PEINR: A Physics-enhanced Implicit Neural Representation for High-Fidelity Flow Field Reconstruction

Implicit neural representation (INR) excels in high-fidelity flow field reconstruction through flexible enhancement of numerical precision and grid resolution. However, its broader adoption faces two barriers: the absence of standardized benchmarks for flow reconstruction tasks, and the impractical grid independence assumption in real-world simulations. Current INR frameworks also struggle to resolve fine-scale structures and spatiotemporal dynamics, particularly under severe temporal-spatial data imbalance, where temporal sensitivity degrades significantly. Tacking these issues, we first introduce HFR-Bench, a 5.4 TB public large-scale CFD dataset with 33,600 unsteady 2D and 3D vector fields for reconstructing high-fidelity flow fields. We further present PEINR, a physics-enhanced INR framework, which is mainly composed of physical encoding and transformer-based spatiotemporal fuser (TransSTF). Physical encoding decouples temporal and spatial components through Gaussian temporal encoding, which can enhance highdimensional features and nonlinear characteristics in temporal information, and localized spatial encoding, which can implement stencil-based discretization in the spatial dimension. TransSTF fuses both spatial and temporal information via transformer for capturing long-range temporal dependencies. Qualitative and quantitative experiments demonstrate that PEINR outperforms stateof-the-art INR-based methods in reconstruction quality. Code and dataset are released here.