{"total":208,"rows":[{"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":"2204.11127","title":"U-NO: U-shaped Neural Operators","created":"2022-04-23","cited_by_count":230,"area":null},{"id":"2104.08938","title":"On the approximation of functions by tanh neural networks","created":"2021-04-18","cited_by_count":81,"area":null},{"id":"2101.11845","title":"POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition","created":"2021-01-28","cited_by_count":79,"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":"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":"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":"2203.09346","title":"Error estimates for physics informed neural networks approximating the Navier-Stokes equations","created":"2022-03-17","cited_by_count":63,"area":null},{"id":"2106.14473","title":"Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs","created":"2021-06-28","cited_by_count":57,"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":"2211.08939","title":"Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology","created":"2022-11-16","cited_by_count":44,"area":null},{"id":"2103.05632","title":"Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps","created":"2021-03-09","cited_by_count":41,"area":null},{"id":"2203.03048","title":"Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors","created":"2022-03-06","cited_by_count":39,"area":null},{"id":"2106.03142","title":"A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation","created":"2021-06-06","cited_by_count":37,"area":null},{"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":"2203.01874","title":"Thermodynamics-informed graph neural networks","created":"2022-03-03","cited_by_count":33,"area":null},{"id":"2209.06257","title":"A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge","created":"2022-09-13","cited_by_count":31,"area":null},{"id":"2102.00491","title":"Learning elliptic partial differential equations with randomized linear algebra","created":"2021-01-31","cited_by_count":29,"area":null},{"id":"2207.08483","title":"wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws","created":"2022-07-18","cited_by_count":29,"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":"2305.15616","title":"Reversible and irreversible bracket-based dynamics for deep graph neural networks","created":"2023-05-24","cited_by_count":26,"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":"2203.11025","title":"Multigrid-augmented deep learning preconditioners for the Helmholtz equation","created":"2022-03-14","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":"2303.01055","title":"Physics-informed neural networks for solving forward and inverse problems in complex beam systems","created":"2023-03-02","cited_by_count":24,"area":null},{"id":"2403.05848","title":"tLaSDI: Thermodynamics-informed latent space dynamics identification","created":"2024-03-09","cited_by_count":23,"area":null},{"id":"2108.03561","title":"Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations","created":"2021-08-08","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":"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":"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":"2204.14030","title":"Neural Implicit Representations for Physical Parameter Inference from a Single Video","created":"2022-04-29","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":"2205.13545","title":"Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data","created":"2022-05-26","cited_by_count":18,"area":null},{"id":"2211.03134","title":"WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming","created":"2022-11-06","cited_by_count":18,"area":null},{"id":"2301.11494","title":"Learning Vortex Dynamics for Fluid Inference and Prediction","created":"2023-01-27","cited_by_count":17,"area":null},{"id":"2105.13011","title":"Neural Network Training Using $\\ell_1$-Regularization and Bi-fidelity Data","created":"2021-05-27","cited_by_count":16,"area":null},{"id":"2110.05445","title":"Data-driven approaches for predicting spread of infectious diseases through DINNs: Disease Informed Neural Networks","created":"2021-10-11","cited_by_count":15,"area":null},{"id":"2207.05779","title":"Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach","created":"2022-07-12","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":"2309.10656","title":"A spectrum of physics-informed Gaussian processes for regression in engineering","created":"2023-09-19","cited_by_count":14,"area":null},{"id":"2503.23616","title":"Interpretable Machine Learning in Physics: A Review","created":"2025-03-30","cited_by_count":14,"area":null},{"id":"2102.02617","title":"A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate","created":"2021-02-04","cited_by_count":13,"area":null},{"id":"2103.03385","title":"Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data","created":"2021-03-04","cited_by_count":13,"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":"2108.04085","title":"Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Data","created":"2021-08-05","cited_by_count":12,"area":null},{"id":"2202.06416","title":"State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning","created":"2022-02-13","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":"2303.02063","title":"Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook","created":"2023-03-03","cited_by_count":11,"area":null},{"id":"2306.17486","title":"Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation using Compact Implicit Layers","created":"2023-06-30","cited_by_count":11,"area":null},{"id":"2410.05592","title":"Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methods","created":"2024-10-08","cited_by_count":11,"area":null},{"id":"2105.12033","title":"TNet: A Model-Constrained Tikhonov Network Approach for Inverse Problems","created":"2021-05-25","cited_by_count":10,"area":null},{"id":"2110.01601","title":"NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs","created":"2021-10-04","cited_by_count":10,"area":null},{"id":"2404.08412","title":"PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction","created":"2024-04-12","cited_by_count":10,"area":"diffusion"},{"id":"2406.03569","title":"GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications","created":"2024-06-05","cited_by_count":10,"area":null},{"id":"2210.13414","title":"Thermodynamics-informed