Fetching the paper…
Reading the bibliography…
Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems.
doi:10.3189/S0022143000010467
L. W. Morland, I. R. Johnson, Steady motion of ice sheets, Journal of Glaciology 25 (92) (1980) 229–246 · 1980
Earlier work this paper cites.
doi:https://doi.org/10.1029/JC088iC10p06043
P. Halfar, On the dynamics of the ice sheets 2, Journal of Geophysical Research: Oceans 88 (C10) (1983) 6043–6051 · 1983
Earlier work this paper cites.
A. Griewank, et al., On automatic differentiation, Mathematical Programming: recent developments and applications 6 (6) (1989) 83–107
1989
Earlier work this paper cites.
D. C. Psichogios, L. H. Ungar, A hybrid neural network-first principles approach to process modeling, AIChE Journal 38 (10) (1992) 1499–1511
1992
Earlier work this paper cites.
H. Wackernagel, Cokriging, in: Multivariate Geostatistics, Springer, 1995, pp. 144–151
1995
Earlier work this paper cites.
T. Chen, H. Chen, Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems, IEEE Transactions on Neural Networks 6 (4) (1995) 911–917
1995
Earlier work this paper cites.
T. Chen, H. Chen, Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks, IEEE Transactions on Neural Networks 6 (4) (1995) 904–910
1995
Earlier work this paper cites.
I. E. Lagaris, A. Likas, D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE transactions on neural networks 9 (5) (1998) 987–1000
1998
Earlier work this paper cites.
A. D. Back, T. Chen, Universal approximation of multiple nonlinear operators by neural networks, Neural Computation 14 (11) (2002) 2561–2566
2002
Earlier work this paper cites.
S. M. Cox, P. C. Matthews, Exponential time differencing for stiff systems, Journal of Computational Physics 176 (2) (2002) 430–455
2002
Earlier work this paper cites.
doi:10.3189/002214310792447851
J. K. Dukowicz, S. F. Price, W. H. Lipscomb, Consistent approximations and boundary conditions for ice-sheet dynamics from a principle of least action, Journal of Glaciology 56 (197) (2010) 480–496 · 2010
Earlier work this paper cites.
doi:10.3189/2012JoG11J063
M. Perego, M. Gunzburger, J. Burkardt, Parallel finite-element implementation for higher-order ice-sheet models, Journal of Glaciology 58 (207) (2012) 76–88 · 2012
Earlier work this paper cites.
doi:10.1002/2014JF003181.Received
M. Perego, S. Price, G. Stadler, Optimal initial conditions for coupling ice sheet models to Earth system models, Journal of Geophysical Research Earth Surface 119 (2014) 1–24 · 2014
Earlier work this paper cites.
doi:10.1137/130934805
N. Petra, J. Martin, G. Stadler, O. Ghattas, A computational framework for infinite-dimensional bayesian inverse problems, part ii: Stochastic newton mcmc with application to ice sheet flow inverse problems, SIAM Journal on Scientific Computing 36 (4) (2014) A1525–A1555 · 2014
Earlier work this paper cites.
T. A. Driscoll, N. Hale, L. N. Trefethen, Chebfun guide (2014)
2014
Earlier work this paper cites.
M. Alnæs, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, G. N. Wells, The fenics project version 1.5, Archive of Numerical Software 3 (100) (2015)
2015
Earlier work this paper cites.
P. Perdikaris, M. Raissi, A. Damianou, N. D. Lawrence, G. E. Karniadakis, Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2198) (2017) 20160751
2017
Earlier work this paper cites.
J. Sirignano, K. Spiliopoulos, DGM: A deep learning algorithm for solving partial differential equations, Journal of Computational Physics 375 (2018) 1339–1364
2018
Earlier work this paper cites.
A. G. Baydin, B. A. Pearlmutter, A. A. Radul, J. M. Siskind, Automatic differentiation in machine learning: a survey, Journal of Marchine Learning Research 18 (2018) 1–43
2018
Earlier work this paper cites.
J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, Q. Zhang, JAX: composable transformations of Python+NumPy programs (2018). URL http://github.com/google/jax
2018
Earlier work this paper cites.
M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational physics 378 (2019) 686–707
2019
Earlier work this paper cites.
D. Liu, Y. Wang, Multi-fidelity physics-constrained neural network and its application in materials modeling, Journal of Mechanical Design 141 (12) (2019)
2019
Cited alongside, same era.
2019
Cited alongside, same era.
H. Babaee, C. Bastidas, M. DeFilippo, C. Chryssostomidis, G. Karniadakis, A multifidelity framework and uncertainty quantification for sea surface temperature in the massachusetts and cape cod bays, Earth and Space Science 7 (2) (2020) e2019EA000954
2020
Cited alongside, same era.
X. Meng, G. E. Karniadakis, A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse pde problems, Journal of Computational Physics 401 (2020) 109020
2020
Cited alongside, same era.
X. Zhang, F. Xie, T. Ji, Z. Zhu, Y. Zheng, Multi-fidelity deep neural network surrogate model for aerodynamic shape optimization, Computer Methods in Applied Mechanics and Engineering 373 (2021) 113485
2021
Later among the works it cites.
