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math.NA2025
Learning Geometric-Aware Quadrature Rules for Functional Minimization
Costas Smaragdakis
Accurate numerical integration over non-uniform point clouds is a challenge for modern mesh-free machine learning solvers for partial differential equations (PDEs) using variationa…
math.NA2025★ 4 cited
Runge-Kutta Physics Informed Neural Networks: Formulation and Analysis
Georgios Akrivis, Charalambos G. Makridakis, Costas Smaragdakis
In this paper we consider time-dependent PDEs discretized by a special class of Physics Informed Neural Networks whose design is based on the framework of Runge--Kutta and related…