2 papers
math.NA2026
Pointwise Error Estimates for Numerical Physics-Informed Neural Networks
Nivar Anwer, Marien Chenaud, José Alves +1
Physics-informed neural networks are often evaluated by residual losses sampled at finitely many points, which do not by themselves certify pointwise values of a partial differenti…
math.NA2024
Physics-Informed Graph-Mesh Networks for PDEs: A hybrid approach for complex problems
Marien Chenaud, Frédéric Magoulès, José Alves
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven…