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

Implicit neural representation (INR) has now been thrust into the limelight with its flexibility in high-fidelity flow field reconstruction tasks. However, the lack of standard benchmarking datasets and the grid independence assumption for INR-based methods hinder progress and adoption in real-world simulation scenarios. Moreover, naive adoptions of existing INR frameworks suffer from limited accuracy in capturing fine-scale structures and spatiotemporal dynamics. Tacking these issues, we first introduce HFR-Beach, 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, to enrich the flow fields by concurrently enhancing numerical-precision and grid-resolution. Specifically, PEINR is mainly composed of physical encoding and transformer-based spatiotemporal fuser (TransSTF). Physical encoding decouples temporal and spatial components, employing Gaussian coordinate encoding and localized encoding techniques to capture the nonlinear characteristics of spatiotemporal dynamics and the stencil discretization of spatial dimensions, respectively. TransSTF fuses both spatial and temporal information via transformer for capturing long-range temporal dependencies. Qualitative and quantitative experiments and demonstrate that PEINR outperforms state-of-the-art INR-based methods in reconstruction quality.

High-fidelity simulations of fluid dynamics are essential for understanding complex physical phenomena in science and engineering. A new class of machine learning models, called Implicit Neural Representations (INRs), can reconstruct these fluid flow fields with impressive detail. However, INR models face major limitations: they often struggle with real-world data, which is imbalanced across space and time, and there is currently no standardized dataset to benchmark progress in this field.To address these challenges, our work contributes two major innovations. First, we release HFR-Bench, a large-scale public dataset containing over 33,000 high-resolution 2D and 3D flow fields. This gives researchers a shared foundation to compare their models and spur further advancements. Second, we introduce PEINR, a novel physics-informed INR model. It encodes spatial and temporal information using techniques inspired by physics and uses transformer-based neural networks to better capture dynamic flow behaviors over time.Our approach leads to significantly better reconstructions than existing methods, particularly in challenging scenarios with complex, time-varying flows. This work sets the stage for more reliable and physically grounded fluid simulations powered by AI.