# Mixture of neural operator experts for learning boundary conditions and model selection

arXiv: https://arxiv.org/abs/2502.04562 · HTML: https://mlsanity.com/paper/2502.04562/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- First posted on arXiv 6 Feb 2025.

## Placed in

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

## Built on by (most cited first, 3 of 3)

- [Generalized Neural Operator for Parametric and Boundary-Value Problems](https://mlsanity.com/paper/2607.21932/) (2026)
- [SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion](https://mlsanity.com/paper/2604.07421/) (2026)
- [Physics-Refined Spatiotemporal Forecasting on Open-Boundary Hydrologic Graphs](https://mlsanity.com/paper/2610.01765/) (2026)

## Abstract (arXiv)

While Fourier-based neural operators are best suited to learning mappings between functions on periodic domains, several works have introduced techniques for incorporating non trivial boundary conditions. However, all previously introduced methods have restrictions that limit their applicability. In this work, we introduce an alternative approach to imposing boundary conditions inspired by volume penalization from numerical methods and Mixture of Experts (MoE) from machine learning. By introducing competing experts, the approach additionally allows for model selection. To demonstrate the method, we combine a spatially conditioned MoE with the Fourier based, Modal Operator Regression for Physics (MOR-Physics) neural operator and recover a nonlinear operator on a disk and quarter disk. Next, we extract a large eddy simulation (LES) model from direct numerical simulation of channel flow and show the domain decomposition provided by our approach. Finally, we train our LES model with Bayesian variational inference and obtain posterior predictive samples of flow far past the DNS simulation time horizon.