Extraction of height-averaged pulsatile flow velocity within hydrogel matrix in a shallow microfluidic channel using a combination of physics-informed neural network and solute dispersion theory

Accurate characterization of flow velocity in shallow microfluidic channels containing porous structures is fundamental to modeling mass transport and dispersion phenomena in micro-scale systems. However, traditional experimental velocimetry techniques are often limited by high costs and operational complexity, while conventional physics-informed neural network (PINN) faces significant computational challenges when solving high-dimensional inverse problems. In this study, we propose an efficient velocity extraction framework combining mathematical dimension reduction with deep learning. Utilizing the central manifold theorem, we derive a one-dimensional approximate transport equation to simplify the high-dimensional convection–diffusion process. This reduced physical law, coupled with a Brinkman-based pulsatile flow model, is embedded into a PINN loss function to minimize sampling requirements and accelerate convergence. Validated against two-dimensional finite difference simulations, the model demonstrates high accuracy and robustness. This integration of the central manifold method and PINN offers a computationally efficient tool for flow velocity reconstruction and transport analysis in complex microfluidic environments.