Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks. - Nikola B. Kovachki; Andrew M. Stuart (CoRR, 2018)

Analysis Of Momentum Methods. - Nikola B. Kovachki; Andrew M. Stuart (CoRR, 2019)

Regression-clustering for Improved Accuracy and Training Cost with Molecular-Orbital-Based Machine Learning. - Lixue Cheng; Nikola B. Kovachki; Matthew Welborn; Thomas F. Miller III (CoRR, 2019)

Multipole Graph Neural Operator for Parametric Partial Differential Equations. - Zongyi Li; Nikola B. Kovachki; Kamyar Azizzadenesheli; Burigede Liu; Andrew M. Stuart; Kaushik Bhattacharya; Anima Anandkumar (NeurIPS, 2020)

Neural Operator: Graph Kernel Network for Partial Differential Equations. - Zongyi Li; Nikola B. Kovachki; Kamyar Azizzadenesheli; Burigede Liu; Kaushik Bhattacharya; Andrew M. Stuart; Anima Anandkumar (CoRR, 2020)

Model Reduction and Neural Networks for Parametric PDEs. - Kaushik Bhattacharya; Bamdad Hosseini; Nikola B. Kovachki; Andrew M. Stuart (CoRR, 2020)

Conditional Sampling With Monotone GANs. - Nikola B. Kovachki; Ricardo Baptista; Bamdad Hosseini; Youssef M. Marzouk (CoRR, 2020)

Fourier Neural Operator for Parametric Partial Differential Equations. - Zongyi Li; Nikola Borislavov Kovachki; Kamyar Azizzadenesheli; Burigede Liu; Kaushik Bhattacharya; Andrew M. Stuart; Anima Anandkumar (ICLR, 2021)

Markov Neural Operators for Learning Chaotic Systems. - Zongyi Li; Nikola B. Kovachki; Kamyar Azizzadenesheli; Burigede Liu; Kaushik Bhattacharya; Andrew M. Stuart; Anima Anandkumar (CoRR, 2021)

Neural Operator: Learning Maps Between Function Spaces. - Nikola B. Kovachki; Zongyi Li; Burigede Liu; Kamyar Azizzadenesheli; Kaushik Bhattacharya; Andrew M. Stuart; Anima Anandkumar (CoRR, 2021)

Physics-Informed Neural Operator for Learning Partial Differential Equations. - Zongyi Li; Hongkai Zheng; Nikola B. Kovachki; David Jin; Haoxuan Chen; Burigede Liu; Kamyar Azizzadenesheli; Anima Anandkumar (CoRR, 2021)

On Universal Approximation and Error Bounds for Fourier Neural Operators. - Nikola B. Kovachki; Samuel Lanthaler; Siddhartha Mishra (J. Mach. Learn. Res., 2021)

Continuous Time Analysis of Momentum Methods. - Nikola B. Kovachki; Andrew M. Stuart (J. Mach. Learn. Res., 2021)

Learning Chaotic Dynamics in Dissipative Systems. - Zongyi Li; Miguel Liu-Schiaffini; Nikola B. Kovachki; Kamyar Azizzadenesheli; Burigede Liu; Kaushik Bhattacharya; Andrew M. Stuart; Anima Anandkumar (NeurIPS, 2022)

Learning Dissipative Dynamics in Chaotic Systems (Datasets). - Zongyi Li; Miguel Liu-Schiaffini; Nikola Borislavov Kovachki; Burigede Liu; Kamyar Azizzadenesheli; Kaushik Bhattacharya; Andrew M. Stuart; Anima Anandkumar (Zenodo, 2022)

Geometry-Informed Neural Operator for Large-Scale 3D PDEs. - Zongyi Li; Nikola B. Kovachki; Christopher B. Choy; Boyi Li; Jean Kossaifi; Shourya Prakash Otta; Mohammad Amin Nabian; Maximilian Stadler; Christian Hundt 002; Kamyar Azizzadenesheli; Animashree Anandkumar (NeurIPS, 2023)

Score-based Diffusion Models in Function Space. - Jae Hyun Lim 001; Nikola B. Kovachki; Ricardo Baptista; Christopher Beckham; Kamyar Azizzadenesheli; Jean Kossaifi; Vikram Voleti; Jiaming Song; Karsten Kreis; Jan Kautz; Christopher Pal; Arash Vahdat; et al. (CoRR, 2023)

Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces. - Miguel Liu-Schiaffini; Clare E. Singer; Nikola B. Kovachki; Tapio Schneider; Kamyar Azizzadenesheli; Anima Anandkumar (CoRR, 2023)

Neural Operators for Accelerating Scientific Simulations and Design. - Kamyar Azizzadenesheli; Nikola B. Kovachki; Zongyi Li; Miguel Liu-Schiaffini; Jean Kossaifi; Anima Anandkumar (CoRR, 2023)

Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs. - Nikola B. Kovachki; Zongyi Li; Burigede Liu; Kamyar Azizzadenesheli; Kaushik Bhattacharya; Andrew M. Stuart; Anima Anandkumar (J. Mach. Learn. Res., 2023)

Convergence Rates for Learning Linear Operators from Noisy Data. - Maarten V. de Hoop; Nikola B. Kovachki; Nicholas H. Nelsen; Andrew M. Stuart (SIAM/ASA J. Uncertain. Quantification, 2023)

Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Models. - Giannis Daras; Weili Nie; Karsten Kreis; Alex Dimakis; Morteza Mardani; Nikola B. Kovachki; Arash Vahdat (NeurIPS, 2024)

Operator Learning: Algorithms and Analysis. - Nikola B. Kovachki; Samuel Lanthaler; Andrew M. Stuart (CoRR, 2024)

Data Complexity Estimates for Operator Learning. - Nikola B. Kovachki; Samuel Lanthaler; Hrushikesh Mhaskar (CoRR, 2024)

Continuum Attention for Neural Operators. - Edoardo Calvello; Nikola B. Kovachki; Matthew E. Levine; Andrew M. Stuart (CoRR, 2024)

A Library for Learning Neural Operators. - Jean Kossaifi; Nikola B. Kovachki; Zongyi Li; David Pitt; Miguel Liu-Schiaffini; Robert Joseph George; Boris Bonev; Kamyar Azizzadenesheli; Julius Berner; Anima Anandkumar (CoRR, 2024)

Conditional Sampling with Monotone GANs: From Generative Models to Likelihood-Free Inference. - Ricardo Baptista; Bamdad Hosseini; Nikola B. Kovachki; Youssef M. Marzouk (SIAM/ASA J. Uncertain. Quantification, 2024)

An approximation theory framework for measure-transport sampling algorithms. - Ricardo Baptista; Bamdad Hosseini; Nikola B. Kovachki; Youssef Marzouk 001; Amir Sagiv (Math. Comput., 2024)

Learning Homogenization for Elliptic Operators. - Kaushik Bhattacharya; Nikola B. Kovachki; Aakila Rajan; Andrew M. Stuart; Margaret Trautner (SIAM J. Numer. Anal., 2024)

Multi-Grid Tensorized Fourier Neural Operator for High- Resolution PDEs. - Jean Kossaifi; Nikola Borislavov Kovachki; Kamyar Azizzadenesheli; Anima Anandkumar (Trans. Mach. Learn. Res., 2024)

InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences. - Hongkai Zheng; Wenda Chu; Bingliang Zhang; Zihui Wu; Austin Wang; Berthy Feng; Caifeng Zou; Yu Sun 022; Nikola Borislavov Kovachki; Zachary E. Ross; Katherine L. Bouman; Yisong Yue (ICLR, 2025)

Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems. - Hongkai Zheng; Wenda Chu; Austin Wang; Nikola Borislavov Kovachki; Ricardo Baptista; Yisong Yue (Trans. Mach. Learn. Res., 2025)

Memorization and Regularization in Generative Diffusion Models. - Ricardo Baptista; Agnimitra Dasgupta; Nikola B. Kovachki; Assad A. Oberai; Andrew M. Stuart (CoRR, 2025)

A Learning-based Domain Decomposition Method. - Rui Wu; Nikola B. Kovachki; Burigede Liu (CoRR, 2025)

Geometric Operator Learning with Optimal Transport. - Xinyi Li; Zongyi Li; Nikola B. Kovachki; Anima Anandkumar (CoRR, 2025)