Operator learning
58 papers with code • 0 benchmarks • 1 datasets
Learn an operator between infinite dimensional Hilbert spaces or Banach spaces
Benchmarks
These leaderboards are used to track progress in Operator learning
Libraries
Use these libraries to find Operator learning models and implementationsMost implemented papers
Choose a Transformer: Fourier or Galerkin
Without softmax, the approximation capacity of a linearized Transformer variant can be proved to be comparable to a Petrov-Galerkin projection layer-wise, and the estimate is independent with respect to the sequence length.
Neural Operator: Learning Maps Between Function Spaces
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets.
Multiwavelet-based Operator Learning for Differential Equations
The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space.
Improved architectures and training algorithms for deep operator networks
In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel (NTK) theory, and reveal a bias that favors the approximation of functions with larger magnitudes.
Fast PDE-constrained optimization via self-supervised operator learning
Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering.
Diffeomorphically Learning Stable Koopman Operators
System representations inspired by the infinite-dimensional Koopman operator (generator) are increasingly considered for predictive modeling.
Learning Operators with Coupled Attention
Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data.
Convolutional Analysis Operator Learning by End-To-End Training of Iterative Neural Networks
Iterative neural networks - which contain the physical model - can overcome these issues.
On the influence of over-parameterization in manifold based surrogates and deep neural operators
In contrast, an even highly over-parameterized DeepONet leads to better generalization for both smooth and non-smooth dynamics.
Multi-Channel Convolutional Analysis Operator Learning for Dual-Energy CT Reconstruction
Extensive experiments with simulated and real computed tomography (CT) data were performed to validate the effectiveness of the proposed methods and we reported increased reconstruction accuracy compared to CAOL and iterative methods with single and joint total-variation (TV) regularization.