Hydrodynamic Memory Kernel Extraction of a Microfluidic Particle with Machine Learning Based Kernel Estimation

Abstract

The accurate simulation of Brownian particles in confined microfluidic environments requires resolving hydrodynamic memory effects, which introduce a nonlocal dependence between the particle’s velocity history and the instantaneous hydrodynamic force. This memory is captured by a convolution integral involving a memory kernel tensor extracted from direct numerical simulations (DNS). However, both DNS and the subsequent kernel optimization are computationally expensive, and the optimization can suffer from numerical artifacts that compromise physical realizability. In this work, we improved the existing kernel optimization framework by refining the simultaneous optimization of the full kernel tensor and implementing corrective measures that enhance accuracy for problematic cases where the original optimization produced erroneous results. Using these improvements, we perform DNS in two confined geometries at three confinement levels. Particle-wall distances are sampled to prioritize resolution of the variation of hydrodynamic memory near walls, edges, and corners. A comprehensive library of memory kernels was generated across 84 unique positions for the cube and 28 positions for the channel. Finally, we developed a machine learning surrogate model that predicts the memory kernel directly from the particle’s position relative to confining walls, bypassing the need for expensive DNS. The surrogate model was trained on the DNS-generated kernel library and demonstrates accurate prediction of particle dynamics at a fraction of the computational cost. A comparison between different models and hyperparameter search led to Long-short term memory unit being the most accurate. This approach provides a pathway toward efficient, physically consistent simulations of particle motion in geometrically complex microfluidic systems.