Physics-Informed Neural Networks for Enhanced Interface Preservation in Lattice Boltzmann Multiphase Simulations

TL;DR

This work tackles the diffusion of interfaces in multiphase LBM and develops a coupled PINN-LBM framework to preserve sharp interfaces while maintaining physical conservation laws. The approach uses a PINN to enforce data consistency, mass/momentum conservation, and a bespoke interface-preservation loss within a sequential coupling with the LBM, and validates on 2D droplet tests with new continuous interface metrics. Results show that PINN-LBM yields sharper interfaces, with $W_{eff}$ reduced by 17% (0.487 vs 0.588) and $E_{int}$ reduced by 35% (0.044 vs 0.068) relative to pure LBM, alongside improved visual coherence and reduced spurious currents. The method offers a practical path to accurate multiphase simulations on coarser grids or larger time steps, with transfer-learning potential and applicability to microfluidics, materials processing, and geophysical flows.

Abstract

This paper presents an improved approach for preserving sharp interfaces in multiphase Lattice Boltzmann Method (LBM) simulations using Physics-Informed Neural Networks (PINNs). Interface diffusion is a common challenge in multiphase LBM, leading to reduced accuracy in simulating phenomena where interfacial dynamics are critical. We propose a coupled PINN-LBM framework that maintains interface sharpness while preserving the physical accuracy of the simulation. Our approach is validated through droplet simulations, with quantitative metrics measuring interface width, maximum gradient, phase separation, effective interface width, and interface energy. The enhanced visualization techniques employed in this work clearly demonstrate the superior performance of PINN-LBM over standard LBM for multiphase simulations, particularly in maintaining well-defined interfaces throughout the simulation. We provide a comprehensive analysis of the results, showcasing how the neural network integration effectively counteracts numerical diffusion, while maintaining physical consistency with the underlying fluid dynamics.

Figures (6)

• Figure 1: Evolution of key interface metrics during the initial 500 LBM steps before PINN integration. The metrics include interface width (left), maximum gradient magnitude (middle), and phase separation (right).
• Figure 2: Performance metrics comparison: Pure LBM vs. PINN-LBM. The figure shows five key metrics: interface width, maximum gradient, phase separation, effective interface width, and interface energy. The results demonstrate PINN-LBM's superior interface preservation capabilities.
• Figure 3: Evolution of interface metrics throughout the simulation. The plots show how each metric changes over time for both pure LBM and PINN-LBM methods, demonstrating the stability and consistency of the PINN-LBM approach.
• Figure 4: Side-by-side comparison of pure LBM (top) and PINN-LBM (bottom). Density fields (left), velocity magnitude (middle), and gradient magnitude (right) clearly demonstrate PINN-LBM's superior interface preservation.
• Figure 5: Initial droplet state: density field (left), velocity magnitude (middle), and density gradient (right), serving as starting point for both simulation approaches.