{"total":65,"rows":[{"id":"2207.05748","title":"Physics-Informed Deep Neural Operator Networks","created":"2022-07-08","cited_by_count":113,"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":"2312.14688","title":"A Mathematical Guide to Operator Learning","created":"2023-12-22","cited_by_count":76,"area":null},{"id":"2304.13221","title":"Nonlocality and Nonlinearity Implies Universality in Operator Learning","created":"2023-04-26","cited_by_count":43,"area":null},{"id":"2305.00478","title":"Domain Agnostic Fourier Neural Operators","created":"2023-04-30","cited_by_count":38,"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":"2212.14365","title":"INO: Invariant Neural Operators for Learning Complex Physical Systems with Momentum Conservation","created":"2022-12-29","cited_by_count":28,"area":null},{"id":"2312.05410","title":"Rethinking materials simulations: Blending direct numerical simulations with neural operators","created":"2023-12-08","cited_by_count":25,"area":null},{"id":"2211.07377","title":"Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing","created":"2022-11-14","cited_by_count":24,"area":null},{"id":"2312.11176","title":"Harnessing the Power of Neural Operators with Automatically Encoded Conservation Laws","created":"2023-12-18","cited_by_count":24,"area":null},{"id":"2402.06031","title":"An operator learning perspective on parameter-to-observable maps","created":"2024-02-08","cited_by_count":22,"area":null},{"id":"2309.15421","title":"Deep Learning in Deterministic Computational Mechanics","created":"2023-09-27","cited_by_count":21,"area":null},{"id":"2204.00205","title":"A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements","created":"2022-04-01","cited_by_count":20,"area":null},{"id":"2301.06701","title":"Improved generalization with deep neural operators for engineering systems: Path towards digital twin","created":"2023-01-17","cited_by_count":19,"area":null},{"id":"2401.06070","title":"Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses","created":"2024-01-11","cited_by_count":18,"area":null},{"id":"2504.03503","title":"Operator Learning: A Statistical Perspective","created":"2025-04-04","cited_by_count":17,"area":null},{"id":"2402.12475","title":"Diffeomorphism Neural Operator for various domains and parameters of partial differential equations","created":"2024-02-19","cited_by_count":15,"area":null},{"id":"2405.09572","title":"Deep Neural Operator Enabled Digital Twin Modeling for Additive Manufacturing","created":"2024-05-13","cited_by_count":14,"area":null},{"id":"2506.10973","title":"Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning","created":"2025-06-12","cited_by_count":12,"area":null},{"id":"2301.12095","title":"MetaNO: How to Transfer Your Knowledge on Learning Hidden Physics","created":"2023-01-28","cited_by_count":10,"area":null},{"id":"2301.13331","title":"Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific ML","created":"2023-01-30","cited_by_count":8,"area":null},{"id":"2504.19452","title":"Geometry-Informed Neural Operator Transformer","created":"2025-04-28","cited_by_count":8,"area":null},{"id":"2602.02788","title":"Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs","created":"2026-02-02","cited_by_count":8,"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":"2409.04779","title":"Component Fourier Neural Operator for Singularly Perturbed Differential Equations","created":"2024-09-07","cited_by_count":7,"area":null},{"id":"2511.06802","title":"Neural-Initialized Newton: Accelerating Nonlinear Finite Elements via Operator Learning","created":"2025-11-10","cited_by_count":7,"area":null},{"id":"2412.09009","title":"A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problems","created":"2024-12-12","cited_by_count":6,"area":null},{"id":"2405.19019","title":"Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media","created":"2024-05-29","cited_by_count":5,"area":null},{"id":"2410.05281","title":"Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materials","created":"2024-09-23","cited_by_count":5,"area":null},{"id":"2502.06250","title":"DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling","created":"2025-02-10","cited_by_count":5,"area":null},{"id":"2506.10352","title":"History-Aware Neural Operator: Robust Data-Driven Constitutive Modeling of Path-Dependent Materials","created":"2025-06-12","cited_by_count":5,"area":null},{"id":"2403.18597","title":"Heterogeneous Peridynamic Neural Operators: Discover Biotissue Constitutive Law and Microstructure From Digital Image Correlation Measurements","created":"2024-03-27","cited_by_count":4,"area":null},{"id":"2301.04540","title":"Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures","created":"2023-01-11","cited_by_count":3,"area":null},{"id":"2407.03593","title":"Green