publications

Publications in reversed chronological order. Please feel free to contact me with questions about any of these works.

2023

  1. JMLR
    Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs
    Kovachki, Nikola B, Li, Zongyi, Liu, Burigede, Azizzadenesheli, Kamyar, Bhattacharya, Kaushik, Stuart, Andrew M, and Anandkumar, Anima
    Journal of Machine Learning 2023
  2. arXiv
    An Approximation Theory Framework for Measure-Transport Sampling Algorithms
    Baptista, Ricardo, Hosseini, Bamdad, Kovachki, Nikola B, Marzouk, Youssef M, and Sagiv, Amir
    CoRR 2023
  3. arXiv
    Geometry-Informed Neural Operator for Large-Scale 3D PDEs
    Li, Zongyi, Kovachki, Nikola B, Choy, Christopher, Li, Boyi, Kossaifi, Jean, Otta, Shourya P, Nabian, Mohammad A, Stadler, Maximilian, Hundt, Christian, Azizzadenesheli, Kamyar, and Anandkumar, Anima
    CoRR 2023
  4. arXiv
    Learning Homogenization for Elliptic Operators
    Bhattacharya, Kaushik, Kovachki, Nikola B, Rajan, Akilla, and Trautner, Margaret
    CoRR 2023
  5. SIAM UQ
    Convergence Rates for Learning Linear Operators from Noisy Data
    Hoop, Maarten V, Kovachki, Nikola B, Nelsen, Nicholas H, and Stuart, Andrew M
    SIAM Journal on Uncertainty Quantification 2023
  6. arXiv
    Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference
    Baptista, Ricardo, Hosseini, Bamdad, Kovachki, Nikola B, and Marzouk, Youssef M
    CoRR 2023
  7. arXiv
    Score-based Diffusion Models in Function Space
    Lim, Jae H, Kovachki, Nikola B, Baptista, Ricardo, Beckham, Christopher, Azizzadenesheli, Kamyar, Kossaifi, Jean, Voleti, Vikram, Song, Jiaming, Kreis, Karsten, Kautz, Jan, Pal, Christopher, Vahdat, Arash, and Anandkumar, Anima
    CoRR 2023
  8. arXiv
    Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs
    Kossaifi, Jean, Kovachki, Nikola B, Azizzadenesheli, Kamyar, and Anandkumar, Anima
    CoRR 2023
  9. arXiv
    Neural Operators for Accelerating Scientific Simulations and Design
    Azizzadenesheli, Kamyar, Kovachki, Nikola B, Li, Zongyi, Liu-Schiaffini, Miguel, Kossaifi, Jean, and Anandkumar, Anima
    CoRR 2023
  10. arXiv
    Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces
    Liu-Schiaffini, Miguel, Singer, Clare E, Kovachki, Nikola B, Schneider, Tapio, Azizzadenesheli, Kamyar, and Anandkumar, Anima
    CoRR 2023

2022

  1. JMPS
    A Learning-based Multiscale Method and its Application to Inelastic Impact Problems
    Liu, Burigede, Kovachki, Nikola B, Li, Zongyi, Azizzadenesheli, Kamyar, Anandkumar, Anima, Stuart, Andrew M, and Bhattacharya, Kaushik
    Journal of the Mechanics and Physics of Solids 2022
  2. MM
    Multiscale Modeling of Materials: Computing, Data Science, Uncertainty and Goal-oriented Optimization
    Kovachki, Nikola B, Liu, Burigede, Sun, Xingsheng, Zhou, Hao, Bhattacharya, Kaushik, Ortiz, Michael, and Stuart, Andrew M
    Mechanics of Materials 2022
  3. NeurIPS
    Learning Dissipative Dynamics in Chaotic Systems
    Li, Zongyi, Kovachki, Nikola B, Azizzadenesheli, Kamyar, Liu, Burigede, Bhattacharya, Kaushik, Stuart, Andrew M, and Anandkumar, Anima
    In Advances in Neural Information Processing Systems (NeurIPS) 2022

2021

  1. ICLR
    Fourier Neural Operator for Parametric Partial Differential Equations
    Li, Zongyi, Kovachki, Nikola B, Azizzadenesheli, Kamyar, Liu, Burigede, Bhattacharya, Kaushik, Stuart, Andrew M, and Anandkumar, Anima
    In International Conference on Learning Representations (ICLR) 2021
  2. SMAI-JCM
    Model Reduction and Neural Networks for Parametric PDEs
    Bhattacharya, Kaushik, Hosseini, Bamdad, Kovachki, Nikola B, and Stuart, Andrew M
    The SMAI journal of computational mathematics 2021
  3. arXiv
    Physics-Informed Neural Operator for Learning Partial Differential Equations
    Li, Zongyi, Zheng, Hongkai, Kovachki, Nikola B, Jin, David, Chen, Haoxuan, Liu, Burigede, Azizzadenesheli, Kamyar, and Anandkumar, Anima
    CoRR 2021
  4. JMLR
    On Universal Approximation and Error Bounds for Fourier Neural Operators
    Kovachki, Nikola B, Lanthaler, Samuel, and Mishra, Siddhartha
    Journal of Machine Learning Research 2021
  5. JMLR
    Continuous Time Analysis of Momentum Methods
    Kovachki, Nikola B, and Stuart, Andrew M
    Journal of Machine Learning Research 2021

2020

  1. NeurIPS
    Multipole Graph Neural Operator for Parametric Partial Differential Equations
    Li, Zongyi, Kovachki, Nikola B, Azizzadenesheli, Kamyar, Liu, Burigede, Stuart, Andrew M, Bhattacharya, Kaushik, and Anandkumar, Anima
    In Advances in Neural Information Processing Systems (NeurIPS) 2020
  2. arXiv
    Neural Operator: Graph Kernel Network for Partial Differential Equations
    Li, Zongyi, Kovachki, Nikola B, Azizzadenesheli, Kamyar, Liu, Burigede, Stuart, Andrew M, Bhattacharya, Kaushik, and Anandkumar, Anima
    CoRR 2020

2019

  1. JCTC
    Regression Clustering for Improved Accuracy and Training Costs with Molecular-Orbital-Based Machine Learning
    Cheng, Lixue, Kovachki, Nikola B, Welborn, Matthew, and Miller, Thomas F
    Journal of Chemical Theory and Computation 2019
  2. IP
    Ensemble Kalman Inversion: a Derivative-free Technique for Machine Learning Tasks
    Kovachki, Nikola B, and Stuart, Andrew M
    Inverse Problems 2019