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We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks.
Lu, L., Jin, P., and Karniadakis, G. E · 1910
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Neural operator: Graph kernel network for partial differential equations
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2003
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Fourier neural operator for parametric partial differential equations
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2010
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Batch normalization: Accelerating deep network training by reducing internal covariate shift
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U-net: Convolutional networks for biomedical image segmentation
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Layer normalization
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He, K., Zhang, X., Ren, S., and Sun, J · 2016
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Neural message passing for quantum chemistry
Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., and Dahl, G. E · 2017
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Relational inductive biases, deep learning, and graph networks
Battaglia, P. W., Hamrick, J. B., Bapst, V., Sanchez-Gonzalez, A., Zambaldi, V., Malinowski, M., Tacchetti, A., Raposo, D., Santoro, A., Faulkner, R., et al · 2018
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The deep ritz method: A deep learning-based numerical algorithm for solving variational problems
E, W. and Yu, B · 2018
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Sparse identification of nonlinear dynamics for model predictive control in the low-data limit
Kaiser, E., Kutz, J. N., and Brunton, S. L · 2018
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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 · 2018
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Graph networks as learnable physics engines for inference and control
Sanchez-Gonzalez, A., Heess, N., Springenberg, J. T., Merel, J., Riedmiller, M., Hadsell, R., and Battaglia, P · 2018
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Dgm: A deep learning algorithm for solving partial differential equations
Sirignano, J. and Spiliopoulos, K · 2018
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Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification
Zhu, Y. and Zabaras, N · 2018
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Graph element networks: adaptive, structured computation and memory
Alet, F., Jeewajee, A. K., Villalonga, M. B., Rodriguez, A., Lozano-Perez, T., and Kaelbling, L · 2019
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Bhatnagar, S., Afshar, Y., Pan, S., Duraisamy, K., and Kaushik, S · 2019
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Multi-fidelity physics-constrained neural network and its application in materials modeling
Liu, D. and Wang, Y · 2019
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Pde-net 2.0: Learning pdes from data with a numeric-symbolic hybrid deep network
Long, Z., Lu, Y., and Dong, B · 2019
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Graph transformer networks
Yun, S., Jeong, M., Kim, R., Kang, J., and Kim, H. J · 2019
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Physics-informed autoencoder for solving nonlinear partial differential equations
Zhu, J., Zou, Y., and Karniadakis, G. E · 2019
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Machine learning for fluid mechanics
Brunton, S. L., Noack, B. R., and Koumoutsakos, P · 2020
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A generalization of transformer networks to graphs
Dwivedi, V. P. and Bresson, X · 2020
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Limitations of physics informed machine learning for nonlinear two-phase transport in porous media
Fuks, O. and Tchelepi, H. A · 2020
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Learning continuous-time pdes from sparse data with graph neural networks
Iakovlev, V., Heinonen, M., and Lähdesmäki, H · 2020
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Transformers for modeling physical systems
Geneva, N. and Zabaras, N · 2022
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Adaptive fourier neural operators: Efficient token mixers for transformers, 2022
Guibas, J., Mardani, M., Li, Z., Tao, A., Anandkumar, A., and Catanzaro, B · 2022
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Predicting physics in mesh-reduced space with temporal attention
Han, X., Gao, H., Pfaff, T., Wang, J.-X., and Liu, L.-P · 2022
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Physics-embedded neural networks: Graph neural pde solvers with mixed boundary conditions
Horie, M. and Mitsume, N · 2022
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Learning operators with coupled attention
Kissas, G., Seidman, J. H., Guilhoto, L. F., Preciado, V. M., Pappas, G. J., and Perdikaris, P · 2022
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Graph neural network-accelerated lagrangian fluid simulation
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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
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Multiwavelet-based operator learning for differential equations
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Learned simulators for turbulence
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Pdebench: An extensive benchmark for scientific machine learning
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Gnot: A general neural operator transformer for operator learning, 2023
Hao, Z., Wang, Z., Su, H., Ying, C., Dong, Y., Liu, S., Cheng, Z., Song, J., and Zhu, J · 2023
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Janny, S., Béneteau, A., Nadri, M., Digne, J., Thome, N., and Wolf, C · 2023
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Space and time continuous physics simulation from partial observations, 2024
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