Error-correcting neural networks for semi-Lagrangian advection in the level-set method
نویسندگان
چکیده
We present a machine learning framework that blends image super-resolution technologies with passive, scalar transport in the level-set method. Here, we investigate whether can compute on-the-fly, data-driven corrections to minimize numerical viscosity coarse-mesh evolution of an interface. The proposed system's starting point is semi-Lagrangian formulation. And, reduce dissipation, introduce error-quantifying multilayer perceptron. role this neural network improve numerically estimated surface trajectory. To do so, it processes localized level-set, velocity, and positional data single time frame for select vertices near moving front. Our main contribution thus novel machine-learning-augmented algorithm operates alongside selective redistancing alternates conventional advection keep adjusted interface trajectory smooth. Consequently, our procedure more efficient than full-scan convolutional-based applications because concentrates computational effort only around free boundary. Also, show through various tests strategy effective at counteracting both diffusion mass loss. In simple problems, example, method achieve same precision as baseline scheme twice resolution but fraction cost. Similarly, hybrid technique produce feasible solidification fronts crystallization processes. On other hand, tangential shear flows highly deforming simulations precipitate bias artifacts inference deterioration. Likewise, stringent design velocity constraints limit solver's application problems involving rapid changes. latter cases, have identified several opportunities enhance robustness without forgoing approach's basic concept.
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2022
ISSN: ['1090-2716', '0021-9991']
DOI: https://doi.org/10.1016/j.jcp.2022.111623