Nikola B. Kovachki

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All published works

Action	Title	Year	Authors
+ PDF Chat	A Library for Learning Neural Operators	2024	Jean Kossaifi Nikola B. Kovachki Zongyi Li David Pitt Miguel Liu-Schiaffini Robert Joseph George Boris Bonev Kamyar Azizzadenesheli Julius Berner Anima Anandkumar
+ PDF Chat	Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Models	2024	Giannis Daras Weili Nie Karsten Kreis Alex Dimakis Morteza Mardani Nikola B. Kovachki Arash Vahdat
+ PDF Chat	Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems	2024	Hongkai Zheng Wenda Chu A L Wang Nikola B. Kovachki R. Baptista Yisong Yue
+	An approximation theory framework for measure-transport sampling algorithms	2024	Ricardo Baptista Bamdad Hosseini Nikola B. Kovachki Youssef Marzouk Amir Sagiv
+ PDF Chat	Conditional Sampling with Monotone GANs: From Generative Models to Likelihood-Free Inference	2024	Ricardo Baptista Bamdad Hosseini Nikola B. Kovachki Youssef Marzouk
+ PDF Chat	Learning Homogenization for Elliptic Operators	2024	Kaushik Bhattacharya Nikola B. Kovachki Aakila Rajan Andrew M. Stuart Margaret Trautner
+ PDF Chat	Continuum Attention for Neural Operators	2024	Edoardo Calvello Nikola B. Kovachki Matthew E. Levine Andrew M. Stuart
+ PDF Chat	Data Complexity Estimates for Operator Learning	2024	Nikola B. Kovachki Samuel Lanthaler H. N. Mhaskar
+ PDF Chat	Operator Learning: Algorithms and Analysis	2024	Nikola B. Kovachki Samuel Lanthaler Andrew M. Stuart
+ PDF Chat	Physics-Informed Neural Operator for Learning Partial Differential Equations	2024	Zongyi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar
+ PDF Chat	Convergence Rates for Learning Linear Operators from Noisy Data	2023	Maarten V. de Hoop Nikola B. Kovachki Nicholas H. Nelsen Andrew M. Stuart
+	Score-based Diffusion Models in Function Space	2023	Jae Hyun Lim Nikola B. Kovachki R. Baptista Christopher Beckham Kamyar Azizzadenesheli Jean Kossaifi Vikram Voleti Jiaming Song Karsten Kreis Jan Kautz
+	An Approximation Theory Framework for Measure-Transport Sampling Algorithms	2023	R. Baptista Bamdad Hosseini Nikola B. Kovachki Youssef Marzouk Amir Sagiv
+	Learning Homogenization for Elliptic Operators	2023	Kaushik Bhattacharya Nikola B. Kovachki Aakila Rajan Andrew M. Stuart Margaret Trautner
+	Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces	2023	Miguel Liu-Schiaffini Clare E. Singer Nikola B. Kovachki Tapio Schneider Kamyar Azizzadenesheli Anima Anandkumar
+	Geometry-Informed Neural Operator for Large-Scale 3D PDEs	2023	Zongyi Li Nikola B. Kovachki Chris Choy Boyi Li Jean Kossaifi Shourya Prakash Otta Mohammad Amin Nabian Maximilian Stadler Christian Hundt Kamyar Azizzadenesheli
+	Neural Operators for Accelerating Scientific Simulations and Design	2023	Kamyar Azzizadenesheli Nikola B. Kovachki Zongyi Li Miguel Liu-Schiaffini Jean Kossaifi Anima Anandkumar
+	Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs	2023	Jean Kossaifi Nikola B. Kovachki Kamyar Azizzadenesheli Anima Anandkumar
+ PDF Chat	Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization	2021	Nikola B. Kovachki Burigede Liu Xingsheng Sun Hao Zhou Kaushik Bhattacharya M. Ortíz Andrew M. Stuart
+ PDF Chat	A learning-based multiscale method and its application to inelastic impact problems	2021	Burigede Liu Nikola B. Kovachki Zongyi Li Kamyar Azizzadenesheli Anima Anandkumar Andrew M. Stuart Kaushik Bhattacharya
+ PDF Chat	Convergence Rates for Learning Linear Operators from Noisy Data	2021	Maarten V. de Hoop Nikola B. Kovachki Nicholas H. Nelsen Andrew M. Stuart
+	Neural Operator: Learning Maps Between Function Spaces.	2021	Nikola B. Kovachki Zongyi Li Burigede Liu Kamyar Azizzadenesheli Kaushik Bhattacharya Andrew M. Stuart Anima Anandkumar
