1.1k citations · 1.9k across the 32 of their papers we have counts for
23 papers · 1 filter
Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting
Jean Kossaifi, Nikola Kovachki, Morteza Mardani +15
The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fun…
Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization
Boyuan Yao, Dingcheng Luo, Lianghao Cao +3
We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFN…
Geometric Operator Learning with Optimal Transport
Xinyi Li, Zongyi Li, Nikola Kovachki +1
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically…
InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences
Hongkai Zheng, Wenda Chu, Bingliang Zhang +9
Plug-and-play diffusion priors (PnPDP) have emerged as a promising research direction for solving inverse problems. However, current studies primarily focus on natural image restor…
Memorization and Regularization in Generative Diffusion Models
Ricardo Baptista, Agnimitra Dasgupta, Nikola B. Kovachki +2
Diffusion models have emerged as a powerful framework for generative modeling. At the heart of the methodology is score matching: learning gradients of families of log-densities fo…
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…
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…
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…
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…
Physics-Informed Neural Operator for Learning Partial Differential Equations
Zongyi Li, Hongkai Zheng, Nikola Kovachki +5
In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric…
Neural Operator: Learning Maps Between Function Spaces
Nikola Kovachki, Zongyi Li, Burigede Liu +4
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of n…
Learning Dissipative Dynamics in Chaotic Systems
Zongyi Li, Miguel Liu-Schiaffini, Nikola Kovachki +5
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many…
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…
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…
Continuous Time Analysis of Momentum Methods
Nikola B. Kovachki, Andrew M. Stuart
Gradient descent-based optimization methods underpin the parameter training of neural networks, and hence comprise a significant component in the impressive test results found in a…
Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks
Nikola B. Kovachki, Andrew M. Stuart
The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and varia…