Machine Learning design of Volume of Fluid schemes for compressible flows

Després, Bruno; Jourdren, Hervé

doi:10.1016/j.jcp.2020.109275

Cited by 23 publications

(9 citation statements)

References 23 publications

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“…To reduce the numerical diffusion of the interfaces, it is common to use interface reconstruction methods [7]. Interface reconstruction itself is a complex task and remains active field of research [8,17,18,2,14]. The aim of this paper is not to compare methods nor to propose innovative ones to compute material interface positions.…”

Section: Interfaces Reconstructionmentioning

confidence: 99%

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Triangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinates

Pino

Marmajou

2023

Journal of Computational Physics

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Section: Interfaces Reconstructionmentioning

confidence: 99%

“…The smoothing procedure consists in replacing the imposed edge lengths in order to reduce the size growth by satisfying (14), see Algorithm 1.…”

mentioning

confidence: 99%

Triangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinates

Pino

Marmajou

2023

Journal of Computational Physics

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“…(1) In the first category, deep neural networks are employed to assist classical numerical methods by improving some limitations, or accelerating certain steps (see, e.g., [1][2][3]). (2) In the second category, neural networks are used to directly approximate the solution of PDEs.…”

Section: Scientific Context and Goalsmentioning

confidence: 99%

Deep Learning-based Schemes for Singularly Perturbed Convection-Diffusion Problems

Beguinet¹,

Ehrlacher²,

Roberta³

et al. 2022

Preprint

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Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at first sight because implementing vanilla versions of PINNs based on strong residual forms is easy, and neural networks offer very high approximation capabilities. However, when the PDE solutions are low regular, an expert insight is required to build deep learning formulations that do not incur in variational crimes. Optimization solvers are also significantly challenged, and can potentially spoil the final quality of the approximated solution due to the convergence to bad local minima, and bad generalization capabilities. In this paper, we present an exhaustive numerical study of the merits and limitations of these schemes when solutions exhibit low-regularity, and compare performance with respect to more benign cases when solutions are very smooth. As a support for our study, we consider singularly perturbed convection-diffusion problems where the regularity of solutions typically degrades as certain multiscale parameters go to zero.

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“…Their systematic approach and optimized networks, in particular, have proven effective in several free-boundary experiments, including standard bubble simulations. Likewise, Després and Jourdren [37] have developed a family of VOF-ML schemes adapted to bi-material compressible Euler calculations on Cartesian grids. The core of their system is a finite-volume flux function embodied in dense-layered neural models trained with lines, arcs, and corners.…”

Section: Introductionmentioning

confidence: 99%

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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Machine Learning design of Volume of Fluid schemes for compressible flows

Cited by 23 publications

References 23 publications

Triangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinates

Triangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinates

Deep Learning-based Schemes for Singularly Perturbed Convection-Diffusion Problems

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

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