publications

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

2022

  1. JMLR
    On Universal Approximation and Error Bounds for Fourier Neural Operators
    Kovachki, Nikola B, Lanthaler, Samuel, and Mishra, Siddhartha
    Accepted: Journal of Machine Learning Research 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
    Accepted: Mechanics of Materials 2022
  3. 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

2021

  1. 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
  2. arXiv
    Convergence Rates for Learning Linear Operators from Noisy Data
    Hoop, Maarten V, Kovachki, Nikola B, Nelsen, Nicholas H, and Stuart, Andrew M
    CoRR 2021
  3. arXiv
    Neural Operator: Learning Maps Between Function Spaces
    Kovachki, Nikola B, Li, Zongyi, Liu, Burigede, Azizzadenesheli, Kamyar, Bhattacharya, Kaushik, Stuart, Andrew M, and Anandkumar, Anima
    CoRR 2021
  4. arXiv
    Markov Neural Operators for Learning Chaotic Systems
    Li, Zongyi, Kovachki, Nikola B, Azizzadenesheli, Kamyar, Liu, Burigede, Bhattacharya, Kaushik, Stuart, Andrew M, and Anandkumar, Anima
    CoRR 2021
  5. 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 9th International Conference on Learning Representations (ICLR) 2021
  6. 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
  7. JMLR
    Continuous Time Analysis of Momentum Methods
    Kovachki, Nikola B, and Stuart, Andrew M
    Journal of Machine Learning Research 2021

2020

  1. arXiv
    Conditional Sampling with Monotone GANs
    Kovachki, Nikola B, Baptista, Ricardo, Hosseini, Bamdad, and Marzouk, Youssef
    CoRR 2020
  2. 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
  3. arXiv
    Neural Operator: Graph Kernel Network for Partial Differential Equations
    Li, Zongyi, Kovachki, Nikola B, Azizzadenesheli, Kamyar, Liu, Burigede, Bhattacharya, Kaushik, Stuart, Andrew M, 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