{"total":525,"rows":[{"id":"2111.03794","title":"Physics-Informed Neural Operator for Learning Partial Differential Equations","created":"2021-11-06","cited_by_count":527,"area":null},{"id":"2108.08481","title":"Neural Operator: Learning Maps Between Function Spaces","created":"2021-08-19","cited_by_count":414,"area":null},{"id":"2105.14995","title":"Choose a Transformer: Fourier or Galerkin","created":"2021-05-31","cited_by_count":343,"area":null},{"id":"2302.14376","title":"GNOT: A General Neural Operator Transformer for Operator Learning","created":"2023-02-28","cited_by_count":336,"area":null},{"id":"2205.13671","title":"Transformer for Partial Differential Equations' Operator Learning","created":"2022-05-26","cited_by_count":283,"area":null},{"id":"2109.13459","title":"Multiwavelet-based Operator Learning for Differential Equations","created":"2021-09-28","cited_by_count":234,"area":null},{"id":"2309.15325","title":"Neural Operators for Accelerating Scientific Simulations and Design","created":"2023-09-27","cited_by_count":221,"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":"2202.06137","title":"MIONet: Learning multiple-input operators via tensor product","created":"2022-02-12","cited_by_count":181,"area":null},{"id":"2203.07404","title":"Respecting causality is all you need for training physics-informed neural networks","created":"2022-03-14","cited_by_count":156,"area":null},{"id":"2403.03542","title":"DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training","created":"2024-03-06","cited_by_count":151,"area":null},{"id":"2107.07871","title":"Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations","created":"2021-07-16","cited_by_count":145,"area":null},{"id":"2305.17560","title":"Scalable Transformer for PDE Surrogate Modeling","created":"2023-05-27","cited_by_count":128,"area":null},{"id":"2207.05748","title":"Physics-Informed Deep Neural Operator Networks","created":"2022-07-08","cited_by_count":113,"area":null},{"id":"2402.01868","title":"Challenges in Training PINNs: A Loss Landscape Perspective","created":"2024-02-02","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":"2108.06905","title":"A physics-informed variational DeepONet for predicting the crack path in brittle materials","created":"2021-08-16","cited_by_count":98,"area":null},{"id":"2204.06684","title":"Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport","created":"2022-04-14","cited_by_count":92,"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":"2407.07218","title":"Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations","created":"2024-07-09","cited_by_count":91,"area":null},{"id":"2201.01032","title":"Learning Operators with Coupled Attention","created":"2022-01-04","cited_by_count":90,"area":null},{"id":"2106.05384","title":"Long-time integration of parametric evolution equations with physics-informed DeepONets","created":"2021-06-09","cited_by_count":89,"area":null},{"id":"2110.01654","title":"Improved architectures and training algorithms for deep operator networks","created":"2021-10-04","cited_by_count":86,"area":null},{"id":"2312.14688","title":"A Mathematical Guide to Operator Learning","created":"2023-12-22","cited_by_count":76,"area":null},{"id":"2204.07230","title":"Learning two-phase microstructure evolution using neural operators and autoencoder architectures","created":"2022-04-11","cited_by_count":72,"area":null},{"id":"2406.11045","title":"Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks","created":"2024-06-16","cited_by_count":67,"area":null},{"id":"2106.13898","title":"Closed-form Continuous-time Neural Models","created":"2021-06-25","cited_by_count":65,"area":null},{"id":"2205.11393","title":"Generic bounds on the approximation error for physics-informed (and) operator learning","created":"2022-05-23","cited_by_count":65,"area":null},{"id":"2109.09338","title":"Learning in Sinusoidal Spaces with Physics-Informed Neural Networks","created":"2021-09-20","cited_by_count":62,"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":"2106.04781","title":"Encoding physics to learn reaction-diffusion processes","created":"2021-06-09","cited_by_count":61,"area":null},{"id":"2305.17289","title":"Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness","created":"2023-05-26","cited_by_count":60,"area":null},{"id":"2204.09157","title":"Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems","created":"2022-04-19","cited_by_count":58,"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":"2405.13998","title":"CViT: Continuous Vision Transformer for Operator Learning","created":"2024-05-22","cited_by_count":51,"area":null},{"id":"2304.13202","title":"Kernel Methods are Competitive for Operator Learning","created":"2023-04-26","cited_by_count":50,"area":null},{"id":"2203.00003","title":"Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems","created":"2022-02-25","cited_by_count":48,"area":null},{"id":"2310.05963","title":"CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics","created":"2023-09-13","cited_by_count":46,"area":null},{"id":"2306.05697","title":"Group Equivariant Fourier Neural Operators for Partial Differential Equations","created":"2023-06-09","cited_by_count":45,"area":null},{"id":"2107.01272","title":"Physics-Guided Deep Learning for Dynamical Systems: A Survey","created":"2021-07-02","cited_by_count":44,"area":null},{"id":"2205.03990","title":"Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics","created":"2022-05-09","cited_by_count":44,"area":null},{"id":"2204.03216","title":"Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data","created":"2022-04-07","cited_by_count":37,"area":null},{"id":"2206.00711","title":"Learning to Solve PDE-constrained Inverse Problems with Graph Networks","created":"2022-06-01","cited_by_count":37,"area":null},{"id":"2111.08823","title":"Meta-Auto-Decoder for Solving Parametric Partial Differential Equations","created":"2021-11-15","cited_by_count":36,"area":null},{"id":"2108.11985","title":"Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural network","created":"2021-08-25","cited_by_count":35,"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":"2210.00124","title":"Implicit Neural Spatial Representations for Time-dependent PDEs","created":"2022-09-30","cited_by_count":35,"area":null},{"id":"2207.08675","title":"Learning differentiable solvers for systems with hard constraints","created":"2022-07-18","cited_by_count":34,"area":null},{"id":"2212.03130","title":"Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems","created":"2022-12-06","cited_by_count":34,"area":null},{"id":"2405.19166","title":"Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity","created":"2024-05-29","cited_by_count":34,"area":null},{"id":"2203.12634","title":"Applications of physics informed neural operators","created":"2022-03-23","cited_by_count":33,"area":null},{"id":"2208.11866","title":"NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators","created":"2022-08-25","cited_by_count":33,"area":null},{"id":"2110.13361","title":"A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs","created":"2021-10-26","cited_by_count":32,"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":"2104.05512","title":"One-shot learning for solution operators of partial differential equations","created":"2021-04-06","cited_by_count":30,"area":null},{"id":"2301.02152","title":"L-HYDRA: Multi-Head Physics-Informed Neural Networks","created":"2023-01-05","cited_by_count":29,"area":null},{"id":"2209.03984","title":"$\\Delta$-PINNs: physics-informed neural networks on complex geometries","created":"2022-09-08","cited_by_count":28,"area":null},{"id":"2212.04663","title":"Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations","created":"2022-12-09","cited_by_count":28,"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":"2311.11262","title":"Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators","created":"2023-11-19","cited_by_count":28,"area":null},{"id":"2312.06398","title":"NVFi: Neural Velocity Fields for 3D Physics Learning from Dynamic Videos","created":"2023-12-11","cited_by_count":28,"area":null},{"id":"2401.08886","title":"RiemannONets: Interpretable Neural Operators for Riemann Problems","created":"2024-01-16","cited_by_count":28,"area":null},{"id":"2204.00997","title":"Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONets","created":"2022-04-03","cited_by_count":27,"area":null},{"id":"2310.05801","title":"An operator preconditioning perspective on training in physics-informed machine learning","created":"2023-10-09","cited_by_count":27,"area":null},{"id":"2204.12789","title":"Learning Green's functions associated with time-dependent partial differential equations","created":"2022-04-27","cited_by_count":26,"area":null},{"id":"2302.12888","title":"Elliptic PDE learning is provably data-efficient","created":"2023-02-24","cited_by_count":26,"area":null},{"id":"2312.15949","title":"HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork","created":"2023-12-26","cited_by_count":26,"area":null},{"id":"2110.13297","title":"Fast PDE-constrained optimization via self-supervised operator learning","created":"2021-10-25","cited_by_count":25,"area":null},{"id":"2201.13323","title":"Constructing coarse-scale bifurcation diagrams from spatio-temporal observations of microscopic simulations: A parsimonious machine learning approach","created":"2022-01-31","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":"2211.05567","title":"Partial Differential Equations Meet Deep Neural Networks: A Survey","created":"2022-10-27","cited_by_count":25,"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":"2411.16063","title":"VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction","created":"2024-11-25","cited_by_count":25,"area":null},{"id":"2107.03673","title":"MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs","created":"2021-07-08","cited_by_count":24,"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":"2311.04293","title":"Lie Point Symmetry and Physics Informed Networks","created":"2023-11-07","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":"2402.03541","title":"HAMLET: Graph Transformer Neural Operator for Partial Differential Equations","created":"2024-02-05","cited_by_count":24,"area":null},{"id":"2410.02698","title":"Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups","created":"2024-10-03","cited_by_count":24,"area":null},{"id":"2207.12800","title":"PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers","created":"2022-07-26","cited_by_count":22,"area":null},{"id":"2209.14977","title":"Transformer Meets Boundary Value Inverse Problems","created":"2022-09-29","cited_by_count":22,"area":null},{"id":"2203.11363","title":"PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations","created":"2022-03-21","cited_by_count":21,"area":null},{"id":"2210.03008","title":"Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems","created":"2022-10-06","cited_by_count":21,"area":null},{"id":"2212.07477","title":"Guiding continuous operator learning through Physics-based boundary constraints","created":"2022-12-14","cited_by_count":21,"area":null},{"id":"2309.15421","title":"Deep Learning in Deterministic Computational Mechanics","created":"2023-09-27","cited_by_count":21,"area":null},{"id":"2311.06483","title":"Stacked networks improve physics-informed training: applications to neural networks and deep operator networks","created":"2023-11-11","cited_by_count":21,"area":null},{"id":"2502.11835","title":"Neural Chaos: A Spectral Stochastic Neural Operator","created":"2025-02-17","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":"2407.01613","title":"Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks","created":"2024-06-28","cited_by_count":20,"area":null},{"id":"2204.11144","title":"Competitive Physics Informed Networks","created":"2022-04-23","cited_by_count":19,"area":null},{"id":"2208.04856","title":"Fully probabilistic deep models for forward and inverse problems in parametric PDEs","created":"2022-08-09","cited_by_count":19,"area":null},{"id":"2209.12871","title":"Variationally Mimetic Operator Networks","created":"2022-09-26","cited_by_count":19,"area":null},{"id":"2301.06676","title":"Explainable, Interpretable & Trustworthy AI for Intelligent Digital Twin: Case Study on Remaining Useful Life","created":"2023-01-17","cited_by_count":19,"area":null},{"id":"2302.01934","title":"A neural operator-based surrogate solver for free-form electromagnetic inverse design","created":"2023-02-04","cited_by_count":19,"area":null},{"id":"2304.07599","title":"Learning in latent spaces improves the predictive accuracy of deep neural operators","created":"2023-04-15","cited_by_count":19,"area":null},{"id":"2402.19242","title":"Derivative-enhanced Deep Operator Network","created":"2024-02-29","cited_by_count":19,"area":null},{"id":"2408.01600","title":"Physics-Informed Geometry-Aware Neural Operator","created":"2024-08-02","cited_by_count":19,"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":"2310.18888","title":"D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators","created":"2023-10-29","cited_by_count":18,"area":null}],"next_cursor":"100"}