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Nikola Kovachki
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Fourier neural operator for parametric partial differential equations
Z Li, N Kovachki, K Azizzadenesheli, B Liu, K Bhattacharya, A Stuart, ...
arXiv preprint arXiv:2010.08895, 2020
19062020
Neural operator: Learning maps between function spaces with applications to pdes
N Kovachki, Z Li, B Liu, K Azizzadenesheli, K Bhattacharya, A Stuart, ...
Journal of Machine Learning Research 24 (89), 1-97, 2023
6172023
Neural operator: Graph kernel network for partial differential equations
Z Li, N Kovachki, K Azizzadenesheli, B Liu, K Bhattacharya, A Stuart, ...
arXiv preprint arXiv:2003.03485, 2020
5592020
Multipole graph neural operator for parametric partial differential equations
Z Li, N Kovachki, K Azizzadenesheli, B Liu, A Stuart, K Bhattacharya, ...
Advances in Neural Information Processing Systems 33, 6755-6766, 2020
3412020
Model reduction and neural networks for parametric PDEs
K Bhattacharya, B Hosseini, NB Kovachki, AM Stuart
The SMAI journal of computational mathematics 7, 121-157, 2021
3342021
Physics-informed neural operator for learning partial differential equations
Z Li, H Zheng, N Kovachki, D Jin, H Chen, B Liu, K Azizzadenesheli, ...
ACM/JMS Journal of Data Science 1 (3), 1-27, 2024
3202024
On universal approximation and error bounds for Fourier neural operators
N Kovachki, S Lanthaler, S Mishra
Journal of Machine Learning Research 22 (290), 1-76, 2021
2342021
Ensemble Kalman inversion: a derivative-free technique for machine learning tasks
NB Kovachki, AM Stuart
Inverse Problems 35 (9), 095005, 2019
1382019
Neural operator: Graph kernel network for partial differential equations
A Anandkumar, K Azizzadenesheli, K Bhattacharya, N Kovachki, Z Li, ...
ICLR 2020 Workshop on Integration of Deep Neural Models and Differential …, 2020
1032020
Burigede liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations
Z Li, NB Kovachki, K Azizzadenesheli
International Conference on Learning Representations 2 (3), 4, 2021
962021
Fourier neural operator for parametric partial differential equations, arXiv
Z Li, N Kovachki, K Azizzadenesheli, B Liu, K Bhattacharya, A Stuart, ...
arXiv preprint arXiv:2010.08895, 2020
932020
Regression clustering for improved accuracy and training costs with molecular-orbital-based machine learning
L Cheng, NB Kovachki, M Welborn, TF Miller III
Journal of Chemical Theory and Computation 15 (12), 6668-6677, 2019
642019
A learning-based multiscale method and its application to inelastic impact problems
B Liu, N Kovachki, Z Li, K Azizzadenesheli, A Anandkumar, AM Stuart, ...
Journal of the Mechanics and Physics of Solids 158, 104668, 2022
612022
Convergence rates for learning linear operators from noisy data
MV de Hoop, NB Kovachki, NH Nelsen, AM Stuart
SIAM/ASA Journal on Uncertainty Quantification 11 (2), 480-513, 2023
512023
Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization
N Kovachki, B Liu, X Sun, H Zhou, K Bhattacharya, M Ortiz, A Stuart
Mechanics of Materials 165, 104156, 2022
422022
Markov neural operators for learning chaotic systems
Z Li, N Kovachki, K Azizzadenesheli, B Liu, K Bhattacharya, A Stuart, ...
arXiv preprint arXiv:2106.06898, 2-3, 2021
422021
Continuous time analysis of momentum methods
NB Kovachki, AM Stuart
Journal of Machine Learning Research 22 (17), 1-40, 2021
322021
Score-based diffusion models in function space
JH Lim, NB Kovachki, R Baptista, C Beckham, K Azizzadenesheli, ...
arXiv preprint arXiv:2302.07400, 2023
302023
Neural operators for accelerating scientific simulations and design
K Azizzadenesheli, N Kovachki, Z Li, M Liu-Schiaffini, J Kossaifi, ...
Nature Reviews Physics, 1-9, 2024
282024
Geometry-informed neural operator for large-scale 3d pdes
Z Li, N Kovachki, C Choy, B Li, J Kossaifi, S Otta, MA Nabian, M Stadler, ...
Advances in Neural Information Processing Systems 36, 2024
282024
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