Learning Droplet Wetting from Kinetic Theory: Lattice-Boltzmann-Driven Physics-Informed Neural Networks for Rough...

We introduce a lattice Boltzmann-driven Kinetic Physics-Informed Neural Network (K-PINN) for the predictive modeling of droplet dynamics on rough and structured surfaces by embedding the continuous, discrete-velocity Boltzmann-BGK equation, evaluated via automatic differentiation, as the physics-informed learning constraint, with discrete lattice Boltzmann method (LBM) simulations used solely to generate reference training data. Unlike conventional PINNs constrained by macroscopic continuum equations, the proposed framework operates at the mesoscopic kinetic level, preserving the essential physics of the lattice Boltzmann method, including Shan-Chen pseudopotential interactions, within a data-efficient neural framework. Across randomly rough substrates and periodically textured pillar arrays, the K-PINN accurately captures complex interfacial phenomena, including contact line pinning, anisotropic spreading, and capillary hysteresis, while maintaining physical consistency, including mass conservation to within 1.5%. A U-Net-based encoder-decoder architecture achieves a 50-75% reduction in prediction error relative to baseline networks, yielding near-perfect agreement with high-resolution lattice Boltzmann simulations (L2 ≈ 0.021-0.026, R2 ≈ 0.999). Robust convergence across diverse surface morphologies is achieved through curriculum-guided training and adaptive two-stage optimization. Once trained, the model delivers real-time predictions exceeding 104 evaluations per second, offering orders-of-magnitude acceleration over direct numerical simulation and enabling rapid parametric exploration and inverse surface design. By integrating a lattice Boltzmann-based kinetic approach with physics-informed learning, this work presents a mesoscopic physics-informed learning framework for the efficient and accurate prediction of multiphase droplet dynamics.