Abstract: Turbulence, a complex multi-scale phenomenon inherent in fluid flow systems, presents critical challenges and opportunities for understanding physical mechanisms across scientific and engineering domains. Although high-resolution (HR) turbulence data remain indispensable for advancing both theoretical insights and engineering solutions, their acquisition is severely limited by prohibitively high computational costs. While deep learning architectures show transformative potential in reconstructing high-fidelity flow representations from sparse measurements, current methodologies suffer from two inherent constraints: strict reliance on perfectly paired training data and inability to perform multi-scale reconstruction within a unified framework. To address these challenges, we propose HADF, a hash-adaptive dynamic fusion implicit network for turbulence reconstruction. Specifically, we develop a low-resolution (LR) consistency loss that facilitates effective model training under conditions of missing paired data, eliminating the conventional requirement for fully matched LR and HR datasets. We further employ hash-adaptive spatial encoding and dynamic feature fusion to extract turbulence features, mapping them with implicit neural representations for reconstruction at arbitrary resolutions. Experimental results demonstrate that HADF achieves superior performance in global reconstruction accuracy and local physical properties compared to state-of-the-art models. It precisely recovers fine turbulence details for partially unpaired data conditions and diverse resolutions by training only once while maintaining robustness against noise.

Key words: Turbulence reconstruction; Deep learning; Unpaired data; Low-resolution consistency loss; Hash-adaptive spatial encoding; Dynamic feature fusion; Implicit neural representations

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