{"total":210,"rows":[{"id":"2103.12828","title":"Learning to Optimize: A Primer and A Benchmark","created":"2021-03-23","cited_by_count":208,"area":null},{"id":"2108.01938","title":"PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations","created":"2021-08-04","cited_by_count":106,"area":null},{"id":"2303.10462","title":"Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review","created":"2023-03-18","cited_by_count":75,"area":null},{"id":"2205.13134","title":"Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search","created":"2022-05-26","cited_by_count":66,"area":null},{"id":"2203.16797","title":"When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning","created":"2022-03-31","cited_by_count":65,"area":null},{"id":"2106.04781","title":"Encoding physics to learn reaction-diffusion processes","created":"2021-06-09","cited_by_count":61,"area":null},{"id":"2102.13156","title":"Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling","created":"2021-02-25","cited_by_count":59,"area":null},{"id":"2210.08772","title":"Signal Processing for Implicit Neural Representations","created":"2022-10-17","cited_by_count":46,"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":"2106.11927","title":"Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)","created":"2021-06-09","cited_by_count":41,"area":null},{"id":"2109.06407","title":"Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling","created":"2021-09-14","cited_by_count":41,"area":null},{"id":"2106.04546","title":"LEADS: Learning Dynamical Systems that Generalize Across Environments","created":"2021-06-08","cited_by_count":40,"area":null},{"id":"2304.14118","title":"Learning Neural PDE Solvers with Parameter-Guided Channel Attention","created":"2023-04-27","cited_by_count":38,"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":"2305.13341","title":"Discovering Causal Relations and Equations from Data","created":"2023-05-21","cited_by_count":36,"area":null},{"id":"2203.08852","title":"Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks","created":"2022-03-16","cited_by_count":34,"area":null},{"id":"2109.12482","title":"Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data","created":"2021-09-26","cited_by_count":31,"area":null},{"id":"2102.10801","title":"Neural Delay Differential Equations","created":"2021-02-22","cited_by_count":26,"area":null},{"id":"2307.12617","title":"Predicting Ordinary Differential Equations with Transformers","created":"2023-07-24","cited_by_count":26,"area":null},{"id":"2106.03603","title":"Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space","created":"2021-06-07","cited_by_count":25,"area":null},{"id":"2101.00962","title":"Hybrid FEM-NN models: Combining artificial neural networks with the finite element method","created":"2021-01-04","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":"2305.03874","title":"Learning Stochastic Dynamical System via Flow Map Operator","created":"2023-05-05","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":"2202.09340","title":"Learning Physics-Informed Neural Networks without Stacked Back-propagation","created":"2022-02-18","cited_by_count":23,"area":null},{"id":"2207.00529","title":"Deep Learning and Symbolic Regression for Discovering Parametric Equations","created":"2022-07-01","cited_by_count":23,"area":null},{"id":"2106.00008","title":"Robust discovery of partial differential equations in complex situations","created":"2021-05-31","cited_by_count":21,"area":null},{"id":"2303.17078","title":"Machine Learning for Partial Differential Equations","created":"2023-03-30","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":"2108.00069","title":"DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization","created":"2021-07-30","cited_by_count":19,"area":null},{"id":"2105.02368","title":"Physics-informed Spline Learning for Nonlinear Dynamics Discovery","created":"2021-05-05","cited_by_count":18,"area":null},{"id":"2206.00860","title":"Self-Consistency of the Fokker-Planck Equation","created":"2022-06-02","cited_by_count":18,"area":null},{"id":"2305.10706","title":"A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data","created":"2023-05-18","cited_by_count":18,"area":null},{"id":"2307.11013","title":"Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks","created":"2023-07-20","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":"2105.11045","title":"Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver","created":"2021-05-23","cited_by_count":15,"area":null},{"id":"2103.11488","title":"The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation","created":"2021-03-21","cited_by_count":14,"area":null},{"id":"2210.04338","title":"A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks","created":"2022-10-09","cited_by_count":14,"area":null},{"id":"2104.04785","title":"Generating