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Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling.
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C. R. Gin, D. E. Shea, S. L. Brunton, and J. N. Kutz, “Deepgreen: deep learning of green’s functions for nonlinear boundary value problems,” Scientific Reports , vol. 11, pp. 1–14, 2021
2021
Later among the works it cites.
S. Cuomo, V. S. Di Cola, F. Giampaolo, G. Rozza, M. Raissi, and F. Piccialli, “Scientific machine learning through physics–informed neural networks: Where we are and what’s next,” Journal of Scientific Computing , vol. 92, no. 88, pp. 1–62, 2022
2022
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S. Lanthaler, M. Siddhartha, and G. E. Karniadakis, “Error estimates for deeponets: a deep learning framework in infinite dimensions,” Transactions of Mathematics and its Applications , vol. 6, no. 1, p. tnac001, 2022
2022
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M. Yin, E. Zhang, Y. Yu, and G. E. Karniadakis, “Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems,” Computer Methods in Applied Mechanics and Engineering , vol. available online, pp. 1–26, 2022
2022
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T. Zhang, K. Innanen, and D. Trad, “Learning the elastic wave equation with fourier neural operators,” in geoconvention 2022 , 2022, pp. 1–5
2022
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J. D. Osorio, Z. Wang, G. Karniadakis, S. Cai, C. Chryssostomidis, M. Panwar, and R. Hovsapian, “Forecasting solar-thermal systems performance under transient operation using a data-driven machine learning approach based on the deep operator network architecture,” Energy Conversion and Management , vol. 252, pp. 1–14, 2022
2022
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B. Yan, B. Chen, D. R. Harp, W. Jia, and R. J. Pawar, “A robust deep learning workflow to predict multiphase flow behavior during geological co2 sequestration injection and post-injection periods,” Journal of Hydrology , vol. 607, pp. 1–10, 2022
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L. Wang, J. Xia, Y. Luo, and A. Bian, “Progress and prospect of surface-wave imaging techniques in near-surface applications,” Reviews of Geophysics and Planetary Physics , vol. 53, no. 0, pp. 1–43, 2022
2022
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X. Zha, H. Chen, T. Li, Z. Qiu, and Y. Feng, “Specific emitter identification based on complex fourier neural network,” IEEE Communications Letters , vol. 26, no. 3, pp. 592–596, 2022
2022
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K. M. Gitushi, R. Ranade, and T. Echekki, “Investigation of deep learning methods for efficient high-fidelity simulations in turbulent combustion,” Combustion and Flame , vol. 236, pp. 1–13, 2022
2022
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C. Song and Y. Wang, “High-frequency wavefield extrapolation using the fourier neural operator,” Journal of Geophysics and Engineering , vol. 19, pp. 269–282, 2022
2022
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A. G. Özbay and S. Laizet, “Deep learning fluid flow reconstruction around arbitrary two-dimensional objects from sparse sensors using conformal mappings,” AIP Advances , vol. 12, pp. 1–22, 2022
2022
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P. Hu, W. Wang, Y. Zhu, and L. Hong, “Revealing hidden dynamics from time-series data by odenet,” Journal of Computational Physics , vol. 461, pp. 1–15, 2022
2022
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S. Mishra and R. Molinaro, “Estimates on the generalization error of physics-informed neural networks for approximating pdes,” IMA Journal of Numerical Analysis , vol. 00, pp. 1–43, 2022
2022
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S. Mishra and R. Molinaro, “Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for pdes,” IMA Journal of Numerical Analysis , vol. 42, no. 2, pp. 981–1022, 2022
2022
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L. Lu, X. Meng, S. Cai, Z. Mao, S. Goswami, Z. Zhang, and G. E. Karniadakis, “A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data,” Computer Methods in Applied Mechanics and Engineering , vol. 393, pp. 1–35, 2022
2022
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J. N. Kutz and S. L. Brunton, “Parsimony as the ultimate regularizer for physics-informed machine learning,” Nonlinear Dynamics , vol. 107, pp. 1801–1817, 2022
2022
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R. G. Patel, I. Manickam, N. A. Trask, M. A. Wood, M. Lee, I. Tomas, and E. C. Cyr, “Thermodynamically consistent physics-informed neural networks for hyperbolic systems,” Journal of Computational Physics , vol. 449, pp. 1–24, 2022
2022
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C. Li, Y. Yang, H. Liang, and B. Wu, “Learning high-order geometric flow based on the level set method,” Nonlinear Dynamics , vol. 107, pp. 2429–2445, 2022
2022
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A. D. Jagtap, Y. Shin, K. Kawaguchi, and G. E. Karniadakis, “Deep kronecker neural networks: A general framework for neural networks with adaptive activation functions,” Neurocomputing , vol. 468, pp. 165–180, 2022
2022
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P. Ren, C. Rao, Y. Liu, J.-X. Wang, and H. Sun, “Phycrnet: Physics-informed convolutional-recurrent network for solving spatiotemporal pdes,” Computer Methods in Applied Mechanics and Engineering , vol. 389, pp. 1–21, 2022
2022
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Y. Gao and M. K. Ng, “Wasserstein generative adversarial uncertainty quantification in physics-informed neural networks,” Journal of Computational Physics , vol. 463, pp. 1–28, 2022
2022
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X. Meng, L. Yang, Z. Mao, J. del Águila Ferrandis, and G. E. Karniadakis, “Learning functional priors and posteriors from data and physics,” Journal of Computational Physics , vol. 457, pp. 1–22, 2022
2022
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G. Wen, Z. Li, K. Azizzadenesheli, A. Anandkumar, and S. M. Benson, “U-fno—an enhanced fourier neural operator-based deep-learning model for multiphase flow,” Advances in Water Resources , vol. 163, pp. 1–14, 2022
2022
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W. Peng, Z. Yuan, and J. Wang, “Attention-enhanced neural network models for turbulence simulation,” Physics of Fluids , vol. 34, no. 2, pp. 1–17, 2022
2022
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A. Kovacs, L. Exl, A. Kornell, J. Fischbacher, M. Hovorka, M. Gusenbauer, L. Breth, H. Oezelt, M. Yano, N. Sakuma, A. Kinoshita, T. Shoji, A. Kato, and T. Schrefl, “Conditional physics informed neural networks,” Communications in Nonlinear Science and Numerical Simulation , vol. 104, pp. 1–15, 2022
2022
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P. Hadorn, Shift-DeepONet: Extending Deep Operator Networks for Discontinuous Output Functions . Master Thesis at Swiss Federal Institute of Technology Zurich, 2022
2022
Closest in time.
C. Hutter, R. Gül, and H. Bölcskei, “Metric entropy limits on recurrent neural network learning of linear dynamical systems,” Applied and Computational Harmonic Analysis , vol. 59, pp. 198–223, 2022
2022
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S. Zeng, Z. Zhang, and Q. Zou, “Adaptive deep neural networks methods for high-dimensional partial differential equations,” Journal of Computational Physics , vol. 463, pp. 1–16, 2022
2022
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S. Wang, X. Yu, and P. Perdikaris, “When and why pinns fail to train: A neural tangent kernel perspective,” Journal of Computational Physics , vol. 449, pp. 1–28, 2022
2022
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R. Mattey and S. Ghosh, “A novel sequential method to train physics informed neural networks for allen cahn and cahn hilliard equations,” Computer Methods in Applied Mechanics and Engineering , vol. 390, pp. 1–29, 2022
2022
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S. Goswami, M. Yin, Y. Yu, and G. E. Karniadakis, “A physics-informed variational deeponet for predicting crack path in quasi-brittle materials,” Computer Methods in Applied Mechanics and Engineering , vol. 391, pp. 1–29, 2022
2022
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H. Wang, R. Planas, A. Chandramowlishwaran, and R. Bostanabad, “Mosaic flows: A transferable deep learning framework for solving pdes on unseen domains,” Computer Methods in Applied Mechanics and Engineering , vol. 389, pp. 1–26, 2022
2022
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R. Gupta and R. Jaiman, “A hybrid partitioned deep learning methodology for moving interface and fluid–structure interaction,” Computers and Fluids , vol. 233, pp. 1–24, 2022
2022
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P. Jin, S. Meng, and L. Lu, “Mionet: Learning multiple-input operators via tensor product,” SIAM Journal on Scientific Computing , vol. 44, no. 6, pp. A3490–A3514, 2022
2022
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L. Lu, R. Pestourie, S. G. Johnson, and G. Romano, “Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport,” Physical Review Research , vol. 4, pp. 1–15, 2022
2022
Closest in time.