Deep multi-operator network for solving fluid mechanics problems

doi:10.1080/19942060.2026.2732842

Deep multi-operator network for solving fluid mechanics problems

2026-09-24

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DOI：10.1080/19942060.2026.2732842

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Deep learning has significantly reduced the computational cost associated with solving complex fluid dynamics problems. However, achieving robust generalization across complex geometries and varying boundary conditions remains a major challenge. To address this issue, this study proposes a novel neural operator architecture, termed DeepMONet. Unlike conventional single-operator architectures, DeepMONet represents different physical quantities using independent branch network functions and enables hierarchical learning of multi-physics field information through stacked operator layers, thereby enhancing its representation and generalization capabilities across complex geometries and diverse flow conditions. The model is evaluated on a series of benchmark problems involving different geometric complexities, boundary conditions, and flow characteristics. Across all test cases, the relative prediction error remains below 4.34%, while the standard deviation of the relative error does not exceed 1.53%. Moreover, DeepMONet maintains stable predictive performance across steady and transient flows, complex pipe networks, valves with varying opening degrees, and noisy training datasets, demonstrating strong generalization capability and broad applicability to flow prediction problems involving complex geometries and varying physical conditions.

Keywords:

Neural networks

complex boundaries

fluid mechanics

neural operators

Deep multi-operator network for solving fluid mechanics problems

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