475 lines
16 KiB
BibTeX
475 lines
16 KiB
BibTeX
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@article{raissi2019pinn,
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title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
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author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E},
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journal={Journal of Computational physics},
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volume={378},
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pages={686--707},
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year={2019},
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publisher={Elsevier}
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}
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@article{yu2018deepritz,
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title={The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems},
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author={Yu, Bing and others},
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journal={Communications in Mathematics and Statistics},
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volume={6},
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number={1},
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pages={1--12},
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year={2018},
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publisher={Springer}
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}
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@article{kharazmi2019vpinn,
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title={Variational physics-informed neural networks for solving partial differential equations},
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author={Kharazmi, Ehsan and Zhang, Zhongqiang and Karniadakis, George Em},
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journal={arXiv preprint arXiv:1912.00873},
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year={2019}
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}
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@article{kharazmi2021hpvpinn,
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title={hp-VPINNs: Variational physics-informed neural networks with domain decomposition},
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author={Kharazmi, Ehsan and Zhang, Zhongqiang and Karniadakis, George Em},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={374},
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pages={113547},
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year={2021},
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publisher={Elsevier}
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}
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@article{jagtap2020conservative,
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title={Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems},
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author={Jagtap, Ameya D and Kharazmi, Ehsan and Karniadakis, George Em},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={365},
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pages={113028},
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year={2020},
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publisher={Elsevier}
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}
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@article{wang2021gradientpathologies,
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title={Understanding and mitigating gradient flow pathologies in physics-informed neural networks},
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author={Wang, Sifan and Teng, Yujun and Perdikaris, Paris},
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journal={SIAM Journal on Scientific Computing},
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volume={43},
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number={5},
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pages={A3055--A3081},
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year={2021},
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publisher={SIAM}
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}
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@inproceedings{krishnapriyan2021failuremodes,
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title={Characterizing possible failure modes in physics-informed neural networks},
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author={Krishnapriyan, Aditi and Gholami, Amir and Zhe, Shandian and Kirby, Robert and Mahoney, Michael W},
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journal={Advances in neural information processing systems},
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volume={34},
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pages={26548--26560},
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year={2021}
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}
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@article{mcclenny2023sapinn,
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title={Self-adaptive physics-informed neural networks},
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author={McClenny, Levi D and Braga-Neto, Ulisses M},
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journal={Journal of Computational Physics},
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volume={474},
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pages={111722},
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year={2023},
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publisher={Elsevier}
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}
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@article{wu2023adaptivesampling,
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title={A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks},
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author={Wu, Chenxi and Zhu, Min and Tan, Qinyang and Kartha, Yadhu and Lu, Lu},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={403},
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pages={115671},
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year={2023},
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publisher={Elsevier}
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}
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@article{wang2024causality,
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title={Respecting causality for training physics-informed neural networks},
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author={Wang, Sifan and Sankaran, Shyam and Perdikaris, Paris},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={421},
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pages={116813},
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year={2024},
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publisher={Elsevier}
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}
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@article{wang2025gradientalignment,
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title={Gradient alignment in physics-informed neural networks: A second-order optimization perspective},
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author={Wang, Sifan and Bhartari, Ananyae Kumar and Li, Bowen and Perdikaris, Paris},
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journal={arXiv preprint arXiv:2502.00604},
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year={2025}
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}
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@article{courant1994variational,
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title={Variational methods for the solution of problems of equilibrium and vibrations},
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author={Courant, Richard and others},
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journal={Lecture notes in pure and applied mathematics},
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pages={1--1},
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year={1994},
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publisher={MARCEL DEKKER AG}
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}
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@book{leveque2002finite,
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title={Finite volume methods for hyperbolic problems},
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author={LeVeque, Randall J},
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volume={31},
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year={2002},