neural networks for physically realistic mixed reality","created":"2022-10-24","cited_by_count":9,"area":null},{"id":"2301.07609","title":"Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification","created":"2023-01-18","cited_by_count":9,"area":null},{"id":"2401.16943","title":"Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference","created":"2024-01-30","cited_by_count":9,"area":null},{"id":"2404.12416","title":"Full Shot Predictions for the DIII-D Tokamak via Deep Recurrent Networks","created":"2024-04-18","cited_by_count":9,"area":null},{"id":"2506.07958","title":"Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs","created":"2025-06-09","cited_by_count":9,"area":null},{"id":"2106.09658","title":"Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operators","created":"2021-06-17","cited_by_count":8,"area":null},{"id":"2109.09363","title":"Performance and accuracy assessments of an incompressible fluid solver coupled with a deep Convolutional Neural Network","created":"2021-09-20","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":"2301.11040","title":"Random Grid Neural Processes for Parametric Partial Differential Equations","created":"2023-01-26","cited_by_count":8,"area":null},{"id":"2402.12360","title":"Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks","created":"2024-02-19","cited_by_count":8,"area":null},{"id":"2410.22193","title":"GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws","created":"2024-10-29","cited_by_count":8,"area":null},{"id":"2108.10639","title":"GrADE: A graph based data-driven solver for time-dependent nonlinear partial differential equations","created":"2021-08-24","cited_by_count":7,"area":null},{"id":"2109.11446","title":"Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint","created":"2021-09-23","cited_by_count":7,"area":null},{"id":"2206.01495","title":"Constraining Gaussian processes for physics-informed acoustic emission mapping","created":"2022-06-03","cited_by_count":7,"area":null},{"id":"2206.05183","title":"GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions","created":"2022-06-10","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":"2209.04741","title":"A Thermal Machine Learning Solver For Chip Simulation","created":"2022-09-10","cited_by_count":7,"area":null},{"id":"2409.13876","title":"Physics-Informed Variational State-Space Gaussian Processes","created":"2024-09-20","cited_by_count":7,"area":null},{"id":"2101.04371","title":"Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning","created":"2021-01-12","cited_by_count":6,"area":null},{"id":"2102.12695","title":"Learning orbital dynamics of binary black hole systems from gravitational wave measurements","created":"2021-02-25","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":"2109.10681","title":"A Latent Restoring Force Approach to Nonlinear System Identification","created":"2021-09-22","cited_by_count":6,"area":null},{"id":"2208.09145","title":"Semi-analytic PINN methods for singularly perturbed boundary value problems","created":"2022-08-19","cited_by_count":6,"area":null},{"id":"2303.17824","title":"Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets","created":"2023-03-31","cited_by_count":6,"area":null},{"id":"2308.06338","title":"Size Lowerbounds for Deep Operator Networks","created":"2023-08-11","cited_by_count":6,"area":null},{"id":"2308.10892","title":"Bayesian polynomial neural networks and polynomial neural ordinary differential equations","created":"2023-08-17","cited_by_count":6,"area":null},{"id":"2402.15492","title":"Mechanics-Informed Autoencoder Enables Automated Detection and Localization of Unforeseen Structural Damage","created":"2024-02-23","cited_by_count":6,"area":null},{"id":"2102.05738","title":"Refinement of polygonal grids using Convolutional Neural Networks with applications to polygonal Discontinuous Galerkin and Virtual Element methods","created":"2021-02-10","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":"2204.12589","title":"Self-scalable Tanh (Stan): Faster Convergence and Better Generalization in Physics-informed Neural Networks","created":"2022-04-26","cited_by_count":5,"area":null},{"id":"2205.09479","title":"Neural ODEs with Irregular and Noisy Data","created":"2022-05-19","cited_by_count":5,"area":null},{"id":"2301.13516","title":"Recurrences reveal shared causal drivers of complex time series","created":"2023-01-31","cited_by_count":5,"area":null},{"id":"2309.11875","title":"Stochastic stiffness identification and response estimation of Timoshenko beams via physics-informed Gaussian processes","created":"2023-09-21","cited_by_count":5,"area":null},{"id":"2311.06028","title":"Symbolic Regression as Feature Engineering Method for Machine and Deep Learning Regression Tasks","created":"2023-11-10","cited_by_count":5,"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":"2412.01181","title":"Training Stiff Neural Ordinary Differential Equations with Explicit Exponential Integration Methods","created":"2024-12-02","cited_by_count":5,"area":null},{"id":"2502.01702","title":"Al-Khwarizmi: Discovering Physical Laws with Foundation Models","created":"2025-02-03","cited_by_count":5,"area":null},{"id":"2103.13496","title":"Similarity-Based Equational Inference in Physics","created":"2021-03-24","cited_by_count":4,"area":null},{"id":"2104.02452","title":"A Latent space solver for PDE generalization","created":"2021-04-06","cited_by_count":4,"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":"2110.01532","title":"Differentiable Spline Approximations","created":"2021-10-04","cited_by_count":4,"area":null},{"id":"2308.02894","title":"Physics-informed Gaussian process model for Euler-Bernoulli beam elements","created":"2023-08-05","cited_by_count":4,"area":null},{"id":"2411.06833","title":"Learning Interpretable Network Dynamics via Universal Neural Symbolic Regression","created":"2024-11-11","cited_by_count":4,"area":null},{"id":"2509.02846","title":"Towards Reasoning for PDE Foundation Models: A Reward-Model-Driven Inference-Time-Scaling Algorithm","created":"2025-09-02","cited_by_count":4,"area":"lr"},{"id":"2510.23810","title":"A Physics-informed Multi-resolution Neural Operator","created":"2025-10-27","cited_by_count":4,"area":null}],"next_cursor":"100"}