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.
翻译:我们提出了一个基于机器学习的新混合战略,其基础是改进水平定位方法的曲度估计的机器学习。 提议的推论系统夫妇增强神经网络, 并采用标准的数字计划来更精确地计算曲度。 我们混合框架的核心是一个转换机制,它依靠成熟的数字技术来测量曲度。 如果曲度规模大于分辨率依赖的临界值, 它使用神经网络来产生更好的近距离。 我们的网络是多层透视器, 适合由各种配置的正弦形和循环界面样本组成的合成数据集。 为了降低数据集的规模和培训复杂性, 我们利用问题的特点对称法, 并在曲线范围的一半上构建我们的模型。 这些节省导致一个强大的推论系统, 能够超越其任何数字或神经组成部分。 与固定的、 光滑的界面实验显示, 我们的混合解解答器在粗格和陡峭的界面区域中, 明显优于常规的数字方法。 与先前的研究相比, 我们观察到了在训练回归模型后在精确度上取得的突出进展, 我们的特征的对称和模型在精确度上建好半曲线频谱谱谱谱谱谱谱谱谱谱谱系上, 。 将比一个特殊的界面 学习方法 。