H. You, Y. Yu, M. D’Elia, T. Gao, S. Silling, Nonlocal kernel network (nkn): a stable and resolution-independent deep neural network, Journal of Computational Physics 469 (2022) 111536
2022
Closest in time.
S. Goswami, M. Yin, Y. Yu, G. E. Karniadakis, A physics-informed variational deeponet for predicting crack path in quasi-brittle materials, Computer Methods in Applied Mechanics and Engineering 391 (2022) 114587
2022
Closest in time.
S. Wang, H. Wang, P. Perdikaris, Improved architectures and training algorithms for deep operator networks, Journal of Scientific Computing 92 (2) (2022) 35
2022
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2020
Cited alongside, same era.
2020
Cited alongside, same era.
S. Karumuri, R. Tripathy, I. Bilionis, J. Panchal, Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks, Journal of Computational Physics 404 (2020) 109120
2020
Cited alongside, same era.
L. Sun, H. Gao, S. Pan, J.-X. Wang, Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data, Computer Methods in Applied Mechanics and Engineering 361 (2020) 112732
2020
Cited alongside, same era.
L. Lu, M. Dao, P. Kumar, U. Ramamurty, G. E. Karniadakis, S. Suresh, Extraction of mechanical properties of materials through deep learning from instrumented indentation, Proceedings of the National Academy of Sciences 117 (13) (2020) 7052–7062
2020
Cited alongside, same era.
S. De, J. Britton, M. Reynolds, R. Skinner, K. Jansen, A. Doostan, On transfer learning of neural networks using bi-fidelity data for uncertainty propagation, International Journal for Uncertainty Quantification 10 (6) (2020)
2020
Cited alongside, same era.
L. Lu, P. Jin, G. Pang, Z. Zhang, G. E. Karniadakis, Learning nonlinear operators via deeponet based on the universal approximation theorem of operators, Nature Machine Intelligence 3 (3) (2021) 218–229
2021
Cited alongside, same era.
M. Sharma Priyadarshini, S. Venturi, M. Panesi, Application of deeponet to model inelastic scattering probabilities in air mixtures, in: AIAA AVIATION 2021 FORUM, 2021, p. 3144
2021
Cited alongside, same era.
M. Penwarden, S. Zhe, A. Narayan, R. M. Kirby, Multifidelity modeling for physics-informed neural networks (pinns), Journal of Computational Physics 451 (2022) 110844
2022
Closest in time.
A. D. Jagtap, D. Mitsotakis, G. E. Karniadakis, Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre–Green–Naghdi equations, Ocean Engineering 248 (2022) 110775
2022
Closest in time.
S. De, A. Doostan, Neural network training using ℓ 1 \ell_{1} -regularization and bi-fidelity data, Journal of Computational Physics (2022) 111010
2022
Closest in time.
K. Harada, D. Rajaram, D. N. Mavris, Application of multi-fidelity physics-informed neural network on transonic airfoil using wind tunnel measurements, in: AIAA SCITECH 2022 Forum, 2022, p. 0386
2022
Closest in time.
L. Lu, R. Pestourie, S. G. Johnson, 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 4 (2) (2022) 023210
2022
Closest in time.
doi:10.5194/tc-16-689-2022
A. Robinson, D. Goldberg, W. H. Lipscomb, A comparison of the stability and performance of depth-integrated ice-dynamics solvers, The Cryosphere 16 (2) (2022) 689–709 · 2022
Closest in time.
doi:10.5194/tc-16-179-2022
T. Dias dos Santos, M. Morlighem, D. Brinkerhoff, A new vertically integrated mono-layer higher-order (molho) ice flow model, The Cryosphere 16 (1) (2022) 179–195 · 2022
Closest in time.
doi:10.5194/tc-2022-20
T. R. Hillebrand, M. J. Hoffman, M. Perego, S. F. Price, I. M. Howat, The contribution of humboldt glacier, north greenland, to sea-level rise through 2100 constrained by recent observations of speedup and retreat, The Cryosphere Discussions 2022 (2022) 1–33 · 2022
Closest in time.
2022
Closest in time.
S. Goswami, M. Yin, Y. Yu, G. E. Karniadakis, A physics-informed variational deeponet for predicting crack path in quasi-brittle materials, Computer Methods in Applied Mechanics and Engineering 391 (2022) 114587
2022
Closest in time.
S. Wang, P. Perdikaris, Long-time integration of parametric evolution equations with physics-informed deeponets, Journal of Computational Physics 475 (2023) 111855
2023
Closest in time.
S. De, M. Reynolds, M. Hassanaly, R. N. King, A. Doostan, Bi-fidelity modeling of uncertain and partially unknown systems using deeponets, Computational Mechanics 71 (6) (2023) 1251–1267
2023
Closest in time.
L. D. McClenny, U. M. Braga-Neto, Self-adaptive physics-informed neural networks, Journal of Computational Physics 474 (2023) 111722
2023
Closest in time.
2023
Closest in time.
S. Koric, D. W. Abueidda, Data-driven and physics-informed deep learning operators for solution of heat conduction equation with parametric heat source, International Journal of Heat and Mass Transfer 203 (2023) 123809
2023
Closest in time.