{"total":134,"rows":[{"id":"2109.01050","title":"Characterizing possible failure modes in physics-informed neural networks","created":"2021-09-02","cited_by_count":643,"area":null},{"id":"2103.10974","title":"Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets","created":"2021-03-19","cited_by_count":540,"area":null},{"id":"2105.09506","title":"Physics-informed neural networks (PINNs) for fluid mechanics: A review","created":"2021-05-20","cited_by_count":473,"area":null},{"id":"2103.11251","title":"Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges","created":"2021-03-20","cited_by_count":367,"area":null},{"id":"2105.14995","title":"Choose a Transformer: Fourier or Galerkin","created":"2021-05-31","cited_by_count":343,"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":"2111.02801","title":"Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems","created":"2021-11-01","cited_by_count":222,"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":"2110.15832","title":"CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method","created":"2021-10-29","cited_by_count":93,"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":"2110.09813","title":"Multi-Objective Loss Balancing for Physics-Informed Deep Learning","created":"2021-10-19","cited_by_count":87,"area":null},{"id":"2103.15341","title":"Stiff Neural Ordinary Differential Equations","created":"2021-03-29","cited_by_count":78,"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":"2110.07374","title":"Physics informed neural networks for continuum micromechanics","created":"2021-10-14","cited_by_count":46,"area":null},{"id":"2107.00940","title":"Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks","created":"2021-07-02","cited_by_count":43,"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":"2104.00615","title":"Physics-informed neural networks for the shallow-water equations on the sphere","created":"2021-04-01","cited_by_count":32,"area":null},{"id":"2111.01495","title":"Constructing Neural Network-Based Models for Simulating Dynamical Systems","created":"2021-11-02","cited_by_count":31,"area":null},{"id":"2202.07176","title":"DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectories","created":"2022-02-15","cited_by_count":30,"area":null},{"id":"2109.04304","title":"DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks","created":"2021-09-09","cited_by_count":28,"area":null},{"id":"2109.05364","title":"Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling","created":"2021-09-11","cited_by_count":27,"area":null},{"id":"2110.03049","title":"Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training","created":"2021-10-06","cited_by_count":26,"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":"2207.04084","title":"Adaptive Self-supervision Algorithms for Physics-informed Neural Networks","created":"2022-07-08","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":"2106.02993","title":"PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics","created":"2021-06-06","cited_by_count":21,"area":null},{"id":"2204.11144","title":"Competitive Physics Informed Networks","created":"2022-04-23","cited_by_count":19,"area":null},{"id":"2205.03377","title":"Physics-informed neural networks for PDE-constrained optimization and control","created":"2022-05-06","cited_by_count":19,"area":null},{"id":"2502.06774","title":"ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection","created":"2025-02-10","cited_by_count":17,"area":null},{"id":"2101.11256","title":"Partition of unity networks: deep hp-approximation","created":"2021-01-27","cited_by_count":16,"area":null},{"id":"2112.05620","title":"How to Avoid Trivial Solutions in Physics-Informed Neural Networks","created":"2021-12-10","cited_by_count":15,"area":null},{"id":"2311.04465","title":"Solving High Frequency and Multi-Scale PDEs with Gaussian Processes","created":"2023-11-08","cited_by_count":14,"area":null},{"id":"2207.14291","title":"Physics-Informed Neural Networks for Shell Structures","created":"2022-07-26","cited_by_count":13,"area":null},{"id":"2203.16577","title":"Calibrating constitutive models with full-field data via physics informed neural networks","created":"2022-03-30","cited_by_count":12,"area":null},{"id":"2201.08363","title":"Physics-informed neural networks for modeling rate- and temperature-dependent plasticity","created":"2022-01-20","cited_by_count":11,"area":null},{"id":"2206.09299","title":"Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations","created":"2022-06-19","cited_by_count":11,"area":null},{"id":"2301.04480","title":"BINN: A deep learning approach for computational mechanics problems based on boundary integral equations","created":"2023-01-11","cited_by_count":11,"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":"2110.04600","title":"A Review of Physics-based Machine Learning in Civil Engineering","created":"2021-10-09","cited_by_count":9,"area":null},{"id":"2105.00557","title":"Hard Encoding of Physics for Learning Spatiotemporal Dynamics","created":"2021-05-02","cited_by_count":8,"area":null},{"id":"2108.07667","title":"SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasets","created":"2021-08-17","cited_by_count":8,"area":null},{"id":"2401.12806","title":"Binary structured physics-informed neural networks for solving equations with rapidly changing solutions","created":"2024-01-23","cited_by_count":8,"area":null},{"id":"2509.12344","title":"FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning","created":"2025-09-15","cited_by_count":8,"area":null},{"id":"2206.15457","title":"PhySRNet: Physics informed super-resolution network for application in computational solid mechanics","created":"2022-06-30","cited_by_count":7,"area":null},{"id":"2208.08635","title":"Physics-Informed Neural Network Method for Parabolic Differential Equations with Sharply Perturbed Initial Conditions","created":"2022-08-18","cited_by_count":7,"area":null},{"id":"2210.12177","title":"An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator","created":"2022-10-21","cited_by_count":7,"area":null},{"id":"2410.03496","title":"Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases","created":"2024-10-04","cited_by_count":7,"area":null},{"id":"2201.13389","title":"Physics-informed neural networks for non-Newtonian fluid thermo-mechanical problems: an application to rubber calendering process","created":"2022-01-31","cited_by_count":6,"area":null},{"id":"2209.03276","title":"Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networks","created":"2022-09-07","cited_by_count":6,"area":null},{"id":"2505.21404","title":"Dual Natural Gradient Descent for Scalable Training of Physics-Informed Neural Networks","created":"2025-05-27","cited_by_count":6,"area":null},{"id":"2511.05452","title":"Self-adaptive weighting and sampling for physics-informed neural networks","created":"2025-11-07","cited_by_count":6,"area":null},{"id":"2106.13638","title":"Transient Stability Analysis with Physics-Informed Neural Networks","created":"2021-06-25","cited_by_count":5,"area":null},{"id":"