@article{sidecarastructurepreservingframeworkfor,
  title = {Sidecar: A Structure-Preserving Framework for Solving Partial Differential Equations with Neural Networks},
  author = {Gaohang Chen and Zhonghua Qiao},
  year = {2025},
  eprint = {2504.10273},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2504.10273v1},
}