penalties on per-atom energy and force discrepancies between models evaluated on shared bulk environments -- forcing the independent models to learn a consistent physical description of the bulk material. We validate this approach on a realistic Pt+CO catalytic system, demonstrating that the co-trained models maintain exact energy conservation, align their bulk mechanical response (e.g., equation of state and bulk modulus), and achieve predictive accuracy comparable to a full high-fidelity simulation at more than twice the computational speed.