Spring 2026

part-1.bib

@@ -0,0 +1,475 @@
+
+@article{raissi2019pinn,
+  title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
+  author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E},
+  journal={Journal of Computational physics},
+  volume={378},
+  pages={686--707},
+  year={2019},
+  publisher={Elsevier}
+}
+
+@article{yu2018deepritz,
+  title={The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems},
+  author={Yu, Bing and others},
+  journal={Communications in Mathematics and Statistics},
+  volume={6},
+  number={1},
+  pages={1--12},
+  year={2018},
+  publisher={Springer}
+}
+
+@article{kharazmi2019vpinn,
+  title={Variational physics-informed neural networks for solving partial differential equations},
+  author={Kharazmi, Ehsan and Zhang, Zhongqiang and Karniadakis, George Em},
+  journal={arXiv preprint arXiv:1912.00873},
+  year={2019}
+}
+
+
+@article{kharazmi2021hpvpinn,
+  title={hp-VPINNs: Variational physics-informed neural networks with domain decomposition},
+  author={Kharazmi, Ehsan and Zhang, Zhongqiang and Karniadakis, George Em},
+  journal={Computer Methods in Applied Mechanics and Engineering},
+  volume={374},
+  pages={113547},
+  year={2021},
+  publisher={Elsevier}
+}
+
+@article{jagtap2020conservative,
+  title={Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems},
+  author={Jagtap, Ameya D and Kharazmi, Ehsan and Karniadakis, George Em},
+  journal={Computer Methods in Applied Mechanics and Engineering},
+  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}
+}
+
+@inproceedings{krishnapriyan2021failuremodes,
+  title={Characterizing possible failure modes in physics-informed neural networks},
+  author={Krishnapriyan, Aditi and Gholami, Amir and Zhe, Shandian and Kirby, Robert and Mahoney, Michael W},
+  journal={Advances in neural information processing systems},
+  volume={34},
+  pages={26548--26560},
+  year={2021}
+}
+
+@article{mcclenny2023sapinn,
+  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}
+}
+
+@article{wu2023adaptivesampling,
+  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}
+}
+
+@article{wang2024causality,
+  title={Respecting causality for training physics-informed neural networks},
+  author={Wang, Sifan and Sankaran, Shyam and Perdikaris, Paris},
+  journal={Computer Methods in Applied Mechanics and Engineering},
+  volume={421},
+  pages={116813},
+  year={2024},
+  publisher={Elsevier}
+}
+
+@article{wang2025gradientalignment,
+  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},
+  journal={arXiv preprint arXiv:2502.00604},
+  year={2025}
+}
+
+@article{courant1994variational,
+  title={Variational methods for the solution of problems of equilibrium and vibrations},
+  author={Courant, Richard and others},
+  journal={Lecture notes in pure and applied mathematics},
+  pages={1--1},
+  year={1994},
+  publisher={MARCEL DEKKER AG}
+}
+
+@book{leveque2002finite,
+  title={Finite volume methods for hyperbolic problems},
+  author={LeVeque, Randall J},
+  volume={31},
+  year={2002},
+  publisher={Cambridge university press}
+}
+
+@book{patankar2018numerical,
+  title={Numerical heat transfer and fluid flow},
+  author={Patankar, Suhas},
+  year={2018},
+  publisher={CRC press}
+}
+
+@article{eshaghi2025variational,
+  title={Variational physics-informed neural operator (VINO) for solving partial differential equations},
+  author={Eshaghi, Mohammad Sadegh and Anitescu, Cosmin and Thombre, Manish and Wang, Yizheng and Zhuang, Xiaoying and Rabczuk, Timon},
+  journal={Computer Methods in Applied Mechanics and Engineering},
+  volume={437},
+  pages={117785},
+  year={2025},
+  publisher={Elsevier}
+}
+
+@article{rojas2024robust,
+  title={Robust variational physics-informed neural networks},
+  author={Rojas, Sergio and Maczuga, Pawe{\l} and Mu{\~n}oz-Matute, Judit and Pardo, David and Paszy{\'n}ski, Maciej},
+  journal={Computer Methods in Applied Mechanics and Engineering},
+  volume={425},
+  pages={116904},
+  year={2024},
+  publisher={Elsevier}
+}
+
+@article{zang2020weak,
+  title={Weak adversarial networks for high-dimensional partial differential equations},
+  author={Zang, Yaohua and Bao, Gang and Ye, Xiaojing and Zhou, Haomin},
+  journal={Journal of Computational Physics},
+  volume={411},
+  pages={109409},
+  year={2020},
+  publisher={Elsevier}
+}
+
+@inproceedings{baez2024guaranteeing,
+  title={Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks},
+  author={Baez, Anthony and Zhang, Wang and Ma, Ziwen and Das, Subhro and Nguyen, Lam M and Daniel, Luca},
+  booktitle={NeurIPS 2024 Workshop on Data-driven and Differentiable Simulations, Surrogates, and Solvers}
+}
+
+@article{zhang2026musa,
+  title={MUSA-PINN: Multi-scale Weak-form Physics-Informed Neural Networks for Fluid Flow in Complex Geometries},
+  author={Zhang, Weizheng and Xie, Xunjie and Pan, Hao and Duan, Xiaowei and Sun, Bingteng and Du, Qiang and Lu, Lin},
+  journal={arXiv preprint arXiv:2603.08465},
+  year={2026}
+}
+
+@article{wang2025wf,
+  title={WF-PINNs: solving forward and inverse problems of burgers equation with steep gradients using weak-form physics-informed neural networks},
+  author={Wang, Xianke and Yi, Shichao and Gu, Huangliang and Xu, Jing and Xu, Wenjie},
+  journal={Scientific Reports},
+  volume={15},
+  number={1},
+  pages={40555},
+  year={2025},
+  publisher={Nature Publishing Group UK London}
+}
+
+@article{wang2022and,
+  title={When and why PINNs fail to train: A neural tangent kernel perspective},
+  author={Wang, Sifan and Yu, Xinling and Perdikaris, Paris},
+  journal={Journal of Computational Physics},
+  volume={449},
+  pages={110768},
+  year={2022},
+  publisher={Elsevier}
+}
+
+@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},
+  author={Wang, Sifan and Wang, Hanwen and Perdikaris, Paris},
+  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},
+  journal={arXiv preprint arXiv:2511.00792},
+  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,
+  title={Respecting causality for training physics-informed neural networks},
+  author={Wang, Sifan and Sankaran, Shyam and Perdikaris, Paris},
+  journal={Computer Methods in Applied Mechanics and Engineering},
+  volume={421},
+  pages={116813},
+  year={2024},
+  publisher={Elsevier}
+}
+
+
+@article{cho2023separable,
+  title={Separable physics-informed neural networks},
+  author={Cho, Junwoo and Nam, Seungtae and Yang, Hyunmo and Yun, Seok-Bae and Hong, Youngjoon and Park, Eunbyung},
+  journal={Advances in Neural Information Processing Systems},
+  volume={36},
+  pages={23761--23788},
+  year={2023}
+}
+
+@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},
+author={Rohan Arni and Carlos Blanco},
+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},
+  author={Tao, Ze and Zhao, Darui and Liu, Fujun and Xu, Ke and Hu, Xiangsheng},
+  journal={arXiv preprint arXiv:2511.12512},
+  year={2025}
+}
+
+@article{sitzmann2020implicit,
+  title={Implicit neural representations with periodic activation functions},
+  author={Sitzmann, Vincent and Martel, Julien and Bergman, Alexander and Lindell, David and Wetzstein, Gordon},
+  journal={Advances in neural information processing systems},
+  volume={33},
+  pages={7462--7473},
+  year={2020}
+}
+
+@article{jagtap2020extended,
+  title={Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations},
+  author={Jagtap, Ameya D and Karniadakis, George Em},
+  journal={Communications in Computational Physics},
+  volume={28},
+  number={5},
+  year={2020},
+  publisher={Brown Univ., Providence, RI (United States)}
+}
+
+@article{moseley2023finite,
+  title={Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations: B. Moseley et al.},
+  author={Moseley, Ben and Markham, Andrew and Nissen-Meyer, Tarje},
+  journal={Advances in Computational Mathematics},
+  volume={49},
+  number={4},
+  pages={62},
+  year={2023},
+  publisher={Springer}
+}
+
+@article{dolean2024multilevel,
+  title={Multilevel domain decomposition-based architectures for physics-informed neural networks},
+  author={Dolean, Victorita and Heinlein, Alexander and Mishra, Siddhartha and Moseley, Ben},
+  journal={Computer Methods in Applied Mechanics and Engineering},
+  volume={429},
+  pages={117116},
+  year={2024},
+  publisher={Elsevier}
+}
+
+@article{botvinick2025ab,
+  title={AB-PINNs: Adaptive-Basis Physics-Informed Neural Networks for Residual-Driven Domain Decomposition},
+  author={Botvinick-Greenhouse, Jonah and Ali, Wael H and Benosman, Mouhacine and Mowlavi, Saviz},
+  journal={arXiv preprint arXiv:2510.08924},
+  year={2025}
+}
+
+@article{bischof2025hypino,
+  title={HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions},
+  author={Bischof, Rafael and Piovar{\v{c}}i, Michal and Kraus, Michael A and Mishra, Siddhartha and Bickel, Bernd},
+  journal={arXiv preprint arXiv:2509.05117},
+  year={2025}
+}
+
+@article{wang2025transfer,
+  title={Transfer learning in physics-informed neurals networks: full fine-tuning, lightweight fine-tuning, and low-rank adaptation},
+  author={Wang, Yizheng and Bai, Jinshuai and Eshaghi, Mohammad Sadegh and Anitescu, Cosmin and Zhuang, Xiaoying and Rabczuk, Timon and Liu, Yinghua},
+  journal={International Journal of Mechanical System Dynamics},
+  volume={5},
+  number={2},
+  pages={212--235},
+  year={2025},
+  publisher={Wiley Online Library}
+}
+
+@article{chung2026hard,
+  title={Hard-constrained Physics-informed Neural Networks for Interface Problems},
+  author={Chung, Seung Whan and Castonguay, Stephen and Roy, Sumanta and Penwarden, Michael and Fu, Yucheng and Roy, Pratanu},
+  journal={arXiv preprint arXiv:2604.08453},
+  year={2026}
+}
+
+@article{li2024physical,
+  title={Physical informed neural networks with soft and hard boundary constraints for solving advection-diffusion equations using Fourier expansions},
+  author={Li, Xi'an and Deng, Jiaxin and Wu, Jinran and Zhang, Shaotong and Li, Weide and Wang, You-Gan},
+  journal={Computers \& Mathematics with Applications},
+  volume={159},
+  pages={60--75},
+  year={2024},
+  publisher={Elsevier}
+}
+
+@article{liu1989limited,
+  title={On the limited memory BFGS method for large scale optimization},
+  author={Liu, Dong C and Nocedal, Jorge},
+  journal={Mathematical programming},
+  volume={45},
+  number={1},
+  pages={503--528},
+  year={1989},
+  publisher={Springer}
+}
+
+@inproceedings{vyas2025soap,
+title={{SOAP}: Improving and Stabilizing Shampoo using Adam for Language Modeling},
+author={Nikhil Vyas and Depen Morwani and Rosie Zhao and Itai Shapira and David Brandfonbrener and Lucas Janson and Sham M. Kakade},
+booktitle={The Thirteenth International Conference on Learning Representations},
+year={2025},
+url={https://openreview.net/forum?id=IDxZhXrpNf}
+}
+
+@article{bischof2025multi,
+  title={Multi-objective loss balancing for physics-informed deep learning},
+  author={Bischof, Rafael and Kraus, Michael A},
+  journal={Computer Methods in Applied Mechanics and Engineering},
+  volume={439},
+  pages={117914},
+  year={2025},
+  publisher={Elsevier}
+}
+
+@article{wu2024ropinn,
+  title={Ropinn: Region optimized physics-informed neural networks},
+  author={Wu, Haixu and Luo, Huakun and Ma, Yuezhou and Wang, Jianmin and Long, Mingsheng},
+  journal={Advances in Neural Information Processing Systems},
+  volume={37},
+  pages={110494--110532},
+  year={2024}
+}
+
+@article{jagtap2020locally,
+  title={Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks},
+  author={Jagtap, Ameya D and Kawaguchi, Kenji and Em Karniadakis, George},
+  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
+  volume={476},
+  number={2239},
+  year={2020},
+  publisher={The Royal Society}
+}
+
+@article{lagaris1998artificial,
+  title={Artificial neural networks for solving ordinary and partial differential equations},
+  author={Lagaris, Isaac E and Likas, Aristidis and Fotiadis, Dimitrios I},
+  journal={IEEE transactions on neural networks},
+  volume={9},
+  number={5},
+  pages={987--1000},
+  year={1998},
+  publisher={IEEE}
+}
+
+@article{lu2021deepxde,
+  title={DeepXDE: A deep learning library for solving differential equations},
+  author={Lu, Lu and Meng, Xuhui and Mao, Zhiping and Karniadakis, George Em},
+  journal={SIAM review},
+  volume={63},
+  number={1},
+  pages={208--228},
+  year={2021},
+  publisher={SIAM}
+}