5 citations · 7 across the 3 of their papers we have counts for
3 papers
math.AP2025
Going with the Flow: Solving for Symmetry-Driven PDE dynamics with Physics-informed Neural Networks
Michail Kavousanakis, Gianluca Fabiani, Anastasia Georgiou +3
In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dyn…
stat.ML2021★ 2 cited
Helmholtzian Eigenmap: Topological feature discovery & edge flow learning from point cloud data
Yu-Chia Chen, Weicheng Wu, Marina Meilă +1
The manifold Helmholtzian (1-Laplacian) operator elegantly generalizes the Laplace-Beltrami operator to vector fields on a manifold . In this work, we propose the…
stat.ML2020★ 5 cited
Particles to Partial Differential Equations Parsimoniously
Hassan Arbabi, Ioannis Kevrekidis
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differentia…