Multigrid Network","created":"2024-07-04","cited_by_count":3,"area":null},{"id":"2410.01065","title":"Structure-Preserving Operator Learning","created":"2024-10-01","cited_by_count":3,"area":null},{"id":"2410.02136","title":"Disentangled Representation Learning for Parametric Partial Differential Equations","created":"2024-10-03","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":"2505.17838","title":"Continuum Transformers Perform In-Context Learning by Operator Gradient Descent","created":"2025-05-23","cited_by_count":3,"area":null},{"id":"2507.12233","title":"Universal Fourier Neural Operators for periodic homogenization problems in linear elasticity","created":"2025-07-16","cited_by_count":3,"area":null},{"id":"2305.11913","title":"Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data","created":"2023-05-18","cited_by_count":2,"area":null},{"id":"2412.18840","title":"Implicit factorized transformer approach to fast prediction of turbulent channel flows","created":"2024-12-25","cited_by_count":2,"area":null},{"id":"2504.13422","title":"Equilibrium Conserving Neural Operators for Super-Resolution Learning","created":"2025-04-18","cited_by_count":2,"area":null},{"id":"2505.23106","title":"Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery","created":"2025-05-29","cited_by_count":2,"area":null},{"id":"2507.13789","title":"Localized FNO for Spatiotemporal Hemodynamic Upsampling in Aneurysm MRI","created":"2025-07-18","cited_by_count":2,"area":null},{"id":"2509.01416","title":"MD-PNOP: Equation-Recast Neural Operators for Minimal-Data Extrapolation and PDE Solver Acceleration","created":"2025-09-01","cited_by_count":2,"area":null},{"id":"2509.09611","title":"ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance","created":"2025-09-11","cited_by_count":2,"area":null},{"id":"2209.14291","title":"Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator","created":"2022-08-29","cited_by_count":1,"area":null},{"id":"2503.19717","title":"Invertible Koopman neural operator for data-driven modeling of partial differential equations","created":"2025-03-25","cited_by_count":1,"area":null},{"id":"2506.11328","title":"An Attention-based Spatio-Temporal Neural Operator for Evolving Physics","created":"2025-06-12","cited_by_count":1,"area":null},{"id":"2603.11854","title":"Inverse Neural Operator for ODE Parameter Optimization","created":"2026-03-12","cited_by_count":1,"area":null},{"id":"2603.12676","title":"Parameterized Temporal Extrapolation of PDEs via Disentangled Latent Dynamics Manifold Fusion","created":"2026-03-13","cited_by_count":1,"area":null},{"id":"2605.08436","title":"A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds","created":"2026-05-08","cited_by_count":1,"area":null},{"id":"2606.27459","title":"Geometry-Conditioned Fourier Neural Operators for Cubic Nonlinear Schrodinger Dynamics on Periodic Domains","created":"2026-06-25","cited_by_count":1,"area":null},{"id":"2607.18043","title":"Adaptive Mamba Neural Operators","created":"2026-07-20","cited_by_count":1,"area":"ssm"},{"id":"2311.13885","title":"Can Physics Informed Neural Operators Self Improve?","created":"2023-11-23","cited_by_count":0,"area":null},{"id":"2410.20331","title":"Embedded Nonlocal Operator Regression (ENOR): Quantifying model error in learning nonlocal operators","created":"2024-10-27","cited_by_count":0,"area":null},{"id":"2503.04024","title":"An optimal Petrov-Galerkin framework for operator networks","created":"2025-03-06","cited_by_count":0,"area":null},{"id":"2505.18784","title":"A physics-guided smoothing method for material modeling with digital image correlation (DIC) measurements","created":"2025-05-24","cited_by_count":0,"area":null},{"id":"2506.07008","title":"Deep regularization networks for inverse problems with noisy operators","created":"2025-06-08","cited_by_count":0,"area":null},{"id":"2603.26030","title":"Constitutive parameterized deep energy method for solid mechanics problems with random material parameters","created":"2026-03-27","cited_by_count":0,"area":null},{"id":"2608.23546","title":"Inertial Manifold Neural Operator for Dissipative Time-Dependent Partial Differential Equations","created":"2026-08-24","cited_by_count":0,"area":null},{"id":"2609.33715","title":"Theory Guided and Interpretable Neural Operator Design for Partial Differential Equation Learning","created":"2026-09-27","cited_by_count":0,"area":null},{"id":"2609.39387","title":"Beyond Simulation: Retain-and-Repair Neural Operators for Real-World Adaptation","created":"2026-09-30","cited_by_count":0,"area":null}],"next_cursor":null}