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Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements.
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G. Kissas, Y. Yang, E. Hwuang, W. R. Witschey, J. A. Detre, P. Perdikaris, Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks, Computer Methods in Applied Mechanics and Engineering 358 (2020) 112623
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Z. Gao, T. Tang, L. Yan, T. Zhou, Failure-informed adaptive sampling for PINNs, part ii: combining with re-sampling and subset simulation, Communications on Applied Mathematics and Computation (2023) 1–22
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H. Gao, L. Sun, J.-X. Wang, PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain, Journal of Computational Physics 428 (2021) 110079
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M. Abdar, F. Pourpanah, S. Hussain, D. Rezazadegan, L. Liu, M. Ghavamzadeh, P. Fieguth, X. Cao, A. Khosravi, U. R. Acharya, et al., A review of uncertainty quantification in deep learning: Techniques, applications and challenges, Information Fusion 76 (2021) 243–297
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L. Yang, X. Meng, G. E. Karniadakis, B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data, Journal of Computational Physics 425 (2021) 109913
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A. Daw, M. Maruf, A. Karpatne, PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics, in: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, 2021, pp. 237–247
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2021
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Z. Chen, Y. Liu, H. Sun, Physics-informed learning of governing equations from scarce data, Nature Communications 12 (1) (2021) 6136
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Z. Chen, D. Xiu, On generalized residual network for deep learning of unknown dynamical systems, Journal of Computational Physics 438 (2021) 110362
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B. Lu, C. Moya, G. Lin, NSGA-PINN: a multi-objective optimization method for physics-informed neural network training, Algorithms 16 (4) (2023) 194
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T. Zhou, X. Zhang, E. L. Droguett, A. Mosleh, A generic physics-informed neural network-based framework for reliability assessment of multi-state systems, Reliability Engineering & System Safety 229 (2023) 108835
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J. Yao, C. Su, Z. Hao, S. Liu, H. Su, J. Zhu, Multiadam: Parameter-wise scale-invariant optimizer for multiscale training of physics-informed neural networks, in: International Conference on Machine Learning, PMLR, 2023, pp. 39702–39721
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J. Müller, M. Zeinhofer, Achieving high accuracy with pinns via energy natural gradient descent, in: International Conference on Machine Learning, PMLR, 2023, pp. 25471–25485
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Q. Chen, Q. Ye, W. Zhang, H. Li, X. Zheng, TGM-Nets: A deep learning framework for enhanced forecasting of tumor growth by integrating imaging and modeling, Engineering Applications of Artificial Intelligence 126 (2023) 106867
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M. Ragoza, K. Batmanghelich, Physics-Informed Neural Networks for Tissue Elasticity Reconstruction in Magnetic Resonance Elastography, Medical Image Computing and Computer-Assisted Intervention (MICCAI) 14229 (2023) 333–343
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M. Movahhedi, X.-Y. Liu, B. Geng, C. Elemans, Q. Xue, J.-X. Wang, X. Zheng, Predicting 3D soft tissue dynamics from 2D imaging using physics informed neural networks, Communications Biology 6 (1) (2023) 541
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K. Sel, A. Mohammadi, R. I. Pettigrew, R. Jafari, Physics-informed neural networks for modeling physiological time series for cuffless blood pressure estimation, npj Digital Medicine 6 (1) (2023) 110
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J. F. Du Toit, R. Laubscher, Evaluation of Physics-Informed Neural Network Solution Accuracy and Efficiency for Modeling Aortic Transvalvular Blood Flow, Mathematical and Computational Applications 28 (2) (2023) 62
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N. V. Jagtap, M. K. Mudunuru, K. B. Nakshatrala, CoolPINNs: A physics-informed neural network modeling of active cooling in vascular systems, Applied Mathematical Modelling 122 (2023) 265–287
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F. Heldmann, S. Berkhahn, M. Ehrhardt, K. Klamroth, Pinn training using biobjective optimization: The trade-off between data loss and residual loss, Journal of Computational Physics 488 (2023) 112211
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M. A. Calicchia, R. Mittal, J.-H. Seo, R. Ni, Reconstructing the pressure field around swimming fish using a physics-informed neural network, Journal of Experimental Biology 226 (8) (2023)
