1.1k citations · 1.9k across the 32 of their papers we have counts for
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Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs
Jean Kossaifi, Nikola Kovachki, Kamyar Azizzadenesheli +1
Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by…
Neural Operators for Accelerating Scientific Simulations and Design
Kamyar Azizzadenesheli, Nikola Kovachki, Zongyi Li +3
Scientific discovery and engineering design are currently limited by the time and cost of physical experiments, selected mostly through trial-and-error and intuition that require d…
Geometry-Informed Neural Operator for Large-Scale 3D PDEs
Zongyi Li, Nikola Borislavov Kovachki, Chris Choy +8
We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying ge…
Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces
Miguel Liu-Schiaffini, Clare E. Singer, Nikola Kovachki +4
Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems. For instance, increased greenhouse gas concentr…
Learning Homogenization for Elliptic Operators
Kaushik Bhattacharya, Nikola Kovachki, Aakila Rajan +2
Multiscale partial differential equations (PDEs) arise in various applications, and several schemes have been developed to solve them efficiently. Homogenization theory is a powerf…
An Approximation Theory Framework for Measure-Transport Sampling Algorithms
Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki +2
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algo…
Score-based Diffusion Models in Function Space
Jae Hyun Lim, Nikola B. Kovachki, Ricardo Baptista +10
Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a r…