One of the biggest challenges in the optimization of micro-scale fluid transport phenomena is the prediction of unsteady fluid flow in the presence of rough channel walls. Even though the accuracy of available computational fluid dynamics (CFD) solvers such as the lattice Boltzmann method (LBM) is satisfactory, the computational cost of design exploration is very high due to the diverse range of geometries and flow regimes involved in microchannel flows. The present paper introduces a revolutionary concept of a ground-breaking physics-informed neural network (PINN) that utilizes sparse lattice Boltzmann data in combination with the Navier-Stokes equations for the prediction of unsteady fluid flow in fractal-rough microchannels. The roughness of the channel walls is represented by the Weierstrass-Mandelbrot function, considering the characteristics of the surface roughness in real-life problems. The constraints of the Navier-Stokes equations are incorporated in the loss function of the PINN concept for achieving accuracy at much lower computational costs of 150-200 times fewer data points. The validation of the accuracy of the reconstruction of the flow fields is carried out for different Reynolds numbers ranging from Re = 1 to 45 and different amplitude values of the rough channel walls ranging from 5 to 20 lattice units.

翻译：微尺度流体输运现象优化面临的最大挑战之一，是含粗糙壁面条件下非定常流体流动的预测。尽管现有计算流体动力学求解器（如格子玻尔兹曼方法）的精度令人满意，但微通道流动涉及的几何结构与流态多样性导致设计探索的计算成本极高。本文提出一种革命性的物理信息神经网络概念，该网络利用稀疏格子玻尔兹曼数据，结合纳维-斯托克斯方程，预测分形粗糙微通道中的非定常流体流动。通道壁面粗糙度采用考虑实际表面粗糙度特征的魏尔斯特拉斯-曼德尔布罗特函数描述。将纳维-斯托克斯方程的约束条件融入物理信息神经网络的损失函数中，通过减少150-200倍的数据点，在极低计算成本下实现高精度预测。针对雷诺数Re=1至45、粗糙壁面振幅5至20个格子单位的多种工况，验证了流场重构的准确性。