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publisher={Cambridge university press}
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}
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@book{patankar2018numerical,
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title={Numerical heat transfer and fluid flow},
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author={Patankar, Suhas},
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year={2018},
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publisher={CRC press}
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}
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@article{eshaghi2025variational,
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title={Variational physics-informed neural operator (VINO) for solving partial differential equations},
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author={Eshaghi, Mohammad Sadegh and Anitescu, Cosmin and Thombre, Manish and Wang, Yizheng and Zhuang, Xiaoying and Rabczuk, Timon},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={437},
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pages={117785},
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year={2025},
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publisher={Elsevier}
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}
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@article{rojas2024robust,
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title={Robust variational physics-informed neural networks},
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author={Rojas, Sergio and Maczuga, Pawe{\l} and Mu{\~n}oz-Matute, Judit and Pardo, David and Paszy{\'n}ski, Maciej},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={425},
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pages={116904},
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year={2024},
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publisher={Elsevier}
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}
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@article{zang2020weak,
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title={Weak adversarial networks for high-dimensional partial differential equations},
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author={Zang, Yaohua and Bao, Gang and Ye, Xiaojing and Zhou, Haomin},
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journal={Journal of Computational Physics},
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volume={411},
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pages={109409},
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year={2020},
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publisher={Elsevier}
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}
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@inproceedings{baez2024guaranteeing,
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title={Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks},
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author={Baez, Anthony and Zhang, Wang and Ma, Ziwen and Das, Subhro and Nguyen, Lam M and Daniel, Luca},
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booktitle={NeurIPS 2024 Workshop on Data-driven and Differentiable Simulations, Surrogates, and Solvers}
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}
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@article{zhang2026musa,
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title={MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries},
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author={Zhang, Weizheng and Xie, Xunjie and Pan, Hao and Duan, Xiaowei and Sun, Bingteng and Du, Qiang and Lu, Lin},
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journal={arXiv preprint arXiv:2603.08465},
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year={2026}
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}
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@article{wang2025wf,
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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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author={Wang, Xianke and Yi, Shichao and Gu, Huangliang and Xu, Jing and Xu, Wenjie},
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journal={Scientific Reports},
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volume={15},
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number={1},
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pages={40555},
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year={2025},
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publisher={Nature Publishing Group UK London}
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}
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@article{wang2022and,
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title={When and why PINNs fail to train: A neural tangent kernel perspective},
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author={Wang, Sifan and Yu, Xinling and Perdikaris, Paris},
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journal={Journal of Computational Physics},
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volume={449},
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pages={110768},
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year={2022},
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publisher={Elsevier}
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}
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@inproceedings{rathore2024challenges,
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title={Challenges in Training PINNs: A Loss Landscape Perspective},
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author={Rathore, Pratik and Lei, Weimu and Frangella, Zachary and Lu, Lu and Udell, Madeleine},
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booktitle={International Conference on Machine Learning},
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pages={42159--42191},
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year={2024},
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organization={PMLR}
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}
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@article{wang2021eigenvector,
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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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author={Wang, Sifan and Wang, Hanwen and Perdikaris, Paris},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={384},
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pages={113938},
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year={2021},
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publisher={Elsevier}
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}
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@article{wang2021understanding,
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title={Understanding and mitigating gradient flow pathologies in physics-informed neural networks},
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author={Wang, Sifan and Teng, Yujun and Perdikaris, Paris},
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journal={SIAM Journal on Scientific Computing},
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volume={43},
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number={5},
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pages={A3055--A3081},
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year={2021},
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publisher={SIAM}
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}
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@article{mcclenny2023self,
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title={Self-adaptive physics-informed neural networks},
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author={McClenny, Levi D and Braga-Neto, Ulisses M},
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journal={Journal of Computational Physics},
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volume={474},
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pages={111722},
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year={2023},
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publisher={Elsevier}
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}
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@inproceedings{wu2026multi,
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title={A Multi-Objective Optimization Framework for Adaptive Weighting in Physics-Informed Machine Learning},
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author={Wu, Guoquan and Wu, Zhe},
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booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
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volume={40},
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number={32},
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pages={26885--26893},
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year={2026}
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}
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@inproceedings{wanggradient,
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title={Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective},
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author={Wang, Sifan and Bhartari, Ananyae Kumar and Li, Bowen and Perdikaris, Paris},
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booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
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year={2025}
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}
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@article{banderwaar2025fast,
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title={Fast PINN Eigensolvers via Biconvex Reformulation},
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author={Banderwaar, Akshay Sai and Gupta, Abhishek},
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journal={arXiv preprint arXiv:2511.00792},
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year={2025}
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}
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@article{wu2023comprehensive,
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title={A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks},
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author={Wu, Chenxi and Zhu, Min and Tan, Qinyang and Kartha, Yadhu and Lu, Lu},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={403},
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pages={115671},
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year={2023},
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publisher={Elsevier BV}
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}
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@inproceedings{
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duan2025copinn,
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title={Co{PINN}: Cognitive Physics-Informed Neural Networks},
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author={Siyuan Duan and Wenyuan Wu and Peng Hu and Zhenwen Ren and Dezhong Peng and Yuan Sun},
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booktitle={Forty-second International Conference on Machine Learning},
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year={2025},
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url={https://openreview.net/forum?id=4vAa0A98xI}
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}
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@article{wang2024respecting,
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title={Respecting causality for training physics-informed neural networks},
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author={Wang, Sifan and Sankaran, Shyam and Perdikaris, Paris},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={421},
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pages={116813},
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year={2024},
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publisher={Elsevier}
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}
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@article{cho2023separable,
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title={Separable physics-informed neural networks},
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author={Cho, Junwoo and Nam, Seungtae and Yang, Hyunmo and Yun, Seok-Bae and Hong, Youngjoon and Park, Eunbyung},
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journal={Advances in Neural Information Processing Systems},
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volume={36},
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pages={23761--23788},
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year={2023}
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}
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@inproceedings{
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zhao2024pinnsformer,
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title={{PINN}sFormer: A Transformer-Based Framework For Physics-Informed Neural Networks},
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author={Zhiyuan Zhao and Xueying Ding and B. Aditya Prakash},
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booktitle={The Twelfth International Conference on Learning Representations},
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year={2024},
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url={https://openreview.net/forum?id=DO2WFXU1Be}
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}
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@inproceedings{
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arni2025physicsinformed,
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title={Physics-Informed Neural Networks with Fourier Features and Attention-Driven Decoding},
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author={Rohan Arni and Carlos Blanco},
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booktitle={NeurIPS 2025 AI for Science Workshop},
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year={2025},
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url={https://openreview.net/forum?id=woq4ZAm1AH}
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}
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@article{tao2025xlstm,
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title={xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning},
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author={Tao, Ze and Zhao, Darui and Liu, Fujun and Xu, Ke and Hu, Xiangsheng},
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journal={arXiv preprint arXiv:2511.12512},
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year={2025}
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}
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@article{sitzmann2020implicit,
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title={Implicit neural representations with periodic activation functions},
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author={Sitzmann, Vincent and Martel, Julien and Bergman, Alexander and Lindell, David and Wetzstein, Gordon},
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journal={Advances in neural information processing systems},
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volume={33},
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pages={7462--7473},
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year={2020}
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}
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@article{jagtap2020extended,
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title={Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations},
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author={Jagtap, Ameya D and Karniadakis, George Em},
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journal={Communications in Computational Physics},
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volume={28},
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number={5},
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year={2020},
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publisher={Brown Univ., Providence, RI (United States)}
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}
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@article{moseley2023finite,
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title={Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations: B. Moseley et al.},
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author={Moseley, Ben and Markham, Andrew and Nissen-Meyer, Tarje},
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journal={Advances in Computational Mathematics},
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volume={49},
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number={4},
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pages={62},
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year={2023},
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publisher={Springer}
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}
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@article{dolean2024multilevel,
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title={Multilevel domain decomposition-based architectures for physics-informed neural networks},