Physically-Consistent Satellite Imagery for Climate Visualizations","created":"2021-04-10","cited_by_count":13,"area":null},{"id":"2202.10337","title":"Integration of knowledge and data in machine learning","created":"2022-02-15","cited_by_count":13,"area":null},{"id":"2203.03979","title":"Online Weak-form Sparse Identification of Partial Differential Equations","created":"2022-03-08","cited_by_count":13,"area":null},{"id":"2209.14430","title":"Minimax Optimal Kernel Operator Learning via Multilevel Training","created":"2022-09-28","cited_by_count":13,"area":null},{"id":"2210.08095","title":"Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty","created":"2022-10-14","cited_by_count":13,"area":null},{"id":"2301.11701","title":"TransNet: Transferable Neural Networks for Partial Differential Equations","created":"2023-01-27","cited_by_count":13,"area":null},{"id":"2411.00040","title":"P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics","created":"2024-10-29","cited_by_count":13,"area":null},{"id":"2207.11417","title":"Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers","created":"2022-07-23","cited_by_count":12,"area":null},{"id":"2311.06380","title":"Theory and implementation of inelastic Constitutive Artificial Neural Networks","created":"2023-11-10","cited_by_count":12,"area":null},{"id":"2204.07234","title":"PARC: Physics-Aware Recurrent Convolutional Neural Networks to Assimilate Meso-scale Reactive Mechanics of Energetic Materials","created":"2022-04-04","cited_by_count":11,"area":null},{"id":"2205.07331","title":"Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent","created":"2022-05-15","cited_by_count":11,"area":null},{"id":"2302.03358","title":"Deep-OSG: Deep Learning of Operators in Semigroup","created":"2023-02-07","cited_by_count":11,"area":null},{"id":"2303.15681","title":"GNN-based physics solver for time-independent PDEs","created":"2023-03-28","cited_by_count":11,"area":null},{"id":"2310.05227","title":"Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology","created":"2023-10-08","cited_by_count":11,"area":null},{"id":"2407.00809","title":"Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning","created":"2024-06-30","cited_by_count":11,"area":null},{"id":"2105.06331","title":"Informed Equation Learning","created":"2021-05-13","cited_by_count":10,"area":null},{"id":"2107.14742","title":"Connections between Numerical Algorithms for PDEs and Neural Networks","created":"2021-07-30","cited_by_count":10,"area":null},{"id":"2304.14374","title":"Pseudo-Hamiltonian neural networks for learning partial differential equations","created":"2023-04-27","cited_by_count":10,"area":null},{"id":"2411.04383","title":"Neuro-Symbolic AI: Explainability, Challenges, and Future Trends","created":"2024-11-07","cited_by_count":10,"area":null},{"id":"2105.02939","title":"PCE-PINNs: Physics-Informed Neural Networks for Uncertainty Propagation in Ocean Modeling","created":"2021-05-05","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":"2111.07671","title":"NeuralPDE: Modelling Dynamical Systems from Data","created":"2021-11-15","cited_by_count":9,"area":null},{"id":"2205.08384","title":"Deep Learning of Chaotic Systems from Partially-Observed Data","created":"2022-05-12","cited_by_count":9,"area":null},{"id":"2208.01462","title":"Physics-informed Deep Super-resolution for Spatiotemporal Data","created":"2022-08-02","cited_by_count":9,"area":null},{"id":"2305.08342","title":"Finite Expression Methods for Discovering Physical Laws from Data","created":"2023-05-15","cited_by_count":9,"area":null},{"id":"2309.09574","title":"Latent assimilation with implicit neural representations for unknown dynamics","created":"2023-09-18","cited_by_count":9,"area":null},{"id":"2405.02351","title":"Towards General Neural Surrogate Solvers with Specialized Neural Accelerators","created":"2024-05-02","cited_by_count":9,"area":null},{"id":"2405.11542","title":"From Fourier to Neural ODEs: Flow Matching for Modeling Complex Systems","created":"2024-05-19","cited_by_count":9,"area":"diffusion"},{"id":"2109.10253","title":"Short-term traffic prediction using physics-aware neural networks","created":"2021-09-21","cited_by_count":8,"area":null},{"id":"2203.17128","title":"Neural Q-learning for solving PDEs","created":"2022-03-31","cited_by_count":8,"area":null},{"id":"2306.04894","title":"A