{"total":583,"rows":[{"id":"2404.19756","title":"KAN: Kolmogorov-Arnold Networks","created":"2024-04-30","cited_by_count":649,"area":null},{"id":"2201.05624","title":"Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next","created":"2022-01-14","cited_by_count":608,"area":null},{"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":"2402.02366","title":"Transolver: A Fast Transformer Solver for PDEs on General Geometries","created":"2024-02-04","cited_by_count":326,"area":null},{"id":"2205.13671","title":"Transformer for Partial Differential Equations' Operator Learning","created":"2022-05-26","cited_by_count":283,"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":"2202.06137","title":"MIONet: Learning multiple-input operators via tensor product","created":"2022-02-12","cited_by_count":181,"area":null},{"id":"2211.01364","title":"An optimal control perspective on diffusion-based generative modeling","created":"2022-11-02","cited_by_count":147,"area":"diffusion"},{"id":"2103.12959","title":"Solving and Learning Nonlinear PDEs with Gaussian Processes","created":"2021-03-24","cited_by_count":129,"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":"2104.12325","title":"Efficient training of physics-informed neural networks via importance sampling","created":"2021-04-26","cited_by_count":110,"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":"2310.02994","title":"Multiple Physics Pretraining for Physical Surrogate Models","created":"2023-10-04","cited_by_count":98,"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":"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":"2301.12664","title":"Solving High-Dimensional PDEs with Latent Spectral Models","created":"2023-01-30","cited_by_count":89,"area":null},{"id":"2306.08827","title":"PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs","created":"2023-06-15","cited_by_count":87,"area":null},{"id":"2307.12306","title":"Tackling the Curse of Dimensionality with Physics-Informed Neural Networks","created":"2023-07-23","cited_by_count":79,"area":null},{"id":"2312.14688","title":"A Mathematical Guide to Operator Learning","created":"2023-12-22","cited_by_count":76,"area":null},{"id":"2410.13228","title":"From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning","created":"2024-10-17","cited_by_count":73,"area":null},{"id":"2201.07395","title":"Overview frequency principle/spectral bias in deep learning","created":"2022-01-19","cited_by_count":69,"area":null},{"id":"2302.04107","title":"Can Physics-Informed Neural Networks beat the Finite Element Method?","created":"2023-02-08","cited_by_count":68,"area":null},{"id":"2112.14038","title":"DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations","created":"2021-12-28","cited_by_count":66,"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":"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":"2210.00279","title":"Failure-informed adaptive sampling for PINNs","created":"2022-10-01","cited_by_count":64,"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":"2106.04781","title":"Encoding physics to learn reaction-diffusion processes","created":"2021-06-09","cited_by_count":61,"area":null},{"id":"2103.09959","title":"Evolutional Deep Neural Network","created":"2021-03-18","cited_by_count":50,"area":null},{"id":"2206.04642","title":"Probability flow solution of the Fokker-Planck equation","created":"2022-06-09","cited_by_count":47,"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":"2112.08125","title":"Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations","created":"2021-12-15","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":"2102.10782","title":"NTopo: Mesh-free Topology Optimization using Implicit Neural Representations","created":"2021-02-22","cited_by_count":41,"area":null},{"id":"2109.14860","title":"Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusion","created":"2021-09-30","cited_by_count":38,"area":null},{"id":"2408.09446","title":"Parameterized Physics-informed Neural Networks for Parameterized PDEs","created":"2024-08-18","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":"2410.01803","title":"On the expressiveness and spectral bias of KANs","created":"2024-10-02","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":"2511.15684","title":"Walrus: A Cross-Domain Foundation Model for Continuum Dynamics","created":"2025-11-19","cited_by_count":36,"area":null},{"id":"2205.01059","title":"Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)","created":"2022-04-29","cited_by_count":35,"area":null},{"id":"2405.03658","title":"A review on data-driven constitutive laws for solids","created":"2024-05-06","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":"2102.13037","title":"SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs","created":"2021-02-25","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":"2104.02746","title":"Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces","created":"2021-04-06","cited_by_count":30,"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":"2103.11181","title":"Adaptive deep density approximation for Fokker-Planck equations","created":"2021-03-20","cited_by_count":28,"area":null},{"id":"2104.09623","title":"The mixed deep energy method for resolving concentration features in finite strain