Papers Operator learning
“Operator learning” 태그가 달린 논문 347편 · 필터 해제
Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks
Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Ope…
Bayesian OptimizationDecision MakingOperator learningSequential Decision MakingA finite operator learning technique for mapping the elastic properties of microstructures to their mechanical deformations
To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural …
Operator learningNonlinear model reduction for operator learning
Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet bas…
modelOperator learningLearning with SASQuaTCh: a Novel Variational Quantum Transformer Architecture with Kernel-Based Self-Attention
The recent exploding growth in size of state-of-the-art machine learning models highlights a well-known issue where exponential parameter growth, which has grown to trillions as in the case of the Generative Pre-trained …
image-classificationImage ClassificationOperator learningBridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural operator learning
The intricate process of bubble growth dynamics involves a broad spectrum of physical phenomena from microscale mechanics of bubble formation to macroscale interplay between bubbles and surrounding thermo-hydrodynamics. …
Operator learningNeural Parameter Regression for Explicit Representations of PDE Solution Operators
We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses t…
Computational EfficiencyOperator learningregressionA Pretraining-Finetuning Computational Framework for Material Homogenization
Homogenization is a fundamental tool for studying multiscale physical phenomena. Traditional numerical homogenization methods, heavily reliant on finite element analysis, demand significant computational resources, espec…
Operator learningDerivative-informed neural operator acceleration of geometric MCMC for infinite-dimensional Bayesian inverse problems
We propose an operator learning approach to accelerate geometric Markov chain Monte Carlo (MCMC) for solving infinite-dimensional Bayesian inverse problems (BIPs). While geometric MCMC employs high-quality proposals that…
Operator learningUncertainty quantification for deeponets with ensemble kalman inversion
In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenari…
Operator learningUncertainty QuantificationDynamic Gaussian Graph Operator: Learning parametric partial differential equations in arbitrary discrete mechanics problems
Deep learning methods have access to be employed for solving physical systems governed by parametric partial differential equations (PDEs) due to massive scientific data. It has been refined to operator learning that foc…
Operator learningLinear quadratic control of nonlinear systems with Koopman operator learning and the Nyström method
In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we …
Operator learningDeep Learning Computed Tomography based on the Defrise and Clack Algorithm
This study presents a novel approach for reconstructing cone beam computed tomography (CBCT) for specific orbits using known operator learning. Unlike traditional methods, this technique employs a filtered backprojection…
Deep LearningOperator learningNeural Operators with Localized Integral and Differential Kernels
Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular a…
Operator learningData-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning
Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-inten…
In-Context LearningOperator learningOperator Learning: Algorithms and Analysis
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expres…
Model DiscoveryOperator learningA novel data generation scheme for surrogate modelling with deep operator networks
Operator-based neural network architectures such as DeepONets have emerged as a promising tool for the surrogate modeling of physical systems. In general, towards operator surrogate modeling, the training data is generat…
GPROperator learningSmooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularization
Spatiotemporal modeling is critical for understanding complex systems across various scientific and engineering disciplines, but governing equations are often not fully known or computationally intractable due to inheren…
Operator learningDiffeomorphism Neural Operator for various domains and parameters of partial differential equations
In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep lear…
Operator learningInvertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems
Fourier Neural Operator (FNO) is a powerful and popular operator learning method. However, FNO is mainly used in forward prediction, yet a great many applications rely on solving inverse problems. In this paper, we propo…
Operator learningSobolev Training for Operator Learning
This study investigates the impact of Sobolev Training on operator learning frameworks for improving model performance. Our research reveals that integrating derivative information into the loss function enhances the tra…
Operator learning