Papers Operator learning
“Operator learning” 태그가 달린 논문 347편 · 필터 해제
FUSE: Fast Unified Simulation and Estimation for PDEs
The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by em…
Operator learningCViT: Continuous Vision Transformer for Operator Learning
Operator learning, which aims to approximate maps between infinite-dimensional function spaces, is an important area in scientific machine learning with applications across various physical domains. Here we introduce the…
Operator learningA finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains
We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The proposed framework employs a …
Operator learningHierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution
In this work, we present an arbitrary-scale super-resolution (SR) method to enhance the resolution of scientific data, which often involves complex challenges such as continuity, multi-scale physics, and the intricacies …
Operator learningSuper-ResolutionEnsemble and Mixture-of-Experts DeepONets For Operator Learning
We present a novel deep operator network (DeepONet) architecture for operator learning, the ensemble DeepONet, that allows for enriching the trunk network of a single DeepONet with multiple distinct trunk networks. This …
Mixture-of-ExpertsOperator learningUnityPositional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning
Operator learning for Partial Differential Equations (PDEs) is rapidly emerging as a promising approach for surrogate modeling of intricate systems. Transformers with the self-attention mechanism$\unicode{x2013}$a powerf…
AllOperator learningPositionNonparametric Sparse Online Learning of the Koopman Operator
The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function spac…
Operator learningSparse LearningNonparametric Control Koopman Operators
This paper presents a novel Koopman (composition) operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By estab…
Learning TheoryModel Predictive ControlOperator learningLearning Flame Evolution Operator under Hybrid Darrieus Landau and Diffusive Thermal Instability
Recent advancements in the integration of artificial intelligence (AI) and machine learning (ML) with physical sciences have led to significant progress in addressing complex phenomena governed by nonlinear partial diffe…
Operator learningDiscretization Error of Fourier Neural Operators
Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is a common model architecture used for operator learning. The …
Operator learningIntroducing a microstructure-embedded autoencoder approach for reconstructing high-resolution solution field data from a reduced parametric space
In this study, we develop a novel multi-fidelity deep learning approach that transforms low-fidelity solution maps into high-fidelity ones by incorporating parametric space information into a standard autoencoder archite…
Computational EfficiencyOperator learningError analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs
In this paper, we provide a theoretical analysis of a type of operator learning method without data reliance based on the classical finite element approximation, which is called the finite element operator network (FEONe…
Operator learningBiLO: Bilevel Local Operator Learning for PDE inverse problems
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimiz…
Bilevel OptimizationOperator learningNeural Operator induced Gaussian Process framework for probabilistic solution of parametric partial differential equations
The study of neural operators has paved the way for the development of efficient approaches for solving partial differential equations (PDEs) compared with traditional methods. However, most of the existing neural operat…
Gaussian ProcessesOperator learningMD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation
We propose a neural operator framework, termed mixture density nonlinear manifold decoder (MD-NOMAD), for stochastic simulators. Our approach leverages an amalgamation of the pointwise operator learning neural architectu…
DecoderOperator learningA Hybrid Kernel-Free Boundary Integral Method with Operator Learning for Solving Parametric Partial Differential Equations In Complex Domains
The Kernel-Free Boundary Integral (KFBI) method presents an iterative solution to boundary integral equations arising from elliptic partial differential equations (PDEs). This method effectively addresses elliptic PDEs o…
Deep LearningOperator learningTowards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, na…
Operator learningLearning epidemic trajectories through Kernel Operator Learning: from modelling to optimal control
Since infectious pathogens start spreading into a susceptible population, mathematical models can provide policy makers with reliable forecasts and scenario analyses, which can be concretely implemented or solely consult…
Operator learningMixture of Experts Soften the Curse of Dimensionality in Operator Learning
In this paper, we construct a mixture of neural operators (MoNOs) between function spaces whose complexity is distributed over a network of expert neural operators (NOs), with each NO satisfying parameter scaling restric…
Mixture-of-ExpertsOperator learningMODNO: Multi Operator Learning With Distributed Neural Operators
The study of operator learning involves the utilization of neural networks to approximate operators. Traditionally, the focus has been on single-operator learning (SOL). However, recent advances have rapidly expanded thi…
Operator learning