@article{avariationalframeworkforresidualbasedada,
  title = {A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning},
  author = {Juan Diego Toscano and Daniel T. Chen and Vivek Oommen and Jérôme Darbon and George Em Karniadakis},
  year = {2025},
  eprint = {2509.14198},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2509.14198},
}