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author={Dolean, Victorita and Heinlein, Alexander and Mishra, Siddhartha and Moseley, Ben},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={429},
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pages={117116},
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year={2024},
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publisher={Elsevier}
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}
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@article{botvinick2025ab,
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title={AB-PINNs: Adaptive-Basis Physics-Informed Neural Networks for Residual-Driven Domain Decomposition},
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author={Botvinick-Greenhouse, Jonah and Ali, Wael H and Benosman, Mouhacine and Mowlavi, Saviz},
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journal={arXiv preprint arXiv:2510.08924},
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year={2025}
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}
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@article{bischof2025hypino,
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title={HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions},
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author={Bischof, Rafael and Piovar{\v{c}}i, Michal and Kraus, Michael A and Mishra, Siddhartha and Bickel, Bernd},
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journal={arXiv preprint arXiv:2509.05117},
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year={2025}
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}
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@article{wang2025transfer,
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title={Transfer learning in physics-informed neurals networks: full fine-tuning, lightweight fine-tuning, and low-rank adaptation},
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author={Wang, Yizheng and Bai, Jinshuai and Eshaghi, Mohammad Sadegh and Anitescu, Cosmin and Zhuang, Xiaoying and Rabczuk, Timon and Liu, Yinghua},
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journal={International Journal of Mechanical System Dynamics},
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volume={5},
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number={2},
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pages={212--235},
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year={2025},
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publisher={Wiley Online Library}
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}
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@article{chung2026hard,
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title={Hard-constrained Physics-informed Neural Networks for Interface Problems},
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author={Chung, Seung Whan and Castonguay, Stephen and Roy, Sumanta and Penwarden, Michael and Fu, Yucheng and Roy, Pratanu},
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journal={arXiv preprint arXiv:2604.08453},
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year={2026}
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}
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@article{li2024physical,
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title={Physical informed neural networks with soft and hard boundary constraints for solving advection-diffusion equations using Fourier expansions},
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author={Li, Xi'an and Deng, Jiaxin and Wu, Jinran and Zhang, Shaotong and Li, Weide and Wang, You-Gan},
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journal={Computers \& Mathematics with Applications},
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volume={159},
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pages={60--75},
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year={2024},
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publisher={Elsevier}
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}
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@article{liu1989limited,
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title={On the limited memory BFGS method for large scale optimization},
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author={Liu, Dong C and Nocedal, Jorge},
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journal={Mathematical programming},
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volume={45},
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number={1},
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year={1989},
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@inproceedings{vyas2025soap,
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title={{SOAP}: Improving and Stabilizing Shampoo using Adam for Language Modeling},
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author={Nikhil Vyas and Depen Morwani and Rosie Zhao and Itai Shapira and David Brandfonbrener and Lucas Janson and Sham M. Kakade},
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booktitle={The Thirteenth International Conference on Learning Representations},
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year={2025},
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url={https://openreview.net/forum?id=IDxZhXrpNf}
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}
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@article{bischof2025multi,
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title={Multi-objective loss balancing for physics-informed deep learning},
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author={Bischof, Rafael and Kraus, Michael A},
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journal={Computer Methods in Applied Mechanics and Engineering},
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volume={439},
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pages={117914},
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year={2025},
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publisher={Elsevier}
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}
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@article{wu2024ropinn,
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title={Ropinn: Region optimized physics-informed neural networks},
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author={Wu, Haixu and Luo, Huakun and Ma, Yuezhou and Wang, Jianmin and Long, Mingsheng},
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journal={Advances in Neural Information Processing Systems},
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volume={37},
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pages={110494--110532},
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year={2024}
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}
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@article{jagtap2020locally,
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title={Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks},
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author={Jagtap, Ameya D and Kawaguchi, Kenji and Em Karniadakis, George},
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journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
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volume={476},
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number={2239},
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year={2020},
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publisher={The Royal Society}
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}
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title={Artificial neural networks for solving ordinary and partial differential equations},
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author={Lagaris, Isaac E and Likas, Aristidis and Fotiadis, Dimitrios I},
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@article{lu2021deepxde,
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title={DeepXDE: A deep learning library for solving differential equations},
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author={Lu, Lu and Meng, Xuhui and Mao, Zhiping and Karniadakis, George Em},
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journal={SIAM review},
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volume={63},
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number={1},
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pages={208--228},
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year={2021},
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publisher={SIAM}
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} |