# COMPOL: A Unified Neural Operator Framework for Scalable Multi-Physics Simulations

arXiv: https://arxiv.org/abs/2501.17296 · HTML: https://mlsanity.com/paper/2501.17296/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 63 references that are in the map.
- First posted on arXiv 28 Jan 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [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)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Multiple Physics Pretraining for Physical Surrogate Models](https://mlsanity.com/paper/2310.02994/) (2023)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [Continuous PDE Dynamics Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2209.14855/) (2022)
- [How to Construct Deep Recurrent Neural Networks](https://mlsanity.com/paper/1312.6026/) (2013)
- [Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs](https://mlsanity.com/paper/2403.12553/) (2024)
- [CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations](https://mlsanity.com/paper/2206.02607/) (2022)
- [MAgNet: Mesh Agnostic Neural PDE Solver](https://mlsanity.com/paper/2210.05495/) (2022)
- [Deep Multi-Fidelity Active Learning of High-dimensional Outputs](https://mlsanity.com/paper/2012.00901/) (2020)
- [Multi-Resolution Active Learning of Fourier Neural Operators](https://mlsanity.com/paper/2309.16971/) (2023)
- [A Deep Learning-Accelerated Data Assimilation and Forecasting Workflow for Commercial-Scale Geologic Carbon Storage](https://mlsanity.com/paper/2105.09468/) (2021)
- [Coupled Multiwavelet Neural Operator Learning for Coupled Partial Differential Equations](https://mlsanity.com/paper/2303.02304/) (2023)
- [Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulations](https://mlsanity.com/paper/2104.03743/) (2021)
- [Learning time-dependent PDE solver using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2204.07651/) (2022)
- [Infinite-Fidelity Coregionalization for Physical Simulation](https://mlsanity.com/paper/2207.00678/) (2022)
- [Multi-fidelity Fourier Neural Operator for Fast Modeling of Large-Scale Geological Carbon Storage](https://mlsanity.com/paper/2308.09113/) (2023)

## Built on by (most cited first, 1 of 1)

- [Multi-Fidelity Flow Matching: Cascaded Refinement of PDE Solutions](https://mlsanity.com/paper/2605.16118/) (2026)

## Abstract (arXiv)

Multiphysics simulations play an essential role in accurately modeling complex interactions across diverse scientific and engineering domains Although neural operators especially the Fourier Neural Operator FNO have significantly improved computational efficiency they often fail to effectively capture intricate correlations inherent in coupled physical processes To address this limitation we introduce COMPOL a novel coupled multiphysics operator learning framework COMPOL extends conventional operator architectures by incorporating sophisticated recurrent and attentionbased aggregation mechanisms effectively modeling interdependencies among interacting physical processes within latent feature spaces Our approach is architectureagnostic and seamlessly integrates into various neural operator frameworks that involve latent space transformations Extensive experiments on diverse benchmarksincluding biological reactiondiffusion systems patternforming chemical reactions multiphase geological flows and thermohydromechanical processes demonstrate that COMPOL consistently achieves superior predictive accuracy compared to stateoftheart methods.