1.1k citations · 1.9k across the 32 of their papers we have counts for
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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…
On universal approximation and error bounds for Fourier Neural Operators
Nikola Kovachki, Samuel Lanthaler, Siddhartha Mishra
Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are un…
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…
Multiscale modeling of materials: Computing, data science,uncertainty and goal-oriented optimization
Nikola Kovachki, Burigede Liu, Xingsheng Sun +4
The recent decades have seen various attempts at accelerating the process of developing materials targeted towards specific applications. The performance required for a particular…
A learning-based multiscale method and its application to inelastic impact problems
Burigede Liu, Nikola Kovachki, Zongyi Li +4
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales:…