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Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions.
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S. Cai, Z. Mao, Z. Wang, M. Yin, and G. E. Karniadakis, “Physics-informed neural networks (pinns) for fluid mechanics: A review,” Acta Mechanica Sinica 37
2021
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C. J. Arthurs and A. P. King, “Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the navier-stokes equations,” Journal of Computational Physics 438
2021
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X. Jin, S. Cai, H. Li, and G. E. Karniadakis, “Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations,” Journal of Computational Physics 426
2021
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E. Kharazmi, Z. Zhang, and G. E. Karniadakis, “hp-vpinns: Variational physics-informed neural networks with domain decomposition,” Computer Methods in Applied Mechanics and Engineering 374
2021
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M. Mahmoudabadbozchelou, G. E. Karniadakis, and S. Jamali, “nn-pinns: Non-newtonian physics-informed neural networks for complex fluid modeling,” Soft Matter 18
2022
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H. Eivazi, M. Tahani, P. Schlatter, and R. Vinuesa, “Physics-informed neural networks for solving reynolds-averaged navier–stokes equations,” Physics of Fluids 34
2022
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V. Kag, K. Seshasayanan, and V. Gopinath, “Physics-informed data based neural networks for two-dimensional turbulence,” Physics of Fluids 34
2022
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S. Li and X. Feng, “Dynamic weight strategy of physics-informed neural networks for the 2d navier–stokes equations,” Entropy 24
2022
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S. Wassing, S. Langer, and P. Bekemeyer, “Physics-informed neural networks for parametric compressible euler equations,” Computers & Fluids 270
2024
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L. Gu, S. Qin, L. Xu, and R. Chen, “Physics-informed neural networks with domain decomposition for the incompressible navier–stokes equations,” Physics of Fluids 36
2024
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2024
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T. Anandh, D. Ghose, and S. Ganesan, “FastVPINNs: An efficient tensor-based Python library for solving partial differential equations using hp-Variational Physics Informed Neural Networks,” Journal of Open Source Software 9
2024
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D. Ghose, T. Anandh, and S. Ganesan, “Fastvpinns: A fast, versatile and robust variational pinns framework for forward and inverse problems in science,” in ICLR 2024 Workshop on AI4DifferentialEquations In Science (2024)
2024
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D. Jalili, S. Jang, M. Jadidi, G. Giustini, A. Keshmiri, and Y. Mahmoudi, “Physics-informed neural networks for heat transfer prediction in two-phase flows,” International Journal of Heat and Mass Transfer 221
2024
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