Papers Operator learning
“Operator learning” 태그가 달린 논문 347편 · 필터 해제
Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning
This paper introduces the Kernel Neural Operator (KNO), a novel operator learning technique that uses deep kernel-based integral operators in conjunction with quadrature for function-space approximation of operators (map…
Numerical IntegrationOperator learningOperator Learning of Lipschitz Operators: An Information-Theoretic Perspective
Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, …
Operator learningAccelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone
Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For such liquid-metal dealloying (LMD) process, phase field models have been developed. However, the governing equations oft…
Operator learningOptimal deep learning of holomorphic operators between Banach spaces
Operator learning problems arise in many key areas of scientific computing where Partial Differential Equations (PDEs) are used to model physical systems. In such scenarios, the operators map between Banach or Hilbert sp…
Deep LearningGeneralization BoundsOperator learningProjection Methods for Operator Learning and Universal Approximation
We obtain a new universal approximation theorem for continuous (possibly nonlinear) operators on arbitrary Banach spaces using the Leray-Schauder mapping. Moreover, we introduce and study a method for operator learning i…
Operator learningHamilton-Jacobi Based Policy-Iteration via Deep Operator Learning
The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently deve…
Operator learningTwo-level overlapping additive Schwarz preconditioner for training scientific machine learning applications
We introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed preconditioner is motivated by the nonlinea…
Operator learningContinuum Attention for Neural Operators
Transformers, and the attention mechanism in particular, have become ubiquitous in machine learning. Their success in modeling nonlocal, long-range correlations has led to their widespread adoption in natural language pr…
Operator learningM2NO: Multiresolution Operator Learning with Multiwavelet-based Algebraic Multigrid Method
Solving partial differential equations (PDEs) effectively necessitates a multi-scale approach, particularly critical in high-dimensional scenarios characterized by increasing grid points or resolution. Traditional method…
Operator learningSuper-ResolutionGFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications
This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in this work, the graph feedforward networ…
Operator learningSolving Partial Differential Equations in Different Domains by Operator Learning method Based on Boundary Integral Equations
This article explores operator learning models that can deduce solutions to partial differential equations (PDEs) on arbitrary domains without requiring retraining. We introduce two innovative models rooted in boundary i…
Operator learningLearning the Hodgkin-Huxley Model with Operator Learning Techniques
We construct and compare three operator learning architectures, DeepONet, Fourier Neural Operator, and Wavelet Neural Operator, in order to learn the operator mapping a time-dependent applied current to the transmembrane…
Operator learningPhysics and geometry informed neural operator network with application to acoustic scattering
In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of …
Operator learningTransformers as Neural Operators for Solutions of Differential Equations with Finite Regularity
Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such op…
Operator learningPoseidon: Efficient Foundation Models for PDEs
We introduce Poseidon, a foundation model for learning the solution operators of PDEs. It is based on a multiscale operator transformer, with time-conditioned layer norms that enable continuous-in-time evaluations. A nov…
Operator learningInfinite-dimensional Diffusion Bridge Simulation via Operator Learning
The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion …
Bayesian InferenceOperator learningSpectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows
Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail consid…
Computational EfficiencyDe-aliasingOperator learningSuper-ResolutionDPHGNN: A Dual Perspective Hypergraph Neural Networks
Message passing on hypergraphs has been a standard framework for learning higher-order correlations between hypernodes. Recently-proposed hypergraph neural networks (HGNNs) can be categorized into spatial and spectral me…
Operator learningDeep Koopman Learning using Noisy Data
This paper proposes a data-driven framework to learn a finite-dimensional approximation of a Koopman operator for approximating the state evolution of a dynamical system under noisy observations. To this end, our propose…
Operator learningData Complexity Estimates for Operator Learning
Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the conditions for efficient operator learn…
Operator learning