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

2026-04-03

AI Summary

This work addresses the challenge of modeling complex wetting behaviors of droplets on rough or structured surfaces—such as contact line pinning, anisotropic spreading, and capillary hysteresis—by proposing a novel physics-informed neural network, termed K-PINN. The method uniquely embeds the mesoscale lattice Boltzmann BGK equation into a U-Net architecture, overcoming the limitation of conventional PINNs that rely solely on macroscopic continuum equations. Integrated with curriculum learning and an adaptive two-stage optimization strategy, K-PINN achieves highly efficient real-time predictions (>10⁴ simulations per second) while maintaining strong physical consistency: mass conservation error remains below 1.5%, L₂ error ranges from 0.021 to 0.026, and R² ≈ 0.999, representing a 50–75% reduction in error compared to traditional neural networks.

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 104 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.

Problem

• droplet wettability
• rough surfaces
• multiphase flows
• contact pinning
• capillary hysteresis

Innovation

• Lattice-Boltzmann
• Physics-Informed Neural Networks
• Kinetic Theory
• Multiphase Flow
• Wettability