Physics-Informed Neural Network Assisted Extraction of Height-averaged Pulsatile Flow Velocity From Scalar Signal Transport in a Shallow Microfluidic Channel

Accurate measurement of height-averaged flow velocity from scalar signal transport is important for shallow microfluidic velocimetry. Conventional scalar imaging velocimetry (SIV) is sensitive to scalar-field noise, while deep neural network-assisted SIV (DNN-SIV) requires extensive labeled velocity data and may exhibit limited generalizability to unseen flow conditions. This study aims to develop an unsupervised physics-informed framework for accurately reconstructing pulsatile flow velocity from concentration signals in a shallow microfluidic channel. Multiscale Perturbation-Enhanced Physics-Informed Neural Network (MPE-PINN) was proposed by decomposing the scalar transport process into steady and pulsatile components and embedding the corresponding perturbation-based governing equations into the loss function. This method was evaluated using numerically generated concentration fields under different scalar transport and flow conditions, and its performance was compared with a conventional PINN using mean absolute percentage error (MAPE), convergence behavior, and noise robustness. Results show that MPE-PINN maintains MAPEs below 1% over a broad operating range with concentration signal frequency fC ≤ 2 Hz and flow frequency fQ ≤ 1.6 Hz. The proposed method also shows improved robustness under noisy concentration fields and better preservation of pulsatile velocity features than the conventional PINN. These results demonstrate that MPE-PINN provides an accurate and robust unsupervised approach for pulsatile velocity extraction in shallow microfluidic channels, offering practical potential for microfluidic flow characterization and biomedical lab-on-a-chip applications.