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Z. Wu, H. Wang, C. He, B. Zhang, T. Xu, Q. Chen, The application of physics-informed machine learning in multiphysics modeling in chemical engineering, Industrial & Engineering Chemistry Research 62 (44) (2023) 18178–18204
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C. P. Batuwatta-Gamage, C. Rathnayaka, H. C. Karunasena, H. Jeong, A. Karim, Y. T. Gu, A novel physics-informed neural networks approach (PINN-MT) to solve mass transfer in plant cells during drying, Biosystems Engineering 230 (2023) 219–241
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W. Xuan, H. Lou, S. Fu, Z. Zhang, N. Ding, Physics-informed deep learning method for the refrigerant filling mass flow metering, Flow Measurement and Instrumentation 93 (2023) 102418
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Q. Hou, H. Du, Z. Sun, J. Wang, X. Wang, J. Wei, PINN-CDR: A neural network-based simulation tool for convection-diffusion-reaction systems, International Journal of Intelligent Systems 2023 (1) (2023) 2973249
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Z. Sun, H. Du, C. Miao, Q. Hou, A physics-informed neural network based simulation tool for reacting flow with multicomponent reactants, Advances in Engineering Software 185 (2023) 103525
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R. Patel, S. Bhartiya, R. Gudi, Optimal temperature trajectory for tubular reactor using physics informed neural networks, Journal of Process Control 128 (2023) 103003
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M. H. Elhareef, Z. Wu, Physics-informed neural network method and application to nuclear reactor calculations: A pilot study, Nuclear Science and Engineering 197 (4) (2023) 601–622
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Y.-T. Liu, C.-Y. Wu, T. Chen, Y. Yao, Multi-fidelity surrogate modeling for chemical processes with physics-informed neural networks, in: Computer Aided Chemical Engineering, Vol. 52, Elsevier, 2023, pp. 57–63
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F. Antonello, J. Buongiorno, E. Zio, Physics informed neural networks for surrogate modeling of accidental scenarios in nuclear power plants, Nuclear Engineering and Technology 55 (9) (2023) 3409–3416
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K. Liu, K. Luo, Y. Cheng, A. Liu, H. Li, J. Fan, S. Balachandar, Surrogate modeling of parameterized multi-dimensional premixed combustion with physics-informed neural networks for rapid exploration of design space, Combustion and Flame 258 (2023) 113094
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S.-Y. Tang, Y.-H. Yuan, Y.-C. Chen, S.-J. Yao, Y. Wang, D.-Q. Lin, Physics-informed neural networks to solve lumped kinetic model for chromatography process, Journal of Chromatography A 1708 (2023) 464346
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Y.-H. Tseng, T.-S. Lin, W.-F. Hu, M.-C. Lai, A cusp-capturing pinn for elliptic interface problems, Journal of Computational Physics 491 (2023) 112359
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A. F. Psaros, X. Meng, Z. Zou, L. Guo, G. E. Karniadakis, Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons, Journal of Computational Physics 477 (2023) 111902
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X. Jiang, X. Wang, Z. Wen, E. Li, H. Wang, Practical uncertainty quantification for space-dependent inverse heat conduction problem via ensemble physics-informed neural networks, International Communications in Heat and Mass Transfer 147 (2023) 106940
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X. Meng, Variational inference in neural functional prior using normalizing flows: application to differential equation and operator learning problems, Applied Mathematics and Mechanics 44 (7) (2023) 1111–1124
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M. Yin, Z. Zou, E. Zhang, C. Cavinato, J. D. Humphrey, G. E. Karniadakis, A generative modeling framework for inferring families of biomechanical constitutive laws in data-sparse regimes, Journal of the Mechanics and Physics of Solids 181 (2023) 105424
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S. Mishra, R. Molinaro, Estimates on the generalization error of physics-informed neural networks for approximating PDEs, IMA Journal of Numerical Analysis 43 (1) (2023) 1–43
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2023
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R. Hu, Q. Lin, A. Raydan, S. Tang, Higher-order error estimates for physics-informed neural networks approximating the primitive equations, Partial Differential Equations and Applications 4 (4) (2023) 34
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Y. Shin, Z. Zhang, G. E. Karniadakis, Error estimates of residual minimization using neural networks for linear PDEs, Journal of Machine Learning for Modeling and Computing 4 (4) (2023)
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D. N. Tanyu, J. Ning, T. Freudenberg, N. Heilenkötter, A. Rademacher, U. Iben, P. Maass, Deep learning methods for partial differential equations and related parameter identification problems, Inverse Problems 39 (10) (2023) 103001
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