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@article{kharazmi2019vpinn,
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  author={Kharazmi, Ehsan and Zhang, Zhongqiang and Karniadakis, George Em},
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  year={2019}
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@article{kharazmi2021hpvpinn,
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  author={Kharazmi, Ehsan and Zhang, Zhongqiang and Karniadakis, George Em},
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  volume={374},
  pages={113547},
  year={2021},
  publisher={Elsevier}
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@article{jagtap2020conservative,
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  volume={365},
  pages={113028},
  year={2020},
  publisher={Elsevier}
}

@article{wang2021gradientpathologies,
  title={Understanding and mitigating gradient flow pathologies in physics-informed neural networks},
  author={Wang, Sifan and Teng, Yujun and Perdikaris, Paris},
  journal={SIAM Journal on Scientific Computing},
  volume={43},
  number={5},
  pages={A3055--A3081},
  year={2021},
  publisher={SIAM}
}

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  title={Characterizing possible failure modes in physics-informed neural networks},
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  year={2021}
}

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  year={2023},
  publisher={Elsevier}
}

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  pages={115671},
  year={2023},
  publisher={Elsevier}
}

@article{wang2024causality,
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  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={421},
  pages={116813},
  year={2024},
  publisher={Elsevier}
}

@article{wang2025gradientalignment,
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  year={2025}
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@inproceedings{baez2024guaranteeing,
  title={Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks},
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}

@article{zhang2026musa,
  title={MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries},
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  year={2026}
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@article{wang2025wf,
  title={WF-PINNs: solving forward and inverse problems of burgers equation with steep gradients using weak-form physics-informed neural networks},
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  number={1},
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  year={2025},
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@article{wang2022and,
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  author={Wang, Sifan and Yu, Xinling and Perdikaris, Paris},
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  volume={449},
  pages={110768},
  year={2022},
  publisher={Elsevier}
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@inproceedings{rathore2024challenges,
  title={Challenges in Training PINNs: A Loss Landscape Perspective},
  author={Rathore, Pratik and Lei, Weimu and Frangella, Zachary and Lu, Lu and Udell, Madeleine},
  booktitle={International Conference on Machine Learning},
  pages={42159--42191},
  year={2024},
  organization={PMLR}
}

@article{wang2021eigenvector,
  title={On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks},
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  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={384},
  pages={113938},
  year={2021},
  publisher={Elsevier}
}

@article{wang2021understanding,
  title={Understanding and mitigating gradient flow pathologies in physics-informed neural networks},
  author={Wang, Sifan and Teng, Yujun and Perdikaris, Paris},
  journal={SIAM Journal on Scientific Computing},
  volume={43},
  number={5},
  pages={A3055--A3081},
  year={2021},
  publisher={SIAM}
}

@article{mcclenny2023self,
  title={Self-adaptive physics-informed neural networks},
  author={McClenny, Levi D and Braga-Neto, Ulisses M},
  journal={Journal of Computational Physics},
  volume={474},
  pages={111722},
  year={2023},
  publisher={Elsevier}
}

@inproceedings{wu2026multi,
  title={A Multi-Objective Optimization Framework for Adaptive Weighting in Physics-Informed Machine Learning},
  author={Wu, Guoquan and Wu, Zhe},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={40},
  number={32},
  pages={26885--26893},
  year={2026}
}

@inproceedings{wanggradient,
  title={Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective},
  author={Wang, Sifan and Bhartari, Ananyae Kumar and Li, Bowen and Perdikaris, Paris},
  booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
  year={2025}
}

@article{banderwaar2025fast,
  title={Fast PINN Eigensolvers via Biconvex Reformulation},
  author={Banderwaar, Akshay Sai and Gupta, Abhishek},
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  year={2025}
}

@article{wu2023comprehensive,
  title={A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks},
  author={Wu, Chenxi and Zhu, Min and Tan, Qinyang and Kartha, Yadhu and Lu, Lu},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={403},
  pages={115671},
  year={2023},
  publisher={Elsevier BV}
}

@inproceedings{
duan2025copinn,
title={Co{PINN}: Cognitive Physics-Informed Neural Networks},
author={Siyuan Duan and Wenyuan Wu and Peng Hu and Zhenwen Ren and Dezhong Peng and Yuan Sun},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=4vAa0A98xI}
}


@article{wang2024respecting,
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  author={Wang, Sifan and Sankaran, Shyam and Perdikaris, Paris},
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  volume={421},
  pages={116813},
  year={2024},
  publisher={Elsevier}
}


@article{cho2023separable,
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  journal={Advances in Neural Information Processing Systems},
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  pages={23761--23788},
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}

@inproceedings{
zhao2024pinnsformer,
title={{PINN}sFormer: A Transformer-Based Framework For Physics-Informed Neural Networks},
author={Zhiyuan Zhao and Xueying Ding and B. Aditya Prakash},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=DO2WFXU1Be}
}

@inproceedings{
arni2025physicsinformed,
title={Physics-Informed Neural Networks with Fourier Features and Attention-Driven Decoding},
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booktitle={NeurIPS 2025 AI for Science Workshop},
year={2025},
url={https://openreview.net/forum?id=woq4ZAm1AH}
}

@article{tao2025xlstm,
  title={xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning},
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  year={2025}
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