Nikola B. Kovachki

Publication Activity (10 Years)

Years Active: 2018-2024
Publications (10 Years): 28

Top Topics

Diffusion Models

Partial Differential Equations

Improved Accuracy

Top Venues

J. Mach. Learn. Res.

SIAM/ASA J. Uncertain. Quantification

Publications

Nikola B. Kovachki, Samuel Lanthaler, Andrew M. Stuart
Operator Learning: Algorithms and Analysis. CoRR (2024)
Nikola B. Kovachki, Samuel Lanthaler, Hrushikesh Mhaskar
Data Complexity Estimates for Operator Learning. CoRR (2024)
Edoardo Calvello, Nikola B. Kovachki, Matthew E. Levine, Andrew M. Stuart
Continuum Attention for Neural Operators. CoRR (2024)
Kaushik Bhattacharya, Nikola B. Kovachki, Aakila Rajan, Andrew M. Stuart, Margaret Trautner
Learning Homogenization for Elliptic Operators. SIAM J. Numer. Anal. 62 (4) (2024)
Kaushik Bhattacharya, Nikola B. Kovachki, Aakila Rajan, Andrew M. Stuart, Margaret Trautner
Learning Homogenization for Elliptic Operators. CoRR (2023)
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 (2023)
Jean Kossaifi, Nikola B. Kovachki, Kamyar Azizzadenesheli, Anima Anandkumar
Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs. CoRR (2023)
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 (2023)
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 (2023)
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) (2023)
Kamyar Azizzadenesheli, Nikola B. Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, Anima Anandkumar
Neural Operators for Accelerating Scientific Simulations and Design. CoRR (2023)
Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki, Youssef M. Marzouk, Amir Sagiv
An Approximation Theory Framework for Measure-Transport Sampling Algorithms. CoRR (2023)
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)
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)
Zongyi Li, Nikola B. Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar
Markov Neural Operators for Learning Chaotic Systems. CoRR (2021)
Maarten V. de Hoop, Nikola B. Kovachki, Nicholas H. Nelsen, Andrew M. Stuart
Convergence Rates for Learning Linear Operators from Noisy Data. CoRR (2021)
Nikola B. Kovachki, Andrew M. Stuart
Continuous Time Analysis of Momentum Methods. J. Mach. Learn. Res. 22 (2021)
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 (2021)
Nikola B. Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar
Neural Operator: Learning Maps Between Function Spaces. CoRR (2021)
Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki, Andrew M. Stuart
Model Reduction and Neural Networks for Parametric PDEs. CoRR (2020)
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)
Nikola B. Kovachki, Ricardo Baptista, Bamdad Hosseini, Youssef M. Marzouk
Conditional Sampling With Monotone GANs. CoRR (2020)
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 (2020)
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 (2020)
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 (2020)
Nikola B. Kovachki, Andrew M. Stuart
Analysis Of Momentum Methods. CoRR (2019)
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 (2019)
Nikola B. Kovachki, Andrew M. Stuart
Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks. CoRR (2018)