Papers Operator learning
“Operator learning” 태그가 달린 논문 347편 · 필터 해제
Mesh-Informed Neural Operator : A Transformer Generative Approach
Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering ap…
Operator learningPrincipled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning
A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typicall…
Operator learningOmniFluids: Unified Physics Pre-trained Modeling of Fluid Dynamics
High-fidelity and efficient simulation of fluid dynamics drive progress in various scientific and engineering applications. Traditional computational fluid dynamics methods offer strong interpretability and guaranteed co…
Operator learningMondrian: Transformer Operators via Domain Decomposition
Operator learning enables data-driven modeling of partial differential equations (PDEs) by learning mappings between function spaces. However, scaling transformer-based operator models to high-resolution, multiscale doma…
Operator learningPMNO: A novel physics guided multi-step neural operator predictor for partial differential equations
Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capac…
Operator learningLearning Where to Learn: Training Distribution Selection for Provable OOD Performance
Out-of-distribution (OOD) generalization remains a fundamental challenge in machine learning. Models trained on one data distribution often experience substantial performance degradation when evaluated on shifted or unse…
Bilevel OptimizationGeneralization BoundsOperator learningRecurrent Neural Operators: Stable Long-Term PDE Prediction
Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mis…
Operator learningPredictionGraph-Based Operator Learning from Limited Data on Irregular Domains
Operator learning seeks to approximate mappings from input functions to output solutions, particularly in the context of partial differential equations (PDEs). While recent advances such as DeepONet and Fourier Neural Op…
Operator learningSelf-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems
We introduce an encoder-only approach to learn the evolution operators of large-scale non-linear dynamical systems, such as those describing complex natural phenomena. Evolution operators are particularly well-suited for…
Learning TheoryOperator learningRepresentation LearningGeometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains
The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator le…
Computational EfficiencyOperator learningOperator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization
We consider the problem of learning the evolution operator for the time-dependent Schr\"{o}dinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental prop…
Generalization BoundsOperator learningNeural Functional: Learning Function to Scalar Maps for Neural PDE Surrogates
Many architectures for neural PDE surrogates have been proposed in recent years, largely based on neural networks or operator learning. In this work, we derive and propose a new architecture, the Neural Functional, which…
Operator learningMulti-Level Monte Carlo Training of Neural Operators
Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on discretization of input and output function…
Computational EfficiencyOperator learningBeyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers
Real-world systems, from aerospace to railway engineering, are modeled with partial differential equations (PDEs) describing the physics of the system. Estimating robust solutions for such problems is essential. Deep lea…
Operator learningPhysics-informed machine learningLearning cardiac activation and repolarization times with operator learning
Solving partial or ordinary differential equation models in cardiac electrophysiology is a computationally demanding task, particularly when high-resolution meshes are required to capture the complex dynamics of the hear…
Operator learningPhysics-informed Multiple-Input Operators for efficient dynamic response prediction of structures
Finite element (FE) modeling is essential for structural analysis but remains computationally intensive, especially under dynamic loading. While operator learning models have shown promise in replicating static structura…
Operator learningSetONet: A Deep Set-based Operator Network for Solving PDEs with permutation invariant variable input sampling
Neural operators, particularly the Deep Operator Network (DeepONet), have shown promise in learning mappings between function spaces for solving differential equations. However, standard DeepONet requires input functions…
Operator learningData-driven operator learning for energy-efficient building control
Energy-efficient ventilation control plays a vital role in reducing building energy consumption while ensuring occupant health and comfort. While Computational Fluid Dynamics (CFD) simulations offer high-fidelity modelin…
Computational EfficiencyManagementOperator learningA Hybrid Framework for Efficient Koopman Operator Learning
Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving e…
Operator learningGeometry aware inference of steady state PDEs using Equivariant Neural Fields representations
Recent advances in Neural Fields have enabled powerful, discretization-invariant methods for learning neural operators that approximate solutions of Partial Differential Equations (PDEs) on general geometries. Building o…
Operator learningSuper-Resolution