A hybrid inference system for improved curvature estimation in the level-set method using machine learning
This work addresses a domain-specific problem in computational fluid dynamics or image processing by improving curvature estimation, though it is incremental as it builds on existing numerical techniques with machine learning enhancements.
The authors tackled the problem of inaccurate curvature estimation in the level-set method by developing a hybrid inference system that combines neural networks with numerical schemes, resulting in superior performance on coarse grids and steep interface regions, with notable gains in precision and reduced mass loss.
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.