May 14, 2024, 4:44 a.m. | Taeyoung Kim, Myungjoo Kang

cs.LG updates on arXiv.org arxiv.org

arXiv:2401.01783v4 Announce Type: replace-cross
Abstract: Traditionally, classical numerical schemes have been employed to solve partial differential equations (PDEs) using computational methods. Recently, neural network-based methods have emerged. Despite these advancements, neural network-based methods, such as physics-informed neural networks (PINNs) and neural operators, exhibit deficiencies in robustness and generalization. To address these issues, numerous studies have integrated classical numerical frameworks with machine learning techniques, incorporating neural networks into parts of traditional numerical methods. In this study, we focus on hyperbolic conservation …

abstract arxiv computational conservation cs.lg cs.na differential fourier laws math.na network networks neural network neural networks numerical operators physics physics-informed replace robustness solve type

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