Bayesian Framework for learning governing Partial Differential Equation from Data","created":"2023-06-08","cited_by_count":8,"area":null},{"id":"2306.05805","title":"DynaBench: A benchmark dataset for learning dynamical systems from low-resolution data","created":"2023-06-09","cited_by_count":8,"area":null},{"id":"2309.07672","title":"Physics-constrained robust learning of open-form partial differential equations from limited and noisy data","created":"2023-09-14","cited_by_count":8,"area":null},{"id":"2504.10373","title":"DUE: A Deep Learning Framework and Library for Modeling Unknown Equations","created":"2025-04-14","cited_by_count":8,"area":null},{"id":"2107.06991","title":"Physics-informed generative neural network: an application to troposphere temperature prediction","created":"2021-07-08","cited_by_count":7,"area":null},{"id":"2109.00538","title":"Physics-integrated hybrid framework for model form error identification in nonlinear dynamical systems","created":"2021-09-01","cited_by_count":7,"area":null},{"id":"2204.07651","title":"Learning time-dependent PDE solver using Message Passing Graph Neural Networks","created":"2022-04-15","cited_by_count":7,"area":null},{"id":"2206.10586","title":"D-CIPHER: Discovery of Closed-form Partial Differential Equations","created":"2022-06-21","cited_by_count":7,"area":null},{"id":"2209.01491","title":"Learning Differential Operators for Interpretable Time Series Modeling","created":"2022-09-03","cited_by_count":7,"area":null},{"id":"2210.08140","title":"A Kernel Approach for PDE Discovery and Operator Learning","created":"2022-10-14","cited_by_count":7,"area":null},{"id":"2301.00776","title":"Physics-Informed Neural Networks for Prognostics and Health Management of Lithium-Ion Batteries","created":"2023-01-02","cited_by_count":7,"area":null},{"id":"2312.10913","title":"GINN-LP: A Growing Interpretable Neural Network for Discovering Multivariate Laurent Polynomial Equations","created":"2023-12-18","cited_by_count":7,"area":null},{"id":"2503.01036","title":"Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis","created":"2025-03-02","cited_by_count":7,"area":null},{"id":"2103.06685","title":"Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary grids","created":"2021-03-11","cited_by_count":6,"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":"2308.02137","title":"Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks","created":"2023-08-04","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":"2506.05513","title":"Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates","created":"2025-06-05","cited_by_count":6,"area":null},{"id":"2104.13962","title":"Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics","created":"2021-04-22","cited_by_count":5,"area":null},{"id":"2105.03336","title":"Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs","created":"2021-05-07","cited_by_count":5,"area":null},{"id":"2203.03458","title":"Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning","created":"2022-03-07","cited_by_count":5,"area":null},{"id":"2401.11825","title":"Sparse discovery of differential equations based on multi-fidelity Gaussian process","created":"2024-01-22","cited_by_count":5,"area":null},{"id":"2412.06158","title":"Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?","created":"2024-12-09","cited_by_count":5,"area":null},{"id":"2501.11350","title":"Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networks","created":"2025-01-20","cited_by_count":5,"area":null},{"id":"2505.01736","title":"PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems","created":"2025-05-03","cited_by_count":5,"area":null},{"id":"2104.14809","title":"Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves","created":"2021-04-30","cited_by_count":4,"area":null},{"id":"2202.01858","title":"Modeling unknown dynamical systems with hidden parameters","created":"2022-02-03","cited_by_count":4,"area":null},{"id":"2206.10480","title":"Learning to Estimate and Refine Fluid Motion with Physical Dynamics","created":"2022-06-21","cited_by_count":4,"area":null},{"id":"2209.02628","title":"Weak Collocation Regression method: fast reveal hidden stochastic dynamics from high-dimensional aggregate data","created":"2022-09-06","cited_by_count":4,"area":null},{"id":"2402.17913","title":"Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics","created":"2024-02-27","cited_by_count":4,"area":null},{"id":"2406.11809","title":"Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Models","created":"2024-06-17","cited_by_count":4,"area":null}],"next_cursor":"100"}