{"total":199,"rows":[{"id":"2207.05209","title":"Fourier Neural Operator with Learned Deformations for PDEs on General Geometries","created":"2022-07-11","cited_by_count":427,"area":null},{"id":"2108.08481","title":"Neural Operator: Learning Maps Between Function Spaces","created":"2021-08-19","cited_by_count":414,"area":null},{"id":"2202.03376","title":"Message Passing Neural PDE Solvers","created":"2022-02-07","cited_by_count":386,"area":null},{"id":"2105.14995","title":"Choose a Transformer: Fourier or Galerkin","created":"2021-05-31","cited_by_count":343,"area":null},{"id":"2109.03697","title":"U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow","created":"2021-09-03","cited_by_count":297,"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":"2302.01178","title":"Convolutional Neural Operators for robust and accurate learning of PDEs","created":"2023-02-02","cited_by_count":214,"area":null},{"id":"2209.15616","title":"Towards Multi-spatiotemporal-scale Generalized PDE Modeling","created":"2022-09-30","cited_by_count":197,"area":null},{"id":"2103.12959","title":"Solving and Learning Nonlinear PDEs with Gaussian Processes","created":"2021-03-24","cited_by_count":129,"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":"2106.14103","title":"PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs","created":"2021-06-26","cited_by_count":98,"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":"2209.04934","title":"Clifford Neural Layers for PDE Modeling","created":"2022-09-08","cited_by_count":92,"area":null},{"id":"2403.14404","title":"Physics-Informed Diffusion Models","created":"2024-03-21","cited_by_count":90,"area":"diffusion"},{"id":"2202.07643","title":"Lie Point Symmetry Data Augmentation for Neural PDE Solvers","created":"2022-02-15","cited_by_count":77,"area":null},{"id":"2310.00120","title":"Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs","created":"2023-09-29","cited_by_count":68,"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":"2410.16415","title":"On conditional diffusion models for PDE simulations","created":"2024-10-21","cited_by_count":60,"area":"diffusion"},{"id":"2312.10527","title":"CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems","created":"2023-12-16","cited_by_count":56,"area":"diffusion"},{"id":"2304.13202","title":"Kernel Methods are Competitive for Operator Learning","created":"2023-04-26","cited_by_count":50,"area":null},{"id":"2302.03026","title":"Sampling-Based Accuracy Testing of Posterior Estimators for General Inference","created":"2023-02-06","cited_by_count":46,"area":null},{"id":"2303.04778","title":"Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration","created":"2023-03-08","cited_by_count":46,"area":null},{"id":"2201.00217","title":"Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces","created":"2022-01-01","cited_by_count":45,"area":null},{"id":"2201.02217","title":"Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network","created":"2022-01-06","cited_by_count":45,"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":"2111.04941","title":"Solving PDE-constrained Control Problems Using Operator Learning","created":"2021-11-09","cited_by_count":42,"area":null},{"id":"2206.07681","title":"Learning to Accelerate Partial Differential Equations via Latent Global Evolution","created":"2022-06-15","cited_by_count":39,"area":null},{"id":"2109.07143","title":"Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNs","created":"2021-09-15","cited_by_count":38,"area":null},{"id":"2104.10873","title":"Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains","created":"2021-04-22","cited_by_count":37,"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":"2111.08823","title":"Meta-Auto-Decoder for Solving Parametric Partial Differential Equations","created":"2021-11-15","cited_by_count":36,"area":null},{"id":"2505.17004","title":"Guided Diffusion Sampling on Function Spaces with Applications to PDEs","created":"2025-05-22","cited_by_count":36,"area":"diffusion"},{"id":"2108.12956","title":"Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models","created":"2021-08-30","cited_by_count":35,"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":"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":"2301.10022","title":"Koopman neural operator as a mesh-free solver of non-linear partial differential equations","created":"2023-01-24","cited_by_count":29,"area":null},{"id":"2103.06183","title":"A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations","created":"2021-03-10","cited_by_count":28,"area":null},{"id":"2103.11181","title":"Adaptive deep density approximation for Fokker-Planck equations","created":"2021-03-20","cited_by_count":28,"area":null},{"id":"2506.08604","title":"Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints","created":"2025-06-10","cited_by_count":28,"area":"diffusion"},{"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":"2201.12354","title":"Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning","created":"2022-01-28","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":"2211.10575","title":"Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants","created":"2022-11-19","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":"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":"2506.17774","title":"PhysiX: A Foundation Model for Physics Simulations","created":"2025-06-21","cited_by_count":22,"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":"2302.13397","title":"Efficient physics-informed neural networks using hash encoding","created":"2023-02-26","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":"2408.06526","title":"Operator Learning Using Random Features: A Tool for Scientific Computing","created":"2024-08-12","cited_by_count":21,"area":null},{"id":"2202.04648","title":"A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems","created":"2022-02-09","cited_by_count":20,"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":"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":"2305.18702","title":"Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs","created":"2023-05-30","cited_by_count":18,"area":null},{"id":"2410.01337","title":"PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems","created":"2024-10-02","cited_by_count":18,"area":null},{"id":"2107.09814","title":"Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models","created":"2021-07-21","cited_by_count":16,"area":null},{"id":"2108.13054","title":"Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks","created":"2021-08-30","cited_by_count":16,"area":null},{"id":"2203.05142","title":"IAE-Net: Integral Autoencoders for Discretization-Invariant Learning","created":"2022-03-10","cited_by_count":15,"area":null},{"id":"2206.07680","title":"Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulator","created":"2022-06-15","cited_by_count":15,"area":null},{"id":"2305.12871","title":"MMGP: a Mesh Morphing Gaussian Process-based machine learning method for regression of physical problems under non-parameterized geometrical variability","created":"2023-05-22","cited_by_count":15,"area":null},{"id":"2105.09468","title":"A Deep Learning-Accelerated Data Assimilation and Forecasting Workflow for Commercial-Scale Geologic Carbon Storage","created":"2021-05-09","cited_by_count":14,"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":"2204.03193","title":"MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problems","created":"2022-04-07","cited_by_count":13,"area":null},{"id":"2102.03169","title":"Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems","created":"2021-02-04","cited_by_count":12,"area":null},{"id":"2302.03580","title":"Multi-Scale Message Passing Neural PDE Solvers","created":"2023-02-07","cited_by_count":12,"area":null},{"id":"2204.11138","title":"Use of Multifidelity Training Data and Transfer Learning for Efficient Construction of Subsurface Flow Surrogate Models","created":"2022-04-23","cited_by_count":11,"area":null},{"id":"2302.10255","title":"NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition","created":"2023-02-20","cited_by_count":11,"area":null},{"id":"2310.17844","title":"Adaptive operator learning for infinite-dimensional Bayesian inverse problems","created":"2023-10-27","cited_by_count":11,"area":null},{"id":"2409.16572","title":"Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration","created":"2024-09-25","cited_by_count":11,"area":null},{"id":"2102.03974","title":"Novel Deep neural networks for solving Bayesian statistical inverse","created":"2021-02-08","cited_by_count":10,"area":null},{"id":"2202.04041","title":"Physics-informed neural networks for solving parametric magnetostatic problems","created":"2022-02-08","cited_by_count":10,"area":null},{"id":"2206.09418","title":"LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data","created":"2022-06-19","cited_by_count":10,"area":null},{"id":"2102.01897","title":"Automatic Segmentation of Organs-at-Risk from Head-and-Neck CT using Separable Convolutional Neural Network with Hard-Region-Weighted Loss","created":"2021-02-03","cited_by_count":9,"area":null},{"id":"2111.01356","title":"DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method","created":"2021-11-02","cited_by_count":9,"area":null},{"id":"2203.13375","title":"Deep reinforcement learning for optimal well control in subsurface systems with uncertain geology","created":"2022-03-24","cited_by_count":9,"area":null},{"id":"2301.01104","title":"KoopmanLab: machine learning for solving complex physics equations","created":"2023-01-03","cited_by_count":9,"area":null},{"id":"2304.00388","title":"Multilevel CNNs for Parametric PDEs","created":"2023-04-01","cited_by_count":9,"area":null},{"id":"2101.04879","title":"Bayesian neural networks for weak solution of PDEs with uncertainty quantification","created":"2021-01-13","cited_by_count":8,"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":"2207.01765","title":"opPINN: Physics-Informed Neural Network with operator learning to approximate solutions to the Fokker-Planck-Landau equation","created":"2022-07-05","cited_by_count":8,"area":null},{"id":"2210.05837","title":"A composable machine-learning approach for steady-state simulations on high-resolution grids","created":"2022-10-11","cited_by_count":8,"area":null},{"id":"2301.11294","title":"Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates","created":"2023-01-26","cited_by_count":8,"area":null},{"id":"2305.16530","title":"Bi-fidelity Variational Auto-encoder for Uncertainty Quantification","created":"2023-05-25","cited_by_count":8,"area":null},{"id":"2401.16645","title":"Speeding up and reducing memory usage for scientific machine learning via mixed precision","created":"2024-01-30","cited_by_count":8,"area":null},{"id":"2510.06646","title":"The False Promise of Zero-Shot Super-Resolution in Machine-Learned Operators","created":"2025-10-08","cited_by_count":8,"area":null},{"id":"2202.11244","title":"A Bayesian Deep Learning Approach to Near-Term Climate Prediction","created":"2022-02-23","cited_by_count":7,"area":null},{"id":"2202.12358","title":"Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations","created":"2022-02-24","cited_by_count":7,"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":"2106.01078","title":"Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations","created":"2021-06-02","cited_by_count":6,"area":null},{"id":"2109.14002","title":"slimTrain -- A Stochastic Approximation Method for Training Separable Deep Neural Networks","created":"2021-09-28","cited_by_count":6,"area":null},{"id":"2207.14366","title":"Semi-supervised Learning of Partial Differential Operators and Dynamical Flows","created":"2022-07-28","cited_by_count":6,"area":null},{"id":"2212.00802","title":"An Introduction to Kernel and Operator Learning Methods for Homogenization by Self-consistent Clustering Analysis","created":"2022-12-01","cited_by_count":6,"area":null},{"id":"2306.07299","title":"Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma","created":"2023-06-11","cited_by_count":6,"area":null},{"id":"2308.09274","title":"A hybrid Decoder-DeepONet operator regression framework for unaligned observation data","created":"2023-08-18","cited_by_count":6,"area":null},{"id":"2101.11254","title":"Automatic Segmentation of Gross Target Volume of Nasopharynx Cancer using Ensemble of Multiscale Deep Neural Networks with Spatial Attention","created":"2021-01-27","cited_by_count":5,"area":null},{"id":"2104.14538","title":"Distributed Multigrid Neural Solvers on Megavoxel Domains","created":"2021-04-29","cited_by_count":5,"area":null},{"id":"2109.07399","title":"Disentangling Generative Factors of Physical Fields Using Variational Autoencoders","created":"2021-09-15","cited_by_count":5,"area":null},{"id":"2110.10080","title":"Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network","created":"2021-10-12","cited_by_count":5,"area":null},{"id":"2205.05187","title":"Multifidelity data fusion in convolutional encoder/decoder networks","created":"2022-05-10","cited_by_count":5,"area":null}],"next_cursor":"100"}