3 papers
math.NA2026
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…
q-fin.CP2025
A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models
Emmanuil H. Georgoulis, Antonis Papapantoleon, Costas Smaragdakis
We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a p…
math.NA2025
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…