[Paper Review] NPLIC: A Machine Learning Approach to Piecewise Linear Interface Construction

Mohammadmehdi Ataei, Markus Bussmann+4 more|arXiv (Cornell University)|Jun 26, 2020

Fluid Dynamics and Heat Transfer42 references30 citations

TL;DR

This paper proposes NPLIC, a deep learning-based method to accelerate Piecewise Linear Interface Construction (PLIC) in Volume of Fluid (VOF) simulations. By training fully-connected neural networks on synthetic datasets of interface normals and volume fractions, NPLIC achieves PLIC accuracy at up to 100× faster speed—especially on complex 3D and triangular meshes—while supporting multiple mesh types with a single model.

ABSTRACT

Volume of fluid (VOF) methods are extensively used to track fluid interfaces in numerical simulations, and many VOF algorithms require that the interface be reconstructed geometrically. For this purpose, the Piecewise Linear Interface Construction (PLIC) technique is most frequently used, which for reasons of geometric complexity can be slow and difficult to implement. Here, we propose an alternative neural network based method called NPLIC to perform PLIC calculations. The model is trained on a large synthetic dataset of PLIC solutions for square, cubic, triangular, and tetrahedral meshes. We show that this data-driven approach results in accurate calculations at a fraction of the usual computational cost, and a single neural network system can be used for interface reconstruction of different mesh types.

Motivation & Objective

• To address the computational cost and implementation complexity of traditional PLIC algorithms in VOF simulations.
• To develop a data-driven, neural network-based alternative to geometric PLIC that maintains high accuracy.
• To enable a single neural network model to handle multiple mesh types (square, cubic, triangular, tetrahedral) without retraining.
• To significantly reduce computational time in interface reconstruction while preserving numerical fidelity in CFD simulations.

Proposed method

• Training fully-connected deep neural networks on large synthetic datasets of PLIC solutions for square, cubic, triangular, and tetrahedral meshes.
• Normalizing mesh geometries using transformation matrices to reduce input dimensionality to interface normal (θ, φ) and volume fraction (α₀).
• Using a shared input layer with a mesh-type identifier (m = 1 for tetrahedral/triangular, m = 0 for cubic/square) to unify models across mesh types.
• Employing mean squared error (MSE) loss during training to minimize prediction error between predicted C and ground-truth PLIC solutions.
• Leveraging optimized deep learning libraries (e.g., PyTorch) for efficient inference on both CPU and GPU hardware.
• Integrating the trained NPLIC model into the Basilisk CFD solver as a drop-in replacement for the original PLIC algorithm.

Experimental results

Research questions

• RQ1 Can a single neural network accurately predict PLIC solutions across diverse mesh types (square, cubic, triangular, tetrahedral)?
• RQ2 How does the inference speed of NPLIC compare to state-of-the-art analytical and iterative PLIC methods?
• RQ3 To what extent does NPLIC preserve accuracy compared to traditional PLIC, especially near α₀ = 0 and α₀ = 1?
• RQ4 Can NPLIC maintain high performance across different mesh resolutions and interface orientations without retraining?
• RQ5 What is the impact of model depth (number of neurons) on the trade-off between accuracy and speed in NPLIC?

Key findings

• NPLIC achieves a mean absolute error (MAE) of approximately 0.1% on test datasets, demonstrating near-parity with traditional PLIC in accuracy.
• For 3D tetrahedral and triangular meshes, NPLIC achieves up to 100× speedup on GPU and over 8× speedup on CPU compared to analytical PLIC methods.
• On square and cubic meshes, NPLIC is over 8× faster on CPU and up to 100× faster on GPU, though analytical PLIC remains faster in some 2D cases.
• The model trained with 48 neurons per hidden layer achieves errors close to 0.1%, comparable to other PLIC approximation techniques.
• NPLIC was successfully integrated into the Basilisk CFD solver, where it reduced interface reconstruction time by approximately 5× with indistinguishable results from PLIC.
• The use of batch inference and hardware-optimized deep learning libraries enables NPLIC to achieve 1.21 TFLOPS on GPU, far exceeding the 2.42 GFLOPS of CPU-based PLIC.