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math.NA2020★ 1 cited
Thermodynamically consistent physics-informed neural networks for hyperbolic systems
Ravi G. Patel, Indu Manickam, Nathaniel A. Trask +4
Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the P…
math.NA2020
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
Yu Leng, Xiaochuan Tian, Nathaniel A. Trask +1
In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilata…