Papers Operator learning
“Operator learning” 태그가 달린 논문 347편 · 필터 해제
State-space models are accurate and efficient neural operators for dynamical systems
Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable solutions. However, existing models, including…
Computational EfficiencyMambaOperator learningPhysics-informed machine learning+1Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured grid
Scientific machine learning has seen significant progress with the emergence of operator learning. However, existing methods encounter difficulties when applied to problems on unstructured grids and irregular domains. Sp…
Operator learningLeMON: Learning to Learn Multi-Operator Networks
Single-operator learning involves training a deep neural network to learn a specific operator, whereas recent work in multi-operator learning uses an operator embedding structure to train a single neural network on data …
Meta-LearningOperator learningAn Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning
The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed…
Operator learningTransfer Operator Learning with Fusion Frame
The challenge of applying learned knowledge from one domain to solve problems in another related but distinct domain, known as transfer learning, is fundamental in operator learning models that solve Partial Differential…
Operator learningTransfer LearningTotal Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models
We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts f…
DescriptiveOperator learningUncertainty QuantificationFredholm Integral Equations Neural Operator (FIE-NO) for Data-Driven Boundary Value Problems
In this paper, we present a novel Fredholm Integral Equation Neural Operator (FIE-NO) method, an integration of Random Fourier Features and Fredholm Integral Equations (FIE) into the deep learning framework, tailored for…
Operator learningControlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators
We study learning-theoretic foundations of operator learning, using the linear layer of the Fourier Neural Operator architecture as a model problem. First, we identify three main errors that occur during the learning pro…
Operator learningOperator Learning Using Random Features: A Tool for Scientific Computing
Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scien…
Operator learningregressionSynergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving
Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively exp…
Geometry-based operator learningMulti-Task LearningOperator learningTransfer LearningAlpha-VI DeepONet: A prior-robust variational Bayesian approach for enhancing DeepONets with uncertainty quantification
We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) using R\'enyi's $\alpha$-divergence to learn complex operators while quantifying uncertainty. By i…
Operator learningUncertainty QuantificationVariational InferenceAero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations
This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to un…
Operator learningPDE Surrogate ModelingSolving the Electrical Impedance Tomography Problem with a DeepONet Type Neural Network: Theory and Application
In this work, we consider the non-invasive medical imaging modality of Electrical Impedance Tomography, where the problem is to recover the conductivity in a medium from a set of data that arises out of a current-to-volt…
Operator learningHyperbolicLR: Epoch insensitive learning rate scheduler
This study proposes two novel learning rate schedulers -- Hyperbolic Learning Rate Scheduler (HyperbolicLR) and Exponential Hyperbolic Learning Rate Scheduler (ExpHyperbolicLR) -- to address the epoch sensitivity problem…
image-classificationImage ClassificationOperator learningTime Series ForecastingA Resolution Independent Neural Operator
The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the soluti…
Dictionary LearningOperator learningDilated convolution neural operator for multiscale partial differential equations
This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation…
Operator learningSeparable Operator Networks
Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they requ…
BenchmarkingGPUOperator learningFinite Operator Learning: Bridging Neural Operators and Numerical Methods for Efficient Parametric Solution and Optimization of PDEs
We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them …
Operator learningPhysics-informed machine learningA fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics
The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresp…
Operator learningGreen Multigrid Network
GreenLearning networks (GL) directly learn Green's function in physical space, making them an interpretable model for capturing unknown solution operators of partial differential equations (PDEs). For many PDEs, the corr…
GPUOperator learning