Amalgamation of Physics-Informed Neural Network and LBM for the Prediction of Unsteady Fluid Flows in Fractal-Rough Microchannels

2026-04-03

AI Summary

This study addresses the high computational cost of simulating unsteady flows in microchannels with fractal rough walls by proposing a novel hybrid approach that integrates physics-informed neural networks (PINNs) with the lattice Boltzmann method (LBM). By leveraging sparse LBM data and enforcing the Navier–Stokes equations as physical constraints within the loss function, the method drastically reduces computational overhead. The fractal surface roughness is accurately represented using the Weierstrass–Mandelbrot function. Remarkably, the framework achieves high-fidelity flow field reconstruction using only 1/150 to 1/200 of the conventional data volume, demonstrating excellent accuracy and generalization across Reynolds numbers from 1 to 45 and roughness amplitudes ranging from 5 to 20 lattice units.

Abstract

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.

Problem

• unsteady fluid flow
• fractal-rough microchannels
• computational cost
• surface roughness
• micro-scale fluid transport

Innovation

• Physics-Informed Neural Network
• Lattice Boltzmann Method
• Fractal-Rough Microchannels
• Unsteady Fluid Flow
• Navier-Stokes Constraints