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Physics-informed Neural Networks (PINNs) have recently achieved remarkable progress in solving Partial Differential Equations (PDEs) in various fields by minimizing a weighted sum of PDE loss and boundary loss.
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Raissi, M., Perdikaris, P., and Karniadakis, G. E · 2019
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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
Zhu, Y., Zabaras, N., Koutsourelakis, P.-S., and Perdikaris, P · 2019
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Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4d flow mri data using physics-informed neural networks
Kissas, G., Yang, Y., Hwuang, E., Witschey, W. R., Detre, J. A., and Perdikaris, P · 2020
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Self-adaptive physics-informed neural networks using a soft attention mechanism
McClenny, L. and Braga-Neto, U · 2020
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Accelerating physics-informed neural network training with prior dictionaries
Peng, W., Zhou, W., Zhang, J., and Yao, W · 2020
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Lu, L., Meng, X., Mao, Z., and Karniadakis, G. E · 2021
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Understanding and mitigating gradient flow pathologies in physics-informed neural networks
Wang, S., Teng, Y., and Perdikaris, P · 2021
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A physics-informed neural network technique based on a modified loss function for computational 2d and 3d solid mechanics
Bai, J., Rabczuk, T., Gupta, A., Alzubaidi, L., and Gu, Y · 2022
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Error analysis for physics-informed neural networks (pinns) approximating kolmogorov pdes
De Ryck, T. and Mishra, S · 2022
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Error estimates for physics informed neural networks approximating the navier-stokes equations
De Ryck, T., Jagtap, A. D., and Mishra, S · 2022
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Raissi, M., Yazdani, A., and Karniadakis, G. E · 2020
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Physics-informed neural networks for cardiac activation mapping
Sahli Costabal, F., Yang, Y., Perdikaris, P., Hurtado, D. E., and Kuhl, E · 2020
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Error estimates of residual minimization using neural networks for linear pdes
Shin, Y., Zhang, Z., and Karniadakis, G. E · 2020
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Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
Sun, L., Gao, H., Pan, S., and Wang, J.-X · 2020
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Solving allen-cahn and cahn-hilliard equations using the adaptive physics informed neural networks
Wight, C. L. and Zhao, J · 2020
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Gradient surgery for multi-task learning
Yu, T., Kumar, S., Gupta, A., Levine, S., Hausman, K., and Finn, C · 2020
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Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., and Yang, L · 2021
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Is L 2 L^{2} physics-informed loss always suitable for training physics-informed neural network?
Wang, C., Li, S., He, D., and Wang, L
Cited in the paper.
Cophy-pgnn: Learning physics-guided neural networks with competing loss functions for solving eigenvalue problems
Elhamod, M., Bu, J., Singh, C., Redell, M., Ghosh, A., Podolskiy, V., Lee, W.-C., and Karpatne, A · 2022
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Physics-informed machine learning: A survey on problems, methods and applications
Hao, Z., Liu, S., Zhang, Y., Ying, C., Feng, Y., Su, H., and Zhu, J · 2022
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Dynamic weight strategy of physics-informed neural networks for the 2d navier–stokes equations
Li, S. and Feng, X · 2022
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Helmholtz equation — Wikipedia, the free encyclopedia
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Poisson’s equation — Wikipedia, the free encyclopedia
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