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Neural operators have emerged as powerful surrogates for modeling complex physical problems.
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Multi-scale deep neural networks for solving high dimensional pdes,
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,
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Fourier features let networks learn high frequency functions in low dimensional domains,
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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks,
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Learning nonlinear operators via deeponet based on the universal approximation theorem of operators,
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Accelerating phase-field-based microstructure evolution predictions via surrogate models trained by machine learning methods,
D. Montes de Oca Zapiain, J. A. Stewart, R. Dingreville, · 2021
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Operator learning for predicting multiscale bubble growth dynamics,
C. Lin, Z. Li, L. Lu, S. Cai, M. Maxey, G. E. Karniadakis, · 2021
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On the eigenvector bias of fourier feature networks: From regression to solving multi-scale pdes with physics-informed neural networks,
S. Wang, H. Wang, P. Perdikaris, · 2021
Super-resolution neural operator,
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Rethinking materials simulations: Blending direct numerical simulations with neural operators,
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Reproducing activation function for deep learning,
S. Liang, L. Lyu, C. Wang, H. Yang, · 2021
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Transformer for partial differential equations’ operator learning,
Z. Li, K. Meidani, A. B. Farimani, · 2022
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Learning two-phase microstructure evolution using neural operators and autoencoder architectures,
V. Oommen, K. Shukla, S. Goswami, R. Dingreville, G. E. Karniadakis, · 2022
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Flash-x: A multiphysics simulation software instrument,
A. Dubey, K. Weide, J. O’Neal, A. Dhruv, S. Couch, J. A. Harris, T. Klosterman, R. Jain, J. Rudi, B. Messer, et al., · 2022
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Deep-learning-based super-resolution reconstruction of high-speed imaging in fluids,
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Flash-x: A multiphysics simulation software instrument,
A. Dubey, K. Weide, J. O’Neal, A. Dhruv, S. Couch, J. A. Harris, T. Klosterman, R. Jain, J. Rudi, B. Messer, et al., · 2022
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P. Wang, W. Zheng, T. Chen, Z. Wang, · 2022
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V. Oommen, K. Shukla, S. Desai, R. Dingreville, G. E. Karniadakis, · 2024
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Bubbleml: A multiphase multiphysics dataset and benchmarks for machine learning,
S. M. S. Hassan, A. Feeney, A. Dhruv, J. Kim, Y. Suh, J. Ryu, Y. Won, A. Chandramowlishwaran, · 2024
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Mitigating spectral bias for the multiscale operator learning,
X. Liu, B. Xu, S. Cao, L. Zhang, · 2024
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From pinns to pikans: Recent advances in physics-informed machine learning,
J. D. Toscano, V. Oommen, A. J. Varghese, Z. Zou, N. A. Daryakenari, C. Wu, G. E. Karniadakis, · 2024
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Blending neural operators and relaxation methods in pde numerical solvers,
E. Zhang, A. Kahana, A. Kopaničáková, E. Turkel, R. Ranade, J. Pathak, G. E. Karniadakis, · 2024
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High-flexibility reconstruction of small-scale motions in wall turbulence using a generalized zero-shot learning,
H. Wu, K. Zhang, D. Zhou, W.-L. Chen, Z. Han, Y. Cao, · 2024
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Generative ai for fast and accurate statistical computation of fluids,
R. Molinaro, S. Lanthaler, B. Raonić, T. Rohner, V. Armegioiu, Z. Y. Wan, F. Sha, S. Mishra, L. Zepeda-Núñez, · 2024
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A generative super-resolution model for enhancing tropical cyclone wind field intensity and resolution,
J. W. Lockwood, A. Gori, P. Gentine, · 2024
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V. Oommen, A. Bora, Z. Zhang, G. E. Karniadakis, · 2024
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Symbolic discovery of optimization algorithms,
X. Chen, C. Liang, D. Huang, E. Real, K. Wang, H. Pham, X. Dong, T. Luong, C.-J. Hsieh, Y. Lu, et al., · 2024
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R. Wan, E. Kharazmi, M. S. Triantafyllou, G. E. Karniadakis, · 2025
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Y. Jiang, Z. Li, Y. Wang, H. Yang, J. Wang, · 2025
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Z.-Q. J. Xu, L. Zhang, W. Cai, · 2025
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Scaling the predictions of multiphase flow through porous media using operator learning,
N. Jain, S. Roy, H. Kodamana, P. Nair, · 2025
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V. Oommen, A. Bora, Z. Zhang, G. E. Karniadakis, Data for “integrating neural operators with diffusion models improves spectral representation in turbulence modeling" (kolmogorov flow case), 2025. URL: https://doi.org/10.6084/m9.figshare.28250960.v1 . doi: 10.6084/m9.figshare.28250960.v1
2025
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