hyperelasticity","created":"2021-04-15","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":"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":"2403.07187","title":"UPS: Efficiently Building Foundation Models for PDE Solving via Cross-Modal Adaptation","created":"2024-03-11","cited_by_count":27,"area":null},{"id":"2110.14121","title":"On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elements","created":"2021-10-27","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":"2106.07539","title":"On the Representation of Solutions to Elliptic PDEs in Barron Spaces","created":"2021-06-14","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":"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":"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":"2105.14094","title":"Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control","created":"2021-05-28","cited_by_count":24,"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":"2201.12354","title":"Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning","created":"2022-01-28","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":"2104.02741","title":"Conditional physics informed neural networks","created":"2021-04-06","cited_by_count":23,"area":null},{"id":"2312.14499","title":"Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks","created":"2023-12-22","cited_by_count":23,"area":null},{"id":"2302.08105","title":"A Neural PDE Solver with Temporal Stencil Modeling","created":"2023-02-16","cited_by_count":22,"area":null},{"id":"2112.03749","title":"Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems","created":"2021-12-07","cited_by_count":21,"area":null},{"id":"2206.10121","title":"Finite Expression Method for Solving High-Dimensional Partial Differential Equations","created":"2022-06-21","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":"2305.04962","title":"Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs","created":"2023-05-08","cited_by_count":21,"area":null},{"id":"2305.08404","title":"Theoretical Analysis of Inductive Biases in Deep Convolutional Networks","created":"2023-05-15","cited_by_count":21,"area":null},{"id":"2309.07049","title":"An Extreme Learning Machine-Based Method for Computational PDEs in Higher Dimensions","created":"2023-09-13","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":"2405.15603","title":"Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networks","created":"2024-05-24","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":"2106.05587","title":"A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems","created":"2021-06-10","cited_by_count":20,"area":null},{"id":"2201.08690","title":"A deep learning energy method for hyperelasticity and viscoelasticity","created":"2022-01-15","cited_by_count":20,"area":null},{"id":"2203.08501","title":"Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations","created":"2022-03-16","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":"2303.14878","title":"GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs","created":"2023-03-27","cited_by_count":20,"area":null},{"id":"2306.17648","title":"Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies","created":"2023-06-30","cited_by_count":20,"area":null},{"id":"2412.00088","title":"Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators","created":"2024-11-27","cited_by_count":20,"area":null},{"id":"2101.04844","title":"Reproducing Activation Function for Deep Learning","created":"2021-01-13","cited_by_count":19,"area":null},{"id":"2105.01228","title":"A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schr\\\"odinger Eigenvalue Problems","created":"2021-05-04","cited_by_count":19,"area":null},{"id":"2204.11144","title":"Competitive Physics Informed Networks","created":"2022-04-23","cited_by_count":19,"area":null},{"id":"2404.14688","title":"FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model","created":"2024-04-23","cited_by_count":19,"area":null},{"id":"2101.01708","title":"A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations","created":"2021-01-05","cited_by_count":18,"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":"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":"2102.11830","title":"Solving high-dimensional parabolic PDEs using the tensor train format","created":"2021-02-23","cited_by_count":17,"area":null},{"id":"2112.14012","title":"Solving time dependent Fokker-Planck equations via temporal normalizing flow","created":"2021-12-28","cited_by_count":17,"area":null},{"id":"2209.09988","title":"Investigating and Mitigating Failure Modes in Physics-informed Neural Networks (PINNs)","created":"2022-09-20","cited_by_count":17,"area":null},{"id":"2210.08424","title":"A cusp-capturing PINN for elliptic interface problems","created":"2022-10-16","cited_by_count":17,"area":null},{"id":"2212.14319","title":"Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients","created":"2022-12-29","cited_by_count":17,"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":"2109.13359","title":"Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation","created":"2021-09-27","cited_by_count":16,"area":null},{"id":"2204.11188","title":"M2N: Mesh Movement Networks for PDE Solvers","created":"2022-04-24","cited_by_count":16,"area":null},{"id":"2209.05150","title":"Bounding the Rademacher Complexity of Fourier neural operators","created":"2022-09-12","cited_by_count":16,"area":null}],"next_cursor":"100"}