3 papers
math.NA2025
Energy minimisation using overlapping tensor-product free-knot B-splines
Alexandre Magueresse, Santiago Badia
Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and…
math.NA2025
A convergence framework for energy minimisation of linear self-adjoint elliptic PDEs in nonlinear approximation spaces
Alexandre Magueresse, Santiago Badia
Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approache…
math.NA2023
Adaptive quadratures for nonlinear approximation of low-dimensional PDEs using smooth neural networks
Alexandre Magueresse, Santiago Badia
Physics-informed neural networks (PINNs) and their variants have recently emerged as alternatives to traditional partial differential equation (PDE) solvers, but little literature…