
arXiv: 2204.13821
AbstractModeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases the computational cost. Although adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh‐based methods to perform while modeling the evolving localizations. In this work, neural network‐enhanced reproducing kernel particle method (NN‐RKPM) is proposed, where the location, orientation, and shape of the solution transition near a localization is automatically captured by the NN approximation via a block‐level neural network (NN) optimization. The weights and biases in the blocked parameterization network control the location and orientation of the localization. The designed basic four‐kernel NN block is capable of capturing a triple junction or a quadruple junction topological pattern, while more complicated localization topological patters are captured by the superposition of multiple four‐kernel NN blocks. The standard RK approximation is then utilized to approximate the smooth part of the solution, which permits a much coarser discretization than the high‐resolution discretization needed to capture sharp solution transitions with the conventional methods. A regularization of the NN approximation is additionally introduced for discretization‐independent material responses. The effectiveness of the proposed NN‐RKPM is verified by a series of numerical verifications.
FOS: Computer and information sciences, Computer Science - Machine Learning, physics-informed neural network, FOS: Physical sciences, Basic methods in fluid mechanics, Numerical Analysis (math.NA), reproducing kernel approximation, Computational Physics (physics.comp-ph), localization, Machine Learning (cs.LG), regularization, Computational Engineering, Finance, and Science (cs.CE), Numerical and other methods in solid mechanics, FOS: Mathematics, Generalities, axiomatics, foundations of continuum mechanics of solids, Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, damage, Physics - Computational Physics
FOS: Computer and information sciences, Computer Science - Machine Learning, physics-informed neural network, FOS: Physical sciences, Basic methods in fluid mechanics, Numerical Analysis (math.NA), reproducing kernel approximation, Computational Physics (physics.comp-ph), localization, Machine Learning (cs.LG), regularization, Computational Engineering, Finance, and Science (cs.CE), Numerical and other methods in solid mechanics, FOS: Mathematics, Generalities, axiomatics, foundations of continuum mechanics of solids, Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, damage, Physics - Computational Physics
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