Lattice-Boltzmann-Driven Physics-Informed Neural Networks for Droplet Wettability on Rough Surfaces

TL;DR

This paper presents a kinetic physics-informed neural network based on Lattice-Boltzmann physics for accurate, real-time modeling of droplet behavior on complex structured surfaces, outperforming traditional methods.

Contribution

The authors develop a mesoscopic K-PINN framework that incorporates Lattice-Boltzmann physics, enabling fast, physically consistent predictions of droplet dynamics on rough and patterned surfaces.

Findings

Achieves mass conservation within 1.5%

Reduces error by 50-75% compared to traditional neural networks

Attains near-perfect agreement with high-resolution simulations

Abstract

We introduce a Lattice-Boltzmann-driven kinetic physics-informed neural network (K-PINN) for predictive modeling of droplet dynamics on structured surfaces, in which the discrete Boltzmann-BGK equation is incorporated into the learning framework. Different from traditional PINNs that are restricted by macroscopic continuum equations, the K-PINN framework is built on the mesoscopic kinetic level, in which the essential Lattice-Boltzmann physics is preserved in the data-efficient neural network. The K-PINN has been successfully employed for modeling non-trivial droplet phenomena such as contact pinning, anisotropic spreading, and capillary hysteresis on substrates of different morphologies, ranging from random roughness to periodic pillar structures. Moreover, strict physical consistency, such as mass conservation within 1.5%, is ensured in the K-PINN framework. Furthermore, the U-Net-based encoder-decoder structure of the K-PINN results in a 50-75% reduction in error compared to traditional neural networks, achieving almost perfect agreement with high-resolution Lattice-Boltzmann simulations $L_2$ ~ 0.021-0.026, $R^2$ ~ 0.999. Robust convergence of the K-PINN to diverse surface morphologies is ensured through curriculum learning and adaptive two-phase optimization. Upon convergence, the K-PINN can perform real-time prediction with over $10^4$ evaluations per second. Through the combination of kinetic theory and physics-informed learning, this work establishes a new paradigm for fast, physically consistent modeling of multiphase flows on complex surfaces.