Level-Set Curvature Neural Networks: A Hybrid Approach

We present a hybrid strategy based on deep learning to compute mean curvature in the level-set method. The proposed inference system combines a dictionary of improved regression models with standard numerical schemes to estimate curvature more accurately. The core of our 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 multi-layer perceptrons fitted to synthetic data sets composed of circular- and sinusoidal-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 result in compact networks able to outperform any of the system's numerical or neural component alone. Experiments with static interfaces show that our hybrid approach is suitable and notoriously superior to conventional numerical methods in under-resolved and steep, concave regions. Compared to prior research, we have observed outstanding gains in precision after including training data pairs from more than a single interface type and other means of input preprocessing. In particular, our findings confirm that machine learning is a promising venue for devising viable solutions to the level-set method's numerical shortcomings.