Compositional Neural Operators for Multi-Dimensional Fluid Dynamics

Hamda Hmida; Hsiu-Wen Chang; Youssef Mesri

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arXiv · 2605.11691

Compositional Neural Operators for Multi-Dimensional Fluid Dynamics

Hamda Hmida·Hsiu-Wen Chang·Youssef Mesri

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Abstract

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim to provide universal surrogates, typical encoding-decoding approaches suffer from high pretraining costs and limited interpretability. In this paper, we propose Compositional Neural Operators (CompNO) for 2D systems, a framework that decomposes complex PDEs into a library of Foundation Blocks. Each block is a specialized Neural Operator pretrained on elementary physics. This modular library contains convection, diffusion, and nonlinear convection blocks as well as a Poisson Solver, enabling the framework to address the pressure-velocity coupling. These experts are assembled via an Adaptation Block featuring an Aggregator. This aggregator learns nonlinear interactions by minimizing data loss and physics-based residuals driven from governing equations. The proposed approach has been evaluated on the Convection-Diffusion equation, the Burgers' equation, and the Incompressible Navier-Stokes equation. Our results demonstrate that learning from elementary operators significantly improves adaptability, enhances model interpretability and facilitates the reuse of pretrained blocks when adapting to new physical systems.

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BibTeX RIS

Hamda Hmida, Hsiu-Wen Chang, Youssef Mesri. 2026-05-12. Compositional Neural Operators for Multi-Dimensional Fluid Dynamics. https://arxiv.org/abs/2605.11691

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