Fetching the paper…
Reading the bibliography…
Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems.
Developments in obtaining transient response using fourier transforms: Part i: Gibbs phenomena and fourier integrals
Day, S. J., Mullineux, N., and Reed, J · 1965
Earlier work this paper cites.
The fast Fourier transform and its applications
Brigham, E. O · 1988
Earlier work this paper cites.
Knowledge-based modeling of material behavior with neural networks
Ghaboussi, J., Garrett Jr, J., and Wu, X · 1991
Earlier work this paper cites.
An augmented Lagrangian treatment of contact problems involving friction
Simo, J. C. and Laursen, T. A · 1992
Earlier work this paper cites.
On the gibbs phenomenon and its resolution
Gottlieb, D. and Shu, C.-W · 1997
Earlier work this paper cites.
Autoprogressive training of neural network constitutive models
Ghaboussi, J., Pecknold, D. A., Zhang, M., and Haj-Ali, R. M · 1998
Earlier work this paper cites.
An arbitrary Lagrangian Eulerian finite element approach for fluid-structure interaction phenomena
Kuhl, E., Hulshoff, S., and de Borst, R · 2003
Earlier work this paper cites.
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
Earlier work this paper cites.
Dynamic fracture modeling with a meshfree peridynamic code
Silling, S. A · 2003
Earlier work this paper cites.
Contact in a multi-material Eulerian finite element formulation
Benson, D. J. and Okazawa, S · 2004
Earlier work this paper cites.
Accelerating the nonuniform fast fourier transform
Greengard, L. and Lee, J.-Y · 2004
Earlier work this paper cites.
“finite-element” displacement fields analysis from digital images: application to portevin–le châtelier bands
Besnard, G., Hild, F., and Roux, S · 2006
Earlier work this paper cites.
Studies of dynamic crack propagation and crack branching with peridynamics
Ha, Y. D. and Bobaru, F · 2010
Earlier work this paper cites.
Computational analysis of an aortic valve jet with Lagrangian coherent structures
Shadden, S. C., Astorino, M., and Gerbeau, J.-F · 2010
Cited alongside, same era.
Predicting crack propagation with peridynamics: a comparative study
Agwai, A., Guven, I., and Madenci, E · 2011
Cited alongside, same era.
X-FEM in isogeometric analysis for linear fracture mechanics
De Luycker, E., Benson, D. J., Belytschko, T., Bazilevs, Y., and Hsu, M.-C · 2011
Cited alongside, same era.
U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
Cited alongside, same era.
Handbook of peridynamic modeling
Bobaru, F., Foster, J. T., Geubelle, P. H., and Silling, S. A · 2016
Cited alongside, same era.
Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming b-splines
Kamensky, D., Hsu, M.-C., Yu, Y., Evans, J. A., Sacks, M. S., and Hughes, T. J · 2017
Multiwavelet-based operator learning for differential equations
Gupta, G., Xiao, X., and Bogdan, P · 2021
Later among the works it cites.
Manifold learning based data-driven modeling for soft biological tissues
He, Q., Laurence, D. W., Lee, C.-H., and Chen, J.-S · 2021
Later among the works it cites.
Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., and Yang, L · 2021
Later among the works it cites.
Physics-informed neural networks ( PINNs
Cai, S., Mao, Z., Wang, Z., Yin, M., and Karniadakis, G. E · 2022
Later among the works it cites.
Physics-informed neural operators
Goswami, S., Bora, A., Yu, Y., and Karniadakis, G. E · 2022
Later among the works it cites.
INO: Invariant neural operators for learning complex physical systems with momentum conservation
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
ReLu deep neural networks and linear finite elements
He, J., Li, L., Xu, J., and Zheng, C · 2018
Cited alongside, same era.
Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics
Zhang, L., Han, J., Wang, H., Car, R., and Weinan, E · 2018
Cited alongside, same era.
Machine learning and the physical sciences
Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., and Zdeborová, L · 2019
Cited alongside, same era.
Lu, L., Jin, P., and Karniadakis, G. E · 2019
Cited alongside, same era.
Multipole graph neural operator for parametric partial differential equations
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Stuart, A., Bhattacharya, K., and Anandkumar, A · 2020
Cited alongside, same era.
Ab initio solution of the many-electron schrödinger equation with deep neural networks
Pfau, D., Spencer, J. S., Matthews, A. G., and Foulkes, W. M. C · 2020
Cited alongside, same era.
Liu, N., Yu, Y., You, H., and Tatikola, N · 2022
Later among the works it cites.
A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
Lu, L., Meng, X., Cai, S., Mao, Z., Goswami, S., Zhang, Z., and Karniadakis, G. E · 2022
Later among the works it cites.
IAE-NET: Integral autoencoders for discretization-invariant learning
Ong, Y. Z., Shen, Z., and Yang, H · 2022
Later among the works it cites.
Factorized fourier neural operators
Tran, A., Mathews, A., Xie, L., and Ong, C. S · 2022
Later among the works it cites.
Wavelet neural operator: a neural operator for parametric partial differential equations
Tripura, T. and Chakraborty, S · 2022
Later among the works it cites.
Learning deep implicit fourier neural operators (IFNOs) with applications to heterogeneous material modeling
You, H., Zhang, Q., Ross, C. J., Lee, C.-H., and Yu, Y · 2022
Later among the works it cites.
Gnot: A general neural operator transformer for operator learning
Hao, Z., Wang, Z., Su, H., Ying, C., Dong, Y., Liu, S., Cheng, Z., Song, J., and Zhu, J · 2023
Closest in time.