Temporal and spatial flow field reconstruction from low-resolution PIV data and pressure probes using physics-informed neural networks

Abstract In this paper, we present an innovative approach using physics-informed neural networks to reconstruct high-frequency, full-field flows, including the pressure field, by integrating sparse, noisy, low-temporal-resolution particle image velocimetry (PIV) data with high-temporal-resolution pressure probe data. This method effectively leverages the spatial richness of PIV data and the temporal abundance of pressure probe data, offering a complementary spatial and temporal data fusion. The incorporation of physical laws via equation constraints enables the neural network to accurately learn and predict complex fluid dynamics, achieving comprehensive flow field reconstructions. Rigorous testing across various flow types—periodic, non-periodic, and complex—against critical parameters like sampling interval (SI), number of grid points per snapshot (NGPIS), and number of pressure probes (NPP) has demonstrated remarkable accuracy. The results show reconstruction errors for velocity components ( u, v ) and pressure ( p ) below 5% with sufficient data, and around 10% for v and p , and below 5% for u in data-limited scenarios. A case study with SI = 30, NGPIS = 2000, NPP = 5 underscores the enhanced robustness and accuracy of random sampling, especially under various noisy conditions. Thus, this approach shows significant potential for temporal and spatial reconstruction of flow fields.