Nikola B. Kovachki

According to our database, Nikola B. Kovachki authored at least 39 papers between 2018 and 2026.

Collaborative distances:

• Dijkstra number of four.
• Erdős number of three.

2026

Operator Learning for Smoothing and Forecasting.

Edoardo Calvello, Elizabeth Carlson, Nikola B. Kovachki, Michael N. Manta, Andrew M. Stuart

CoRR, March, 2026

Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting.

Jean Kossaifi, Nikola B. Kovachki, Morteza Mardani, Daniel V. Leibovici, Suman Ravuri, Ira Shokar, Edoardo Calvello, Mohammad Shoaib Abbas, Peter Harrington, Ashay Subramaniam, Noah D. Brenowitz, Boris Bonev, Wonmin Byeon, Karsten Kreis, Dale R. Durran, Arash Vahdat, Mike Pritchard, Jan Kautz

CoRR, January, 2026

2025

Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization.

Boyuan Yao, Dingcheng Luo, Lianghao Cao, Nikola B. Kovachki, Thomas O'Leary-Roseberry, Omar Ghattas

CoRR, December, 2025

Extension and neural operator approximation of the electrical impedance tomography inverse map.

Maarten V. de Hoop, Nikola B. Kovachki, Matti Lassas, Nicholas H. Nelsen

CoRR, November, 2025

A Learning-based Domain Decomposition Method.

Rui Wu, Nikola B. Kovachki, Burigede Liu

CoRR, July, 2025

Memorization and Regularization in Generative Diffusion Models.

Ricardo Baptista, Agnimitra Dasgupta, Nikola B. Kovachki, Assad A. Oberai, Andrew M. Stuart

CoRR, January, 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

Geometric Operator Learning with Optimal Transport.

Xinyi Li, Zongyi Li, Nikola B. Kovachki, Anima Anandkumar

J. Mach. Learn. Res., 2025

Continuum Attention for Neural Operators.

Edoardo Calvello, Nikola B. Kovachki, Matthew E. Levine, Andrew M. Stuart

J. Mach. Learn. Res., 2025

Score-Based Diffusion Models in Function Space.

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

J. Mach. Learn. Res., 2025

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, Nikola Borislavov Kovachki, Zachary E. Ross, Katherine L. Bouman, Yisong Yue

Proceedings of the Thirteenth International Conference on Learning Representations, 2025

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

Learning Homogenization for Elliptic Operators.

Kaushik Bhattacharya, Nikola B. Kovachki, Aakila Rajan, Andrew M. Stuart, Margaret Trautner

SIAM J. Numer. Anal., 2024

An approximation theory framework for measure-transport sampling algorithms.

Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki, Youssef Marzouk, Amir Sagiv

Math. Comput., 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

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

Data Complexity Estimates for Operator Learning.

Nikola B. Kovachki, Samuel Lanthaler, Hrushikesh Mhaskar

CoRR, 2024

Operator Learning: Algorithms and Analysis.

Nikola B. Kovachki, Samuel Lanthaler, Andrew M. Stuart

CoRR, 2024

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

Proceedings of the Advances in Neural Information Processing Systems 37: Annual Conference on Neural Information Processing Systems 2024, 2024

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, June, 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

Neural Operators for Accelerating Scientific Simulations and Design.

Kamyar Azizzadenesheli, Nikola B. Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, Anima Anandkumar

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

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, Kamyar Azizzadenesheli, Animashree Anandkumar

Proceedings of the Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, 2023

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

Dataset, November, 2022

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

Proceedings of the Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, 2022

2021

Continuous Time Analysis of Momentum Methods.

Nikola B. Kovachki, Andrew M. Stuart

J. Mach. Learn. Res., 2021

On Universal Approximation and Error Bounds for Fourier Neural Operators.

Nikola B. Kovachki, Samuel Lanthaler, Siddhartha Mishra

J. Mach. Learn. Res., 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

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

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

Fourier Neural Operator for Parametric Partial Differential Equations.

Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, Anima Anandkumar

Proceedings of the 9th International Conference on Learning Representations, 2021

2020

Conditional Sampling With Monotone GANs.

Nikola B. Kovachki, Ricardo Baptista, Bamdad Hosseini, Youssef M. Marzouk

CoRR, 2020

Model Reduction and Neural Networks for Parametric PDEs.

Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki, Andrew M. Stuart

CoRR, 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

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

Proceedings of the Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, 2020

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

Analysis Of Momentum Methods.

Nikola B. Kovachki, Andrew M. Stuart

CoRR, 2019

2018

Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks.

Nikola B. Kovachki, Andrew M. Stuart

CoRR, 2018