{"total":90,"rows":[{"id":"2309.00583","title":"Geometry-Informed Neural Operator for Large-Scale 3D PDEs","created":"2023-09-01","cited_by_count":303,"area":null},{"id":"2205.13671","title":"Transformer for Partial Differential Equations' Operator Learning","created":"2022-05-26","cited_by_count":283,"area":null},{"id":"2302.01178","title":"Convolutional Neural Operators for robust and accurate learning of PDEs","created":"2023-02-02","cited_by_count":214,"area":null},{"id":"2405.19101","title":"Poseidon: Efficient Foundation Models for PDEs","created":"2024-05-29","cited_by_count":200,"area":null},{"id":"2202.06137","title":"MIONet: Learning multiple-input operators via tensor product","created":"2022-02-12","cited_by_count":181,"area":null},{"id":"2306.00258","title":"Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior","created":"2023-06-01","cited_by_count":131,"area":null},{"id":"2207.05748","title":"Physics-Informed Deep Neural Operator Networks","created":"2022-07-08","cited_by_count":113,"area":null},{"id":"2304.07993","title":"In-Context Operator Learning with Data Prompts for Differential Equation Problems","created":"2023-04-17","cited_by_count":101,"area":null},{"id":"2209.04934","title":"Clifford Neural Layers for PDE Modeling","created":"2022-09-08","cited_by_count":92,"area":null},{"id":"2211.08064","title":"Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications","created":"2022-11-15","cited_by_count":92,"area":null},{"id":"2206.03551","title":"NOMAD: Nonlinear Manifold Decoders for Operator Learning","created":"2022-06-07","cited_by_count":83,"area":null},{"id":"2312.14688","title":"A Mathematical Guide to Operator Learning","created":"2023-12-22","cited_by_count":76,"area":null},{"id":"2203.08205","title":"Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling","created":"2022-03-15","cited_by_count":65,"area":null},{"id":"2301.11167","title":"Neural Inverse Operators for Solving PDE Inverse Problems","created":"2023-01-26","cited_by_count":65,"area":null},{"id":"2212.06347","title":"Reliable extrapolation of deep neural operators informed by physics or sparse observations","created":"2022-12-13","cited_by_count":62,"area":null},{"id":"2305.19913","title":"Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning","created":"2023-05-31","cited_by_count":57,"area":null},{"id":"2208.13273","title":"Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers","created":"2022-08-28","cited_by_count":54,"area":null},{"id":"2304.13202","title":"Kernel Methods are Competitive for Operator Learning","created":"2023-04-26","cited_by_count":50,"area":null},{"id":"2210.10890","title":"Mitigating spectral bias for the multiscale operator learning","created":"2022-10-19","cited_by_count":44,"area":null},{"id":"2204.12670","title":"SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability","created":"2022-04-27","cited_by_count":35,"area":null},{"id":"2301.11509","title":"Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation","created":"2023-01-27","cited_by_count":32,"area":null},{"id":"2303.02243","title":"Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks","created":"2023-03-03","cited_by_count":32,"area":null},{"id":"2309.01020","title":"On the training and generalization of deep operator networks","created":"2023-09-02","cited_by_count":31,"area":null},{"id":"2401.07364","title":"PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws","created":"2024-01-14","cited_by_count":31,"area":null},{"id":"2210.01074","title":"Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities","created":"2022-10-03","cited_by_count":30,"area":null},{"id":"2205.11404","title":"Variable-Input Deep Operator Networks","created":"2022-05-23","cited_by_count":25,"area":null},{"id":"2209.02772","title":"Semi-supervised Invertible Neural Operators for Bayesian Inverse Problems","created":"2022-09-06","cited_by_count":25,"area":null},{"id":"2211.15188","title":"Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEs","created":"2022-11-28","cited_by_count":25,"area":null},{"id":"2404.07200","title":"Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective","created":"2024-04-10","cited_by_count":25,"area":null},{"id":"2402.03541","title":"HAMLET: Graph Transformer Neural Operator for Partial Differential Equations","created":"2024-02-05","cited_by_count":24,"area":null},{"id":"2209.14977","title":"Transformer Meets Boundary Value Inverse Problems","created":"2022-09-29","cited_by_count":22,"area":null},{"id":"2302.10351","title":"Variational Autoencoding Neural Operators","created":"2023-02-20","cited_by_count":22,"area":null},{"id":"2506.17774","title":"PhysiX: A Foundation Model for Physics Simulations","created":"2025-06-21","cited_by_count":22,"area":null},{"id":"2305.08757","title":"Physics Informed Token Transformer for Solving Partial Differential Equations","created":"2023-05-15","cited_by_count":21,"area":null},{"id":"2305.19663","title":"Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains","created":"2023-05-31","cited_by_count":21,"area":null},{"id":"2302.03271","title":"IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learning","created":"2023-02-07","cited_by_count":18,"area":null},{"id":"2303.10506","title":"Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs","created":"2023-03-18","cited_by_count":18,"area":null},{"id":"2405.09285","title":"Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning","created":"2024-05-15","cited_by_count":17,"area":null},{"id":"2307.09072","title":"Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO)","created":"2023-07-18","cited_by_count":16,"area":null},{"id":"2308.12939","title":"Learning Only On Boundaries: a Physics-Informed Neural operator for Solving Parametric Partial Differential Equations in Complex Geometries","created":"2023-08-24","cited_by_count":13,"area":null},{"id":"2308.03985","title":"Fourier neural operator for real-time simulation of 3D dynamic urban microclimate","created":"2023-08-08","cited_by_count":12,"area":null},{"id":"2410.01990","title":"Deep Learning Alternatives of the Kolmogorov Superposition Theorem","created":"2024-10-02","cited_by_count":12,"area":null},{"id":"2502.09346","title":"Machine learning for modelling unstructured grid data in computational physics: a review","created":"2025-02-13","cited_by_count":12,"area":null},{"id":"2210.01476","title":"Learning-based Design of Luenberger Observers for Autonomous Nonlinear Systems","created":"2022-10-04","cited_by_count":11,"area":null},{"id":"2306.17486","title":"Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation using Compact Implicit Layers","created":"2023-06-30","cited_by_count":11,"area":null},{"id":"2309.05812","title":"Interpretable learning of effective dynamics for multiscale systems","created":"2023-09-11","cited_by_count":11,"area":null},{"id":"2405.17211","title":"Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows","created":"2024-05-27","cited_by_count":11,"area":null},{"id":"2404.03099","title":"Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networks","created":"2024-04-03","cited_by_count":10,"area":null},{"id":"2201.11967","title":"Pseudo-Differential Neural Operator: Generalized Fourier Neural Operator for Learning Solution Operators of Partial Differential Equations","created":"2022-01-28","cited_by_count":8,"area":null},{"id":"2405.14558","title":"FUSE: Fast Unified Simulation and Estimation for PDEs","created":"2024-05-23","cited_by_count":8,"area":null},{"id":"2210.15799","title":"Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows","created":"2022-10-27","cited_by_count":7,"area":null},{"id":"2304.04234","title":"Variational operator learning: A unified paradigm marrying training neural operators and solving partial differential equations","created":"2023-04-09","cited_by_count":7,"area":null},{"id":"2511.19980","title":"Operator Learning at Machine Precision","created":"2025-11-25","cited_by_count":7,"area":null},{"id":"2405.07395","title":"CaFA: Global Weather Forecasting with Factorized Attention on Sphere","created":"2024-05-12","cited_by_count":6,"area":null},{"id":"2402.17853","title":"Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations","created":"2024-02-27","cited_by_count":5,"area":null},{"id":"2303.11379","title":"Solving High-Dimensional Inverse Problems with Auxiliary Uncertainty via Operator Learning with Limited Data","created":"2023-03-20","cited_by_count":4,"area":null},{"id":"2308.05061","title":"Fine-Tune Language Models as Multi-Modal Differential Equation Solvers","created":"2023-08-09","cited_by_count":4,"area":null},{"id":"2402.00825","title":"Resolution invariant deep operator network for PDEs with complex geometries","created":"2024-02-01","cited_by_count":4,"area":null},{"id":"2312.12869","title":"Parameterized Projected Bellman Operator","created":"2023-12-20","cited_by_count":3,"area":null},{"id":"2402.15636","title":"Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularization","created":"2024-02-23","cited_by_count":3,"area":null},{"id":"2407.03261","title":"Magnetic Hysteresis Modeling with Neural Operators","created":"2024-07-03","cited_by_count":3,"area":null},{"id":"2407.03593","title":"Green Multigrid Network","created":"2024-07-04","cited_by_count":3,"area":null},{"id":"2501.02791","title":"Orthogonal greedy algorithm for linear operator learning with shallow neural network","created":"2025-01-06","cited_by_count":3,"area":null},{"id":"2502.08683","title":"A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs","created":"2025-02-12","cited_by_count":3,"area":null},{"id":"2511.12890","title":"Method of Manufactured Learning for Solver-free Training of Neural Operators","created":"2025-11-17","cited_by_count":3,"area":null},{"id":"2212.00881","title":"Investigating Deep Learning Model Calibration for Classification Problems in Mechanics","created":"2022-12-01","cited_by_count":2,"area":null},{"id":"2302.00328","title":"Learning Functional Transduction","created":"2023-02-01","cited_by_count":2,"area":null},{"id":"2307.01354","title":"Learning Generic Solutions for Multiphase Transport in Porous Media via the Flux Functions Operator","created":"2023-07-03","cited_by_count":2,"area":null},{"id":"2509.26186","title":"PDE Solvers Should Be Local: Fast, Stable Rollouts with Learned Local Stencils","created":"2025-09-30","cited_by_count":2,"area":null},{"id":"2510.01365","title":"RheOFormer: A generative transformer model for simulation of complex fluids and flows","created":"2025-10-01","cited_by_count":2,"area":null},{"id":"2605.24658","title":"WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations","created":"2026-05-23","cited_by_count":2,"area":null},{"id":"2311.16519","title":"B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functions","created":"2023-11-28","cited_by_count":1,"area":null},{"id":"2312.02450","title":"GIT-Net: Generalized Integral Transform for Operator Learning","created":"2023-12-05","cited_by_count":1,"area":null},{"id":"2503.14053","title":"ON-Traffic: An Operator Learning Framework for Online Traffic Flow Estimation and Uncertainty Quantification from Lagrangian Sensors","created":"2025-03-18","cited_by_count":1,"area":null},{"id":"2505.04738","title":"SetONet: A Set-Based Operator Network for Solving PDEs with Variable-Input Sampling","created":"2025-05-07","cited_by_count":1,"area":null},{"id":"2505.07090","title":"Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structures","created":"2025-05-11","cited_by_count":1,"area":null},{"id":"2505.18923","title":"Graph-Based Operator Learning from Limited Data on Irregular Domains","created":"2025-05-25","cited_by_count":1,"area":null},{"id":"2507.18813","title":"Scale-Consistent Learning for Partial Differential Equations","created":"2025-07-24","cited_by_count":1,"area":null},{"id":"2507.22493","title":"LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process","created":"2025-07-30","cited_by_count":1,"area":null},{"id":"2510.16816","title":"Efficient High-Accuracy PDEs Solver with the Linear Attention Neural Operator","created":"2025-10-19","cited_by_count":1,"area":null},{"id":"2303.15659","title":"Boundary-to-Solution Mapping for Groundwater Flows in a Toth Basin","created":"2023-03-28","cited_by_count":0,"area":null},{"id":"2303.16656","title":"Learning Flow Functions from Data with Applications to Nonlinear Oscillators","created":"2023-03-29","cited_by_count":0,"area":null},{"id":"2502.15913","title":"Connecting the geometry and dynamics of many-body complex systems with message passing neural operators","created":"2025-02-21","cited_by_count":0,"area":null},{"id":"2505.11766","title":"Reformulating Neural Operators in $d+1$ Dimensions for Embedding Evolution","created":"2025-05-17","cited_by_count":0,"area":null},{"id":"2507.07292","title":"Discretization-independent operator learning for partial differential equations","created":"2025-07-09","cited_by_count":0,"area":null},{"id":"2602.05187","title":"SpectraKAN: Conditioning Spectral Operators","created":"2026-02-05","cited_by_count":0,"area":null},{"id":"2605.24876","title":"IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients","created":"2026-05-24","cited_by_count":0,"area":null},{"id":"2606.20015","title":"Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridges","created":"2026-06-18","cited_by_count":0,"area":null},{"id":"2610.05100","title":"METRO: Metric-Enhanced Token Routing Operator","created":"2026-10-04","cited_by_count":0,"area":null},{"id":"2610.20120","title":"A Bregman Proximal Viewpoint on Neural Operators","created":"2026-10-14","cited_by_count":0,"area":null}],"next_cursor":null}