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

arXiv: https://arxiv.org/abs/2504.10539 · HTML: https://mlsanity.com/paper/2504.10539/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 13 Apr 2025.

## Builds on (most cited first, 6 of 6)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability](https://mlsanity.com/paper/1906.03663/) (2019)
- [Adaptive Optimization for Enhanced Efficiency in Large-Scale Language Model Training](https://mlsanity.com/paper/2412.04718/) (2024)

## Built on by (most cited first, 4 of 4)

- [Does Bigger Mean Better? Comparitive Analysis of CNNs and Biomedical Vision Language Modles in Medical Diagnosis](https://mlsanity.com/paper/2510.00411/) (2025)
- [LBM-GNN: Graph Neural Network Enhanced Lattice Boltzmann Method](https://mlsanity.com/paper/2504.14494/) (2025)
- [Dynamic Graph Neural Networks for Physiological Based Pharmacokinetic Modeling: A Novel Data Driven Approach to Drug Concentration Prediction](https://mlsanity.com/paper/2510.22096/) (2025)
- [Physiologically Informed Deep Learning: A Multi-Scale Framework for Next-Generation PBPK Modeling](https://mlsanity.com/paper/2602.18472/) (2026)

## Abstract (arXiv)

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.