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As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.
Neural network method for solving partial differential equations
Aarts, L. P. and der Veer, P. V · 2004
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The graph neural network model
Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., and Monfardini, G · 2009
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Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2014
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Interaction networks for learning about objects, relations and physics
Battaglia, P. W., Pascanu, R., Lai, M., Rezende, D. J., and Kavukcuoglu, K · 2016
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Convolutional neural networks on graphs with fast localized spectral filtering
Defferrard, M., Bresson, X., and Vandergheynst, P · 2016
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Solving PDEs in python: the FEniCS tutorial I
Langtangen, H. P. and Logg, A · 2017
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Prediction of aerodynamic flow fields using convolutional neural networks
Afshar, Y., Bhatnagar, S., Pan, S., Duraisamy, K., and Kaushik, S · 2019
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Graph element networks: adaptive, structured computation and memory
Alet, F., Jeewajee, A. K., Bauzá, M., Rodriguez, A., Lozano-Perez, T., and Kaelbling, L. P · 2019
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Falcon, W. and the PyTorch Lightning team · 2019
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Fast graph representation learning with PyTorch Geometric
Fey, M. and Lenssen, J. E · 2019
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Learning neural pde solvers with convergence guarantees
Hsieh, J.-T., Zhao, S., Eismann, S., Mirabella, L., and Ermon, S · 2019
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Pytorch: An imperative style, high-performance deep learning library
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S · 2019
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Combining differentiable pde solvers and graph neural networks for fluid flow prediction
de Avila Belbute-Peres, F., Economon, T. D., and Kolter, J. Z · 2020
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A physics-informed neural network framework for pdes on 3d surfaces: Time independent problems
Fang, Z. and Zhan, J. Z · 2020
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Neural operator: Graph kernel network for partial differential equations
Li, Z.-Y., Kovachki, N. B., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2020
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Molecule attention transformer, 2020
Maziarka, L., Danel, T., Mucha, S., Rataj, K., Tabor, J., and Jastrzebski, S · 2020
Graph neural networks for laminar flow prediction around random two-dimensional shapes
Chen, J., Hachem, E., and Viquerat, J · 2021
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Improving molecular graph neural network explainability with orthonormalization and induced sparsity, 2021
Henderson, R., Clevert, D.-A., and Montanari, F · 2021
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Highly accurate protein structure prediction with alphafold
Jumper, J. M., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., Tunyasuvunakool, K., Bates, R., Zídek, A., Potapenko, A., Bridgland, A., Meyer, C., Kohl, S. A. A., Ballard, A., Cowie, A., Romera-Paredes, B., Nikolov, S., Jain, R., Adler, J., Back, T., Petersen, S., Reiman, D. A., Clancy, E., Zielinski, M., Steinegger, M., Pacholska, M., Berghammer, T., Bodenstein, S., Silver, D., Vinyals, O., Senior, A. W., Kavukcuoglu, K., Kohli, P., and Hassabis, D · 2021
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Fourier neural operator for parametric partial differential equations
Li, Z.-Y., Kovachki, N. B., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2021
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Neural network approach for solving nonlocal boundary value problems
Palade, V., Petrov, M. S., and Todorov, T. D · 2020
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Learning to simulate complex physics with graph networks
Sanchez-Gonzalez, A., Godwin, J., Pfaff, T., Ying, R., Leskovec, J., and Battaglia, P. W · 2020
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Fea-net: A physics-guided data-driven model for efficient mechanical response prediction
Yao, H., Gao, Y., and Liu, Y · 2020
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Combinatorial optimization and reasoning with graph neural networks
Cappart, Q., Chételat, D., Khalil, E., Lodi, A., Morris, C., and Veličković, P · 2021
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Grand: Graph neural diffusion
Chamberlain, B. P., Rowbottom, J. R., Gorinova, M. I., Webb, S., Rossi, E., and Bronstein, M. M · 2021
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Mayr, A., Lehner, S., Mayrhofer, A., Kloss, C., Hochreiter, S., and Brandstetter, J · 2021
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Learning mesh-based simulation with graph networks
Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A., and Battaglia, P. W · 2021
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Neural stochastic partial differential equations
Salvi, C. and Lemercier, M · 2021
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Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes, 2021
Scroggs, M. W., Dokken, J. S., Richardson, C. N., and Wells, G. N · 2021
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Message passing neural pde solvers
Brandstetter, J., Worrall, D. E., and Welling, M · 2022
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Physics-informed neural networks (pinns) for fluid mechanics: A review
Cai, S., Mao, Z., Wang, Z., Yin, M., and Karniadakis, G. E · 2022
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