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 .
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 static , 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 .
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novel
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deep learning to compute mean curvature
machine learning to improve curvature estimation
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combines a dictionary of improved regression models
couples enhanced neural networks
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estimate
compute
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hybrid
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well-established
well established
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multi-layer
multilayer
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circular- and sinusoidal-interface
sinusoidal- and circular-interface
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result in compact networks
lead to a powerful inference system
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the system's
its
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, smooth
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approach is suitable and notoriously
solver is notably
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under-resolved and steep, concave
coarse grids and along steep interface
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including training
training the regression model with
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other means of
transforming data with specialized
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devising viable solutions to
reducing or removing mass loss in
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's numerical shortcomings