149 citations · 414 across the 23 of their papers we have counts for
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A class of Discontinuous Galerkin methods for nonlinear variational problems
Georgios Grekas, Konstantinos Koumatos, Charalambos Makridakis +1
In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming f…
On the Stability and Convergence of Physics Informed Neural Networks
Dimitrios Gazoulis, Ioannis Gkanis, Charalambos G. Makridakis
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and…
A new approach to generalisation error of machine learning algorithms: Estimates and convergence
Michail Loulakis, Charalambos G. Makridakis
In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set…