1.1k citations · 1.9k across the 32 of their papers we have counts for
35 papers
CANTO: CAD-Native Transformer Operators for AI-Aided Engineering
Daniel Leibovici, Nikola Borislavov Kovachki, Dawon Ahn +8
Modern engineering systems, from automobiles to aircraft, are designed by using precise, continuous parametric computer-aided design (CAD) models. Evaluating design changes through…
Operator Learning for Smoothing and Forecasting
Edoardo Calvello, Elizabeth Carlson, Nikola Kovachki +2
Machine learning has opened new frontiers in purely data-driven algorithms for data assimilation in, and for forecasting of, dynamical systems; the resulting methods are showing so…
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…
Extension and neural operator approximation of the electrical impedance tomography inverse map
Maarten V. de Hoop, Nikola B. Kovachki, Matti Lassas +1
This paper considers the problem of noise-robust neural operator approximation for the solution map of Calderón's inverse conductivity problem. In this continuum model of electrica…
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…
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…
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…
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…
Convergence Rates for Learning Linear Operators from Noisy Data
Maarten V. de Hoop, Nikola B. Kovachki, Nicholas H. Nelsen +1
This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and th…
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…