A physics-informed neural network framework for multi-physics coupling microfluidic problems

Microfluidic systems have various scientific and industrial applications, providing a powerful means to manipulate fluids and particles on a small scale. As a crucial method to underlying mechanisms and guiding the design of microfluidic devices, traditional numerical methods such as the Finite Element Method (FEM) simulating microfluidic systems are limited by the computational cost and mesh generating of resolving the smaller spatiotemporal features. Recently, a Physics-informed neural network (PINN) was introduced as a powerful numerical tool for solving partial differential equations (PDEs). PINN simplifies discretizing computational domains, ensuring accurate results and significantly improving computational efficiency after training. Therefore, we propose a PINN-based modeling framework to solve the governing equations of electrokinetic microfluidic systems. The neural networks, designed to respect the governing physics law such as Nernst-Planck, Poisson, and Navier-Stokes (NPN) equations defined by PDEs, are trained to approximate accurate solutions without requiring any labeled data. Several typical electrokinetic problems, such as Electromigration, Ion concentration polarization (ICP), and Electroosmotic flow (EOF), were investigated in this study. Notably, the findings demonstrate the exceptional capacity of the PINN framework to deliver high-precision outcomes for highly coupled multi-physics problems, particularly highlighted by the EOF case. When using 20 x 10 sample points to train the model (the same mesh nodes used for FEM), the relative error of EOF velocity from the PINN is similar to 0.02 %, whereas the relative error of the FEM is similar to 1.23 %. In addition, PINNs demonstrate excellent interpolation capability, the relative error of the EOF velocity decreases slightly at the interpolation points compared to training points, approximately 0.0001 %. More importantly, in simulating strongly nonlinear problems such as the ICP case, PINNs exhibit a unique advantage as they can provide accurate solutions with sparse sample points, whereas FEM fails to produce correct physical results using the same mesh nodes. Although the training time for PINN (100-200 min) is higher than the FEM computational time, the ability of PINN to achieve high accuracy results on sparse sample points, strong capability to fit nonlinear problems highlights its potential for reducing computational resources. We also demonstrate the ability of PINN to solve inverse problems in microfluidic systems and use transfer learning to accelerate PINN training for various species parameter settings. The numerical results demonstrate that the PINN model shows promising advantages in achieving high-accuracy solutions, modeling strong nolinear problems, strong interpolation capability, and inferring unknown parameters in simulating multi-physics coupling microfluidic systems.