Papers Operator learning
“Operator learning” 태그가 달린 논문 347편 · 필터 해제
Dimension reduction for derivative-informed operator learning: An analysis of approximation errors
We study the derivative-informed learning of nonlinear operators between infinite-dimensional separable Hilbert spaces by neural networks. Such operators can arise from the solution of partial differential equations (PDE…
Dimensionality ReductionExperimental DesignOperator learningOperator Learning: A Statistical Perspective
Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate…
Operator learningUncertainty QuantificationDeepOHeat-v1: Efficient Operator Learning for Fast and Trustworthy Thermal Simulation and Optimization in 3D-IC Design
Thermal analysis is crucial in three-dimensional integrated circuit (3D-IC) design due to increased power density and complex heat dissipation paths. Although operator learning frameworks such as DeepOHeat have demonstra…
GPUKolmogorov-Arnold NetworksOperator learningA Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometries
In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decod…
DecoderMeta-LearningOperator learningSuper-ResolutionInverted Gaussian Process Optimization for Nonparametric Koopman Operator Discovery
The Koopman Operator Theory opens the door for application of rich linear systems theory for computationally efficient modeling and optimal control of nonlinear systems by providing a globally linear representation for c…
GPROperator learningUncertainty QuantificationTowards scientific machine learning for granular material simulations -- challenges and opportunities
Micro-scale mechanisms, such as inter-particle and particle-fluid interactions, govern the behaviour of granular systems. While particle-scale simulations provide detailed insights into these interactions, their computat…
Operator learningNew universal operator approximation theorem for encoder-decoder architectures (Preprint)
Motivated by the rapidly growing field of mathematics for operator approximation with neural networks, we present a novel universal operator approximation theorem for a broad class of encoder-decoder architectures. In th…
DecoderOperator learningDeepOFormer: Deep Operator Learning with Domain-informed Features for Fatigue Life Prediction
Fatigue life characterizes the duration a material can function before failure under specific environmental conditions, and is traditionally assessed using stress-life (S-N) curves. While machine learning and deep learni…
Operator learningPredictionEquiNO: A Physics-Informed Neural Operator for Multiscale Simulations
Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, e.g., …
Operator learningUncertainty QuantificationData-Driven, ML-assisted Approaches to Problem Well-Posedness
Classically, to solve differential equation problems, it is necessary to specify sufficient initial and/or boundary conditions so as to allow the existence of a unique solution. Well-posedness of differential equation pr…
Operator learningInvertible Koopman neural operator for data-driven modeling of partial differential equations
Koopman operator theory is a popular candidate for data-driven modeling because it provides a global linearization representation for nonlinear dynamical systems. However, existing Koopman operator-based methods suffer f…
Operator learningTheory-to-Practice Gap for Neural Networks and Neural Operators
This work studies the sampling complexity of learning with ReLU neural networks and neural operators. For mappings belonging to relevant approximation spaces, we derive upper bounds on the best-possible convergence rate …
Operator learningPhysics-Informed Deep B-Spline Networks for Dynamical Systems
Physics-informed machine learning provides an approach to combining data and governing physics laws for solving complex partial differential equations (PDEs). However, efficiently solving PDEs with varying parameters and…
Operator learningPhysics-informed machine learningON-Traffic: An Operator Learning Framework for Online Traffic Flow Estimation and Uncertainty Quantification from Lagrangian Sensors
Accurate traffic flow estimation and prediction are critical for the efficient management of transportation systems, particularly under increasing urbanization. Traditional methods relying on static sensors often suffer …
ManagementOperator learningUncertainty QuantificationActive operator learning with predictive uncertainty quantification for partial differential equations
In this work, we develop a method for uncertainty quantification in deep operator networks (DeepONets) using predictive uncertainty estimates calibrated to model errors observed during training. The uncertainty framework…
Active LearningOperator learningUncertainty QuantificationImprove Representation for Imbalanced Regression through Geometric Constraints
In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-repre…
Operator learningregressionRepresentation LearningCauchy Random Features for Operator Learning in Sobolev Space
Operator learning is the approximation of operators between infinite dimensional Banach spaces using machine learning approaches. While most progress in this area has been driven by variants of deep neural networks such …
GPUOperator learningDeepONet Augmented by Randomized Neural Networks for Efficient Operator Learning in PDEs
Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have sh…
Operator learningLearning Hamiltonian Density Using DeepONet
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods…
Operator learningHigh-fidelity Multiphysics Modelling for Rapid Predictions Using Physics-informed Parallel Neural Operator
Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challeng…
Computational EfficiencyEnsemble LearningOperator learning