# Magnetohydrodynamics with Physics Informed Neural Operators

arXiv: https://arxiv.org/abs/2302.08332 · HTML: https://mlsanity.com/paper/2302.08332/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 58 references that are in the map.
- First posted on arXiv 13 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Applications of physics informed neural operators](https://mlsanity.com/paper/2203.12634/) (2022)

## Built on by (most cited first, 7 of 7)

- [Neural Operators Learn the Local Physics of Magnetohydrodynamics](https://mlsanity.com/paper/2404.16015/) (2024)
- [MMET: A Multi-Input and Multi-Scale Transformer for Efficient PDEs Solving](https://mlsanity.com/paper/2506.17230/) (2025)
- [Transformers for dynamical systems learn transfer operators in-context](https://mlsanity.com/paper/2602.18679/) (2026)
- [Learning Galaxy Intrinsic Alignment Correlations](https://mlsanity.com/paper/2404.13702/) (2024)
- [Learning Neural Operator Surrogates for the Black Hole Accretion Code](https://mlsanity.com/paper/2604.25985/) (2026)
- [PHASE: Multi-Regime Modeling of Incompressible Magnetohydrodynamics](https://mlsanity.com/paper/2609.37609/) (2026)
- [Inferring physical fields in coupled systems with unknown parameters from incomplete observations using physics-constrained attentive neural operators](https://mlsanity.com/paper/2610.05723/) (2026)

## Abstract (arXiv)

The modeling of multi-scale and multi-physics complex systems typically involves the use of scientific software that can optimally leverage extreme scale computing. Despite major developments in recent years, these simulations continue to be computationally intensive and time consuming. Here we explore the use of AI to accelerate the modeling of complex systems at a fraction of the computational cost of classical methods, and present the first application of physics informed neural operators to model 2D incompressible magnetohydrodynamics simulations. Our AI models incorporate tensor Fourier neural operators as their backbone, which we implemented with the TensorLY package. Our results indicate that physics informed neural operators can accurately capture the physics of magnetohydrodynamics simulations that describe laminar flows with Reynolds numbers Re≤250. We also explore the applicability of our AI surrogates for turbulent flows, and discuss a variety of methodologies that may be incorporated in future work to create AI models that provide a computationally efficient and high fidelity description of magnetohydrodynamics simulations for a broad range of Reynolds numbers. The scientific software developed in this project is released with this manuscript.