160 citations · 238 across the 22 of their papers we have counts for
5 papers · 1 filter
Fourier Neural Operator for Parametric Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural o…
Multipole Graph Neural Operator for Parametric Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data…
Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference
Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki +1
We present a novel framework for conditional sampling of probability measures, using block triangular transport maps. We develop the theoretical foundations of block triangular tra…
Model Reduction and Neural Networks for Parametric PDEs
Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki +1
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of…
Neural Operator: Graph Kernel Network for Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli +4
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Eu…