Papers Operator learning
“Operator learning” 태그가 달린 논문 347편 · 필터 해제
DeepSeek vs. ChatGPT: A Comparative Study for Scientific Computing and Scientific Machine Learning Tasks
Large Language Models (LLMs) have emerged as powerful tools for tackling a wide range of problems, including those in scientific computing, particularly in solving partial differential equations (PDEs). However, differen…
Operator learningConnecting the geometry and dynamics of many-body complex systems with message passing neural operators
The relationship between scale transformations and dynamics established by renormalization group techniques is a cornerstone of modern physical theories, from fluid mechanics to elementary particle physics. Integrating r…
Inductive BiasOperator learningTANTE: Time-Adaptive Operator Learning via Neural Taylor Expansion
Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely…
Computational EfficiencyLanguage ModelingLanguage ModellingOperator learningPseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Data
Neural operators have shown great potential in surrogate modeling. However, training a well-performing neural operator typically requires a substantial amount of data, which can pose a major challenge in complex applicat…
Operator learningOptimization for Neural Operators can Benefit from Width
Neural Operators that directly learn mappings between function spaces, such as Deep Operator Networks (DONs) and Fourier Neural Operators (FNOs), have received considerable attention. Despite the universal approximation …
Operator learningRIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domains
Learning the solution operators of PDEs on arbitrary domains is challenging due to the diversity of possible domain shapes, in addition to the often intricate underlying physics. We propose an end-to-end graph neural net…
DiversityGraph Neural NetworkOperator learningMulti-Physics Simulations via Coupled Fourier Neural Operator
Physical simulations are essential tools across critical fields such as mechanical and aerospace engineering, chemistry, meteorology, etc. While neural operators, particularly the Fourier Neural Operator (FNO), have show…
Operator learningPhysical SimulationsIn-Context Operator Learning for Linear Propagator Models
We study operator learning in the context of linear propagator models for optimal order execution problems with transient price impact \`a la Bouchaud et al. (2004) and Gatheral (2010). Transient price impact persists an…
Operator learningTransfer LearningMeshONet: A Generalizable and Efficient Operator Learning Method for Structured Mesh Generation
Mesh generation plays a crucial role in scientific computing. Traditional mesh generation methods, such as TFI and PDE-based methods, often struggle to achieve a balance between efficiency and mesh quality. To address th…
Operator learningELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines
Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training DeepONets typically requires significant …
Operator learningPhysics-Informed Latent Neural Operator for Real-time Predictions of Complex Physical Systems
Deep operator network (DeepONet) has shown great promise as a surrogate model for systems governed by partial differential equations (PDEs), learning mappings between infinite-dimensional function spaces with high accura…
GPUOperator learningOrthogonal greedy algorithm for linear operator learning with shallow neural network
Greedy algorithms, particularly the orthogonal greedy algorithm (OGA), have proven effective in training shallow neural networks for fitting functions and solving partial differential equations (PDEs). In this paper, we …
Operator learningOperator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach
Machine learning methods have shown great success in various scientific areas, including fluid mechanics. However, reconstruction problems, where full velocity fields must be recovered from partial observations, remain c…
GeophysicsGPUOperator learningApproximation Rates in Fréchet Metrics: Barron Spaces, Paley-Wiener Spaces, and Fourier Multipliers
Operator learning is a recent development in the simulation of Partial Differential Equations (PDEs) by means of neural networks. The idea behind this approach is to learn the behavior of an operator, such that the resul…
Operator learningPoint-DeepONet: A Deep Operator Network Integrating PointNet for Nonlinear Analysis of Non-Parametric 3D Geometries and Load Conditions
Nonlinear structural analyses in engineering often require extensive finite element simulations, limiting their applicability in design optimization, uncertainty quantification, and real-time control. Conventional deep l…
Operator learningUncertainty QuantificationKKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a new two-block architecture that combines r…
Kolmogorov-Arnold NetworksOperator learningPhysics-informed machine learningA Library for Learning Neural Operators
We present NeuralOperator, an open-source Python library for operator learning. Neural operators generalize neural networks to maps between function spaces instead of finite-dimensional Euclidean spaces. They can be trai…
Operator learningA physics-informed transformer neural operator for learning generalized solutions of initial boundary value problems
Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these eq…
Operator learningOperator Learning for Robust Stabilization of Linear Markov-Jumping Hyperbolic PDEs
In this paper, we address the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 x 2 heterogeneous hyperbolic PDE and pr…
Computational EfficiencyOperator learningConformal Prediction on Quantifying Uncertainty of Dynamic Systems
Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of …
Conformal PredictionOperator learningPredictionTime Series