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ORCIDNikola B. Kovachki
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2020 – today
- 2024
[j6]Ricardo Baptista, Bamdad Hosseini
, Nikola B. Kovachki, Youssef M. Marzouk:
Conditional Sampling with Monotone GANs: From Generative Models to Likelihood-Free Inference. SIAM/ASA J. Uncertain. Quantification 12(3): 868-900 (2024)- [j5]Kaushik Bhattacharya, Nikola B. Kovachki, Aakila Rajan, Andrew M. Stuart, Margaret Trautner:
Learning Homogenization for Elliptic Operators. SIAM J. Numer. Anal. 62(4): 1844-1873 (2024) - [i23]Nikola B. Kovachki, Samuel Lanthaler, Andrew M. Stuart:
Operator Learning: Algorithms and Analysis. CoRR abs/2402.15715 (2024) - [i22]Nikola B. Kovachki, Samuel Lanthaler, Hrushikesh Mhaskar:
Data Complexity Estimates for Operator Learning. CoRR abs/2405.15992 (2024) - [i21]Edoardo Calvello, Nikola B. Kovachki, Matthew E. Levine, Andrew M. Stuart:
Continuum Attention for Neural Operators. CoRR abs/2406.06486 (2024) - 2023
- [j4]Nikola B. Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar:
Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs. J. Mach. Learn. Res. 24: 89:1-89:97 (2023) - [j3]Maarten V. de Hoop, Nikola B. Kovachki, Nicholas H. Nelsen, Andrew M. Stuart:
Convergence Rates for Learning Linear Operators from Noisy Data. SIAM/ASA J. Uncertain. Quantification 11(2): 480-513 (2023) - [c4]Zongyi Li, Nikola B. Kovachki, Christopher B. Choy, Boyi Li, Jean Kossaifi, Shourya Prakash Otta, Mohammad Amin Nabian, Maximilian Stadler, Christian Hundt, Kamyar Azizzadenesheli, Animashree Anandkumar:
Geometry-Informed Neural Operator for Large-Scale 3D PDEs. NeurIPS 2023 - [i20]Jae Hyun Lim, Nikola B. Kovachki, Ricardo Baptista, Christopher Beckham, Kamyar Azizzadenesheli, Jean Kossaifi, Vikram Voleti, Jiaming Song, Karsten Kreis, Jan Kautz, Christopher Pal, Arash Vahdat, Anima Anandkumar:
Score-based Diffusion Models in Function Space. CoRR abs/2302.07400 (2023) - [i19]Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki, Youssef M. Marzouk, Amir Sagiv:
An Approximation Theory Framework for Measure-Transport Sampling Algorithms. CoRR abs/2302.13965 (2023) - [i18]Kaushik Bhattacharya, Nikola B. Kovachki, Aakila Rajan, Andrew M. Stuart, Margaret Trautner:
Learning Homogenization for Elliptic Operators. CoRR abs/2306.12006 (2023) - [i17]Miguel Liu-Schiaffini, Clare E. Singer, Nikola B. Kovachki, Tapio Schneider, Kamyar Azizzadenesheli, Anima Anandkumar:
Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces. CoRR abs/2308.08794 (2023) - [i16]Zongyi Li, Nikola Borislavov Kovachki, Christopher B. Choy, Boyi Li, Jean Kossaifi, Shourya Prakash Otta, Mohammad Amin Nabian, Maximilian Stadler, Christian Hundt, Kamyar Azizzadenesheli, Anima Anandkumar:
Geometry-Informed Neural Operator for Large-Scale 3D PDEs. CoRR abs/2309.00583 (2023) - [i15]Kamyar Azizzadenesheli, Nikola B. Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, Anima Anandkumar:
Neural Operators for Accelerating Scientific Simulations and Design. CoRR abs/2309.15325 (2023) - [i14]Jean Kossaifi, Nikola B. Kovachki, Kamyar Azizzadenesheli, Anima Anandkumar:
Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs. CoRR abs/2310.00120 (2023) - 2022
- [c3]Zongyi Li, Miguel Liu-Schiaffini, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar:
Learning Chaotic Dynamics in Dissipative Systems. NeurIPS 2022 - [d1]Zongyi Li, Miguel Liu-Schiaffini, Nikola Borislavov Kovachki, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar:
Learning Dissipative Dynamics in Chaotic Systems (Datasets). Zenodo, 2022
- 2021
- [j2]Nikola B. Kovachki, Andrew M. Stuart:
Continuous Time Analysis of Momentum Methods. J. Mach. Learn. Res. 22: 17:1-17:40 (2021) - [j1]Nikola B. Kovachki, Samuel Lanthaler, Siddhartha Mishra:
On Universal Approximation and Error Bounds for Fourier Neural Operators. J. Mach. Learn. Res. 22: 290:1-290:76 (2021) - [c2]Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar:
Fourier Neural Operator for Parametric Partial Differential Equations. ICLR 2021 - [i13]Zongyi Li, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar:
Markov Neural Operators for Learning Chaotic Systems. CoRR abs/2106.06898 (2021) - [i12]Nikola B. Kovachki, Samuel Lanthaler, Siddhartha Mishra:
On universal approximation and error bounds for Fourier Neural Operators. CoRR abs/2107.07562 (2021) - [i11]Nikola B. Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar:
Neural Operator: Learning Maps Between Function Spaces. CoRR abs/2108.08481 (2021) - [i10]Maarten V. de Hoop, Nikola B. Kovachki, Nicholas H. Nelsen, Andrew M. Stuart:
Convergence Rates for Learning Linear Operators from Noisy Data. CoRR abs/2108.12515 (2021) - [i9]Zongyi Li, Hongkai Zheng, Nikola B. Kovachki, David Jin, Haoxuan Chen, Burigede Liu, Kamyar Azizzadenesheli, Anima Anandkumar:
Physics-Informed Neural Operator for Learning Partial Differential Equations. CoRR abs/2111.03794 (2021) - 2020
- [c1]Zongyi Li, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Andrew M. Stuart, Kaushik Bhattacharya, Anima Anandkumar:
Multipole Graph Neural Operator for Parametric Partial Differential Equations. NeurIPS 2020 - [i8]Zongyi Li, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar:
Neural Operator: Graph Kernel Network for Partial Differential Equations. CoRR abs/2003.03485 (2020) - [i7]Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki, Andrew M. Stuart:
Model Reduction and Neural Networks for Parametric PDEs. CoRR abs/2005.03180 (2020) - [i6]Nikola B. Kovachki, Ricardo Baptista, Bamdad Hosseini, Youssef M. Marzouk:
Conditional Sampling With Monotone GANs. CoRR abs/2006.06755 (2020) - [i5]Zongyi Li, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar:
Multipole Graph Neural Operator for Parametric Partial Differential Equations. CoRR abs/2006.09535 (2020) - [i4]Zongyi Li, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar:
Fourier Neural Operator for Parametric Partial Differential Equations. CoRR abs/2010.08895 (2020)
2010 – 2019
- 2019
- [i3]Nikola B. Kovachki, Andrew M. Stuart:
Analysis Of Momentum Methods. CoRR abs/1906.04285 (2019) - [i2]Lixue Cheng, Nikola B. Kovachki, Matthew Welborn, Thomas F. Miller III:
Regression-clustering for Improved Accuracy and Training Cost with Molecular-Orbital-Based Machine Learning. CoRR abs/1909.02041 (2019) - 2018
- [i1]Nikola B. Kovachki, Andrew M. Stuart:
Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks. CoRR abs/1808.03620 (2018)
Coauthor Index
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