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A Library for Learning Neural Operators
Jean Kossaifi, Nikola Kovachki, Zongyi Li +8
We present NeuralOperator, an open-source Python library for operator learning. Neural operators generalize neural networks to maps between function spaces instead of finite-dimens…
Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Models
Giannis Daras, Weili Nie, Karsten Kreis +4
Using image models naively for solving inverse video problems often suffers from flickering, texture-sticking, and temporal inconsistency in generated videos. To tackle these probl…
Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problems
Hongkai Zheng, Wenda Chu, Austin Wang +3
When solving inverse problems, one increasingly popular approach is to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward mo…
Continuum Attention for Neural Operators
Edoardo Calvello, Nikola B. Kovachki, Matthew E. Levine +1
Transformers, and the attention mechanism in particular, have become ubiquitous in machine learning. Their success in modeling nonlocal, long-range correlations has led to their wi…
Data Complexity Estimates for Operator Learning
Nikola B. Kovachki, Samuel Lanthaler, Hrushikesh Mhaskar
Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the…
Operator Learning: Algorithms and Analysis
Nikola B. Kovachki, Samuel Lanthaler, Andrew M. Stuart
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators…