Key Takeaways & Executive Findings
- •• Proposes HADF, a hash-adaptive dynamic fusion implicit network that reconstructs high-resolution turbulent flows from low-resolution inputs, addressing paired-data scarcity and multi-scale requirements. • Introduces a low-resolution consistency loss enabling training with partially unpaired datasets, eliminating the need for perfectly matched LR/HR pairs. • Employs hash-adaptive spatial encoding and dynamic feature fusion with implicit neural representations, allowing arbitrary-resolution reconstruction in a unified framework. • Demonstrates superior global and local reconstruction accuracy, robustness to noise, and one-time training for diverse resolutions, significantly reducing computational costs of turbulence data acquisition.
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.
1. Introduction
Turbulence is present in diverse engineering and natural systems, including aerospace propulsion, combustion engines, wind energy infrastructure, and atmospheric dynamics (Davidson, 2015). The inherent nonlinearity and multiscale characteristics of turbulent flows significantly influence system performance and stability (Wang et al., 2022). A comprehensive understanding of turbulent processes is therefore critical for optimizing system design and driving technological innovation. To resolve the intricate details of turbulence, acquiring high-resolution (HR) data has become imperative which provides the foundation for accurate characterization and modeling of these dynamic phenomena.
Turbulence data can be directly obtained through professional measurement techniques, such as tomography (Pareja et al., 2019) and laser diagnostics (Liu N and Ma, 2020). These approaches are constrained by instrument precision and experimental complexity, preventing them from fully capturing the HR details of turbulent flows (Liu HC et al., 2019). Alternatively, scientific computing approaches have been developed to simulate complex turbulent flows. These methods resolve the physical conservation equations over fine-grained computational grids to capture HR turbulence structures (Chen XH et al., 2021b). Nevertheless, they typically require complex mesh generation and expensive numerical iterations, leading to substantial computational costs (Cant et al., 2022; Chen XH et al., 2024).
Super-resolution reconstruction provides an optional strategy to address the limitations by recovering HR turbulent flows from low-resolution (LR) inputs (Fukami et al., 2023). Traditional methods, such as interpolation, are commonly employed to generate HR outputs by estimating intermediate values from surrounding LR data. However, because these methods rely only on simplistic data calculations without accounting for relevant physical constraints, they fail to reconstruct the nonlinear turbulent features governed by the Navier–Stokes equations. Recently, deep learning techniques have been employed to extract features from LR data and upsample these latent features to reconstruct HR flow fields (Fukami et al., 2019). By capturing the complex and nonlinear characteristics of turbulent flows, deep learning methods enable accurate reconstruction of intricate turbulence details.
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Yunfei LIU, Xinhai CHEN, Gen ZHANG, Qingyang ZHANG, Qinglin WANG, Jie LIU (2025). HADF: a hash-adaptive dual fusion implicit network for super-resolution of turbulent flows. Frontiers of Information Technology & Electronic Engineering. https://doi.org/10.1631/FITEE_2500419
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Frequently Asked Questions
What is the key innovation of the HADF network?
HADF is a hash-adaptive dynamic fusion implicit network that reconstructs high-resolution turbulent flows from low-resolution data. It removes the need for perfectly paired LR-HR training data by using a low-resolution consistency loss, and supports arbitrary resolution reconstruction through implicit neural representations.
How does HADF handle unpaired training data?
It introduces a low-resolution (LR) consistency loss that allows effective training even when only partially matched LR and HR datasets are available, eliminating the strict requirement for fully paired samples.
What are the main advantages of HADF compared to existing super-resolution models?
HADF achieves superior global reconstruction accuracy and preserves local physical properties, while maintaining robustness to noise. It also enables multi-scale reconstruction from a single trained model, reducing computational costs.
What is the significance of turbulence super-resolution in engineering?
High-resolution turbulence data are crucial for understanding fluid dynamics in aerospace, combustion, wind energy, and atmospheric systems. HADF provides a cost-effective way to obtain accurate HR flow fields from sparse LR measurements, supporting better system design and analysis.
Which applications can benefit from HADF?
Any field requiring high-fidelity turbulence data—such as aerospace propulsion, combustion engines, wind energy infrastructure, and atmospheric modeling—can benefit from HADF's efficient and robust super-resolution capabilities.
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