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| 1 | +@article{haghighat2021sciann, |
| 2 | + title={SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks}, |
| 3 | + author={Haghighat, Ehsan and Juanes, Ruben}, |
| 4 | + journal={Computer Methods in Applied Mechanics and Engineering}, |
| 5 | + volume={373}, |
| 6 | + pages={113552}, |
| 7 | + year={2021}, |
| 8 | + publisher={Elsevier}, |
| 9 | + url={https://www.sciencedirect.com/science/article/pii/S0045782520307374} |
| 10 | +} |
| 11 | + |
| 12 | +@article{raissi2019physics, |
| 13 | + title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations}, |
| 14 | + author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E}, |
| 15 | + journal={Journal of Computational Physics}, |
| 16 | + volume={378}, |
| 17 | + pages={686--707}, |
| 18 | + year={2019}, |
| 19 | + publisher={Elsevier}, |
| 20 | + url={https://www.sciencedirect.com/science/article/pii/S0021999118307125} |
| 21 | +} |
| 22 | + |
| 23 | +@article{wang2020gp, |
| 24 | + title={Understanding and mitigating gradient pathologies in physics-informed neural networks}, |
| 25 | + author={Wang, Sifan and Teng, Yujun and Perdikaris, Paris}, |
| 26 | + journal={arXiv preprint arXiv:2001.04536}, |
| 27 | + year={2020}, |
| 28 | + url={https://arxiv.org/abs/2001.04536} |
| 29 | +} |
| 30 | + |
| 31 | +@article{wang2020ntk, |
| 32 | + title={When and why PINNs fail to train: A neural tangent kernel perspective}, |
| 33 | + author={Wang, Sifan and Yu, Xinling and Perdikaris, Paris}, |
| 34 | + journal={arXiv preprint arXiv:2007.14527}, |
| 35 | + year={2020}, |
| 36 | + url={https://arxiv.org/abs/2007.14527} |
| 37 | +} |
| 38 | + |
| 39 | +@article{li2017visualizing, |
| 40 | + title={Visualizing the loss landscape of neural nets}, |
| 41 | + author={Li, Hao and Xu, Zheng and Taylor, Gavin and Studer, Christoph and Goldstein, Tom}, |
| 42 | + journal={arXiv preprint arXiv:1712.09913}, |
| 43 | + year={2017}, |
| 44 | + url={https://arxiv.org/abs/1712.09913} |
| 45 | +} |
| 46 | + |
| 47 | +@article{wang2020eigenvector, |
| 48 | + title={On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks}, |
| 49 | + author={Wang, Sifan and Wang, Hanwen and Perdikaris, Paris}, |
| 50 | + journal={arXiv preprint arXiv:2012.10047}, |
| 51 | + year={2020}, |
| 52 | + url={https://arxiv.org/abs/2012.10047} |
| 53 | +} |
| 54 | + |
| 55 | +@article{jagtap2020locally, |
| 56 | + title={Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks}, |
| 57 | + author={Jagtap, Ameya D and Kawaguchi, Kenji and Em Karniadakis, George}, |
| 58 | + journal={Proceedings of the Royal Society A}, |
| 59 | + volume={476}, |
| 60 | + number={2239}, |
| 61 | + pages={20200334}, |
| 62 | + year={2020}, |
| 63 | + publisher={The Royal Society}, |
| 64 | + url={https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2020.0334} |
| 65 | +} |
| 66 | + |
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