+	On universal approximation and error bounds for Fourier Neural Operators	2021	Nikola B. Kovachki Samuel Lanthaler Siddhartha Mishra
+ PDF Chat	Model Reduction And Neural Networks For Parametric PDEs	2021	Kaushik Bhattacharya Bamdad Hosseini Nikola B. Kovachki Andrew M. Stuart
+	Markov Neural Operators for Learning Chaotic Systems.	2021	Zongyi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu Kaushik Bhattacharya Andrew M. Stuart Anima Anandkumar
+	Multiscale modeling of materials: Computing, data science,uncertainty and goal-oriented optimization	2021	Nikola B. Kovachki Burigede Liu Xingsheng Sun Hao Zhou Kaushik Bhattacharya M. Ortíz Andrew M. Stuart
+	A learning-based multiscale method and its application to inelastic impact problems	2021	Burigede Liu Nikola B. Kovachki Zongyi Li Kamyar Azizzadenesheli Anima Anandkumar Andrew M. Stuart Kaushik Bhattacharya
+	Physics-Informed Neural Operator for Learning Partial Differential Equations	2021	Zongyi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar
+	On Universal Approximation and Error Bounds for Fourier Neural Operators	2021	Nikola B. Kovachki Samuel Lanthaler Siddhartha Mishra
+	Convergence Rates for Learning Linear Operators from Noisy Data	2021	Maarten V. de Hoop Nikola B. Kovachki Nicholas H. Nelsen Andrew M. Stuart
+	Neural Operator: Learning Maps Between Function Spaces	2021	Nikola B. Kovachki Zongyi Li Burigede Liu Kamyar Azizzadenesheli Kaushik Bhattacharya Andrew M. Stuart Anima Anandkumar
+	On universal approximation and error bounds for Fourier Neural Operators	2021	Nikola B. Kovachki Samuel Lanthaler Siddhartha Mishra
+	Multiscale modeling of materials: Computing, data science,uncertainty and goal-oriented optimization	2021	Nikola B. Kovachki Burigede Liu Xingsheng Sun Hao Zhou Kaushik Bhattacharya M. Ortíz Andrew M. Stuart
+	Learning Dissipative Dynamics in Chaotic Systems	2021	Zongyi Li Miguel Liu-Schiaffini Nikola B. Kovachki Burigede Liu Kamyar Azizzadenesheli Kaushik Bhattacharya Andrew M. Stuart Anima Anandkumar
+	Conditional Sampling With Monotone GANs.	2020	Nikola B. Kovachki Ricardo Baptista Bamdad Hosseini Youssef Marzouk
+	Model Reduction and Neural Networks for Parametric PDEs	2020	Kaushik Bhattacharya Bamdad Hosseini Nikola B. Kovachki Andrew M. Stuart
+	Neural Operator: Graph Kernel Network for Partial Differential Equations	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	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	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	2020	Zongyi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu Kaushik Bhattacharya Andrew M. Stuart Anima Anandkumar
+	Model Reduction and Neural Networks for Parametric PDEs	2020	Kaushik Bhattacharya Bamdad Hosseini Nikola B. Kovachki Andrew M. Stuart
+	Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference	2020	R. Baptista Bamdad Hosseini Nikola B. Kovachki Youssef Marzouk
+ PDF Chat	Regression Clustering for Improved Accuracy and Training Costs with Molecular-Orbital-Based Machine Learning	2019	Lixue Cheng Nikola B. Kovachki Matthew Welborn Thomas F. Miller
+	Analysis Of Momentum Methods	2019	Nikola B. Kovachki Andrew M. Stuart
+ PDF Chat	Ensemble Kalman inversion: a derivative-free technique for machine learning tasks	2019	Nikola B. Kovachki Andrew M. Stuart
+	Regression-clustering for Improved Accuracy and Training Cost with Molecular-Orbital-Based Machine Learning	2019	Lixue Cheng Nikola B. Kovachki Matthew Welborn Thomas F. Miller
+	Continuous Time Analysis of Momentum Methods	2019	Nikola B. Kovachki Andrew M. Stuart

Common Coauthors

Coauthor	Papers Together
Andrew M. Stuart	26
Anima Anandkumar	18
Kaushik Bhattacharya	18
Kamyar Azizzadenesheli	17
Burigede Liu	15
Zongyi Li	15
Bamdad Hosseini	8
Ricardo Baptista	6
Samuel Lanthaler	5
Jean Kossaifi	5
Youssef Marzouk	5
Miguel Liu-Schiaffini	4
M. Ortíz	3
Maarten V. de Hoop	3
Xingsheng Sun	3
Nicholas H. Nelsen	3
Siddhartha Mishra	3
Hongkai Zheng	3
Karsten Kreis	2
Amir Sagiv	2
Margaret Trautner	2
Thomas F. Miller	2
Hao Zhou	2
Haoxuan Chen	2
David Jin	2
Aakila Rajan	2
Lixue Cheng	2
Arash Vahdat	2
Matthew Welborn	2
Chris Choy	1
Alex Dimakis	1
Jae Hyun Lim	1
Jiaming Song	1
Mohammad Amin Nabian	1
Vikram Voleti	1
Christian Hundt	1
Tapio Schneider	1
Christopher Beckham	1
Ricardo Baptista	1
Weili Nie	1
Matthew E. Levine	1
Boris Bonev	1
Wenda Chu	1
H. N. Mhaskar	1
Jan Kautz	1
Morteza Mardani	1
Shourya Prakash Otta	1
Robert Joseph George	1
Clare E. Singer	1
Boyi Li	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems	2018	E Weinan Bing Yu	9
+	Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators	2021	Lu Lu Pengzhan Jin Guofei Pang Zhongqiang Zhang George Em Karniadakis	8
+ PDF Chat	Deep Residual Learning for Image Recognition	2016	Kaiming He Xiangyu Zhang Shaoqing Ren Jian Sun	8
+ PDF Chat	Model Reduction And Neural Networks For Parametric PDEs	2021	Kaushik Bhattacharya Bamdad Hosseini Nikola B. Kovachki Andrew M. Stuart	7
+	MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster	2013	Simon L. Cotter Gareth O. Roberts Andrew M. Stuart David White	6
+ PDF Chat	Prediction of aerodynamic flow fields using convolutional neural networks	2019	Saakaar Bhatnagar Yaser Afshar Shaowu Pan Karthik Duraisamy Shailendra Kaushik	6
+ PDF Chat	Solving ill-posed inverse problems using iterative deep neural networks	2017	Jonas Adler Ozan Öktem	6
+ PDF Chat	Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification	2018	Yinhao Zhu Nicholas Zabaras	6
+	Model Reduction and Neural Networks for Parametric PDEs	2020	Kaushik Bhattacharya Bamdad Hosseini Nikola B. Kovachki Andrew M. Stuart	6
+ PDF Chat	Inverse problems: A Bayesian perspective	2010	Andrew M. Stuart	5
+	Neural Message Passing for Quantum Chemistry	2017	Justin Gilmer Samuel S. Schoenholz Patrick Riley Oriol Vinyals George E. Dahl	5
+ PDF Chat	Approximation of high-dimensional parametric PDEs	2015	Albert Cohen Ronald DeVore	5
+	Neural Operator: Graph Kernel Network for Partial Differential Equations	2020	Zongyi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu Kaushik Bhattacharya Andrew M. Stuart Anima Anandkumar	5
+	Self-Normalizing Neural Networks	2017	Günter Klambauer Thomas Unterthiner Andreas Mayr Sepp Hochreiter	5
+ PDF Chat	A physics-informed operator regression framework for extracting data-driven continuum models	2020	Ravi G. Patel Nathaniel Trask Mitchell Wood Eric C. Cyr	5
+ PDF Chat	Hierarchical multiscale quantification of material uncertainty	2021	Burigede Liu Xingsheng Sun Kaushik Bhattacharya M. Ortíz	4
+	Unsupervised Deep Learning Algorithm for PDE-based Forward and Inverse Problems	2019	Leah Bar Nir Sochen	4
+ PDF Chat	Hybrid neural network potential for multilayer graphene	2019	Mingjian Wen Ellad B. Tadmor	4
+ PDF Chat	Solving parametric PDE problems with artificial neural networks	2020	Yuehaw Khoo Jianfeng Lu Lexing Ying	4
+	The Random Feature Model for Input-Output Maps between Banach Spaces	2020	Nicholas H. Nelsen Andrew M. Stuart	4
+ PDF Chat	A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials	2018	Zeliang Liu Cheng Wu M. Koishi	4
+	Fourier Neural Operator for Parametric Partial Differential Equations	2020	Zongyi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu Kaushik Bhattacharya Andrew M. Stuart Anima Anandkumar	4
+	Towards Physics-informed Deep Learning for Turbulent Flow Prediction	2020	Rui Wang Karthik Kashinath Mustafa Mustafa Adrian Albert Rose Yu	4
+	EikoNet: Solving the Eikonal equation with Deep Neural Networks	2020	Jonathan Smith Kamyar Azizzadenesheli Zachary E. Ross	4
+ PDF Chat	The Random Feature Model for Input-Output Maps between Banach Spaces	2021	Nicholas H. Nelsen Andrew M. Stuart	3
+ PDF Chat	Error bounds for approximations with deep ReLU networks	2017	Dmitry Yarotsky	3
+	Semi-Supervised Classification with Graph Convolutional Networks	2016	Thomas Kipf Max Welling	3
+ PDF Chat	A learning-based multiscale method and its application to inelastic impact problems	2021	Burigede Liu Nikola B. Kovachki Zongyi Li Kamyar Azizzadenesheli Anima Anandkumar Andrew M. Stuart Kaushik Bhattacharya	3
+	A differential equation for modeling Nesterov's accelerated gradient method: theory and insights	2016	Weijie Su Stephen Boyd Emmanuel J. Candès	3
+	Reduced Basis Methods for Partial Differential Equations: An Introduction	2015	Alfio Quarteroni Andrea Manzoni Federico Negri	3
+ PDF Chat	Operator learning for predicting multiscale bubble growth dynamics	2021	Chensen Lin Zhen Li Lu Lu Shengze Cai Martin Maxey George Em Karniadakis	3
+	DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators	2020	Zhiping Mao Lu Lu Olaf Marxen Tamer A. Zaki George Em Karniadakis	3
+ PDF Chat	Transport Map Accelerated Markov Chain Monte Carlo	2018	Matthew Parno Youssef Marzouk	3
+ PDF Chat	DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks	2021	Shengze Cai Zhicheng Wang Lu Lu Tamer A. Zaki George Em Karniadakis	3
+ PDF Chat	ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S	2011	Albert Cohen Ronald DeVore Christoph Schwab	3
+ PDF Chat	Stable architectures for deep neural networks	2017	Eldad Haber Lars Ruthotto	3
+ PDF Chat	Normalizing Flows: An Introduction and Review of Current Methods	2020	Ivan Kobyzev Simon J. D. Prince Marcus A. Brubaker	3
+	Adam: A Method for Stochastic Optimization	2014	Diederik P. Kingma Jimmy Ba	3
+	MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework	2020	Chiyu Max Jiang Soheil Esmaeilzadeh Kamyar Azizzadenesheli Karthik Kashinath Mustafa Mustafa Hamdi A. Tchelepi Philip Marcus Prabhat Anima Anandkumar	3
+	Learning to Optimize Multigrid PDE Solvers	2019	Daniel Greenfeld Meirav Galun Ronen Basri Irad Yavneh Ron Kimmel	3
+	Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs	2018	Ryan L. Murphy Balasubramaniam Srinivasan Vinayak Rao Bruno Ribeiro	3
+	Relational inductive biases, deep learning, and graph networks	2018	Peter Battaglia Jessica B. Hamrick Victor Bapst Álvaro Sánchez‐González Vinícius Zambaldi Mateusz Malinowski Andrea Tacchetti David Raposo Adam Santoro Ryan Faulkner	3
+ PDF Chat	Coupling Techniques for Nonlinear Ensemble Filtering	2022	Alessio Spantini Ricardo Baptista Youssef Marzouk	3
+ PDF Chat	Well-posed Bayesian geometric inverse problems arising in subsurface flow	2014	Marco Iglesias Kui Lin Andrew M. Stuart	3
+	The Marginal Value of Adaptive Gradient Methods in Machine Learning	2017	Ashia C. Wilson Rebecca Roelofs Mitchell Stern Nathan Srebro Benjamin Recht	3
+ PDF Chat	Bayesian inference with optimal maps	2012	Tarek Moselhy Youssef Marzouk	3
+	Graph Attention Networks	2017	Petar Veličković Guillem Cucurull Arantxa Casanova Adriana Romero Píetro Lió Yoshua Bengio	3
+	Sampling via Measure Transport: An Introduction	2016	Youssef Marzouk Tarek Moselhy Matthew Parno Alessio Spantini	3
+	An FFT-based Galerkin method for homogenization of periodic media	2014	Jaroslav Vondřejc Jan Zeman Ivo Marek	2
+ PDF Chat	Quantum-chemical insights from deep tensor neural networks	2017	Kristof T. Schütt Farhad Arbabzadah Stefan Chmiela K. Müller Alexandre Tkatchenko	2