A hybrid inference system for improved curvature estimation in the level-set method using machine learning

TL;DR

This paper introduces a hybrid approach combining neural networks and traditional numerical schemes to enhance curvature estimation in the level-set method, significantly improving accuracy especially in coarse grids and steep regions.

Contribution

The authors develop a novel hybrid inference system that adaptively switches between neural networks and numerical methods based on curvature magnitude, outperforming standalone techniques.

Findings

Hybrid system outperforms numerical methods in coarse grids

Neural networks improve accuracy in steep interface regions

Training on diverse interface data enhances precision

Abstract

We present a novel hybrid strategy based on machine learning to improve curvature estimation in the level-set method. The proposed inference system couples enhanced neural networks with standard numerical schemes to compute curvature more accurately. The core of our hybrid framework is a switching mechanism that relies on well established numerical techniques to gauge curvature. If the curvature magnitude is larger than a resolution-dependent threshold, it uses a neural network to yield a better approximation. Our networks are multilayer perceptrons fitted to synthetic data sets composed of sinusoidal- and circular-interface samples at various configurations. To reduce data set size and training complexity, we leverage the problem's characteristic symmetry and build our models on just half of the curvature spectrum. These savings lead to a powerful inference system able to outperform any of its numerical or neural component alone. Experiments with stationary, smooth interfaces show that our hybrid solver is notably superior to conventional numerical methods in coarse grids and along steep interface regions. Compared to prior research, we have observed outstanding gains in precision after training the regression model with data pairs from more than a single interface type and transforming data with specialized input preprocessing. In particular, our findings confirm that machine learning is a promising venue for reducing or removing mass loss in the level-set method.