A Deep Learning Approach for the Computation of Curvature in the Level-Set Method

Larios-Cárdenas, Luis Ángel; Gibou, Frédéric

doi:10.1137/20m1316755

Cited by 17 publications

(22 citation statements)

References 63 publications

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“…However, one opts for a signed distance level-set function in practice because it helps to simplify computations (e.g., ∇φ(x) 2 = 1), reduce artificial mass loss, and produce robust numerical results [5]. Also, previous studies [1,32] have shown that the signed distance property is beneficial for improving the accuracy and performance of neural networks that estimate curvature. Thus, since the numerical solution of eq.…”

Section: The Level-set Methodsmentioning

confidence: 99%

“…Here, we describe our hybrid solver based on neural corrections. Our approach improves the frameworks in [1] and [32] by incorporating the error-correcting notion of [42] and the ML enhancements of [41]. The key components that make up the proposed curvature solver appear in fig.…”

Section: Methodsmentioning

confidence: 99%

“…Figure 2 outlines the structure of our neural network. Unlike [1,32] in the level-set method and [33,36] in the VOF framework, F κ (•) digests more statistical information (e.g., gradient data) than just level-set or volume-fraction values. In addition, besides its ε-reconstructing feedforward architecture, our model features a skip connection that carries the hκ input to a non-trainable unit that assembles hκ F .…”

Section: N P U T L a Y E R Hi D D E N L A Y E R S Ou T P U T L A Y E Rmentioning

confidence: 99%

“…In a prior study [32], we introduced level-set curvature neural networks analogous to [33]. Instead of volume fractions, these models ingested nine-point-stencil level-set values and produced the dimensionless curvature for interface nodes 1 .…”

Section: Introductionmentioning

confidence: 99%

“…In addition, these models were trained only on half of the curvature spectrum, thus leading to higher capacity and fewer degrees of freedom in the observed input patterns. The work in [32], however, left a few questions unanswered. The most important ones referred to overfitting and the lack of learning data-set scalability for highly resolved grids.…”

Section: Introductionmentioning

confidence: 99%

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Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-Set Method

Larios-Cárdenas,

Gibou

2022

Preprint

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We present an error-neural-modeling-based strategy for approximating two-dimensional curvature in the level-set method. Our main contribution is a redesigned hybrid solver [1]) that relies on numerical schemes to enable machine-learning operations on demand. In particular, our routine features double predicting to harness curvature symmetry invariance in favor of precision and stability. As in [1], the core of this solver is a multilayer perceptron trained on circular-and sinusoidal-interface samples. Its role is to quantify the error in numerical curvature approximations and emit corrected estimates for select grid vertices along the free boundary. These corrections arise in response to preprocessed context level-set, curvature, and gradient data. To promote neural capacity, we have adopted sample negative-curvature normalization, reorientation, and reflection-based augmentation. In the same manner, our system incorporates dimensionality reduction, well-balancedness, and regularization to minimize outlying effects. Our training approach is likewise scalable across mesh sizes. For this purpose, we have introduced dimensionless parametrization and probabilistic subsampling during data production. Together, all these elements have improved the accuracy and efficiency of curvature calculations around under-resolved regions. In most experiments, our strategy has outperformed the numerical baseline at twice the number of redistancing steps while requiring only a fraction of the cost.

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Section: The Level-set Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: N P U T L a Y E R Hi D D E N L A Y E R S Ou T P U T L A Y E Rmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-Set Method

Larios-Cárdenas,

Gibou

2022

Preprint

Self Cite

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Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-set Method

Larios-Cárdenas

Gibou

2022

J Sci Comput

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Hybridization of front tracking and level set for multiphase flow simulations: a machine learning approach

Yoon,

Chergui,

Juric

et al. 2023

J Mech Sci Technol

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In the present study, a machine learning (ML) based approach is proposed to hybridize two well-established methods for multiphase flow simulations, namely the Front Tracking (FT) and the Level Set (LS) methods. Based on the geometric information of the Lagrangian marker elements which represents the phase interface in FT simulations, the distance function field which is the key feature for describing the interface in LS simulations is predicted using a ML model. The trained ML model is implemented in our conventional numerical framework, and we finally demonstrate that the FT-based interface representation can easily and immediately be switched to a LS-based representation whenever needed during the simulation period.

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A Deep Learning Approach for the Computation of Curvature in the Level-Set Method

Cited by 17 publications

References 63 publications

Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-Set Method

Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-Set Method

Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-set Method

Hybridization of front tracking and level set for multiphase flow simulations: a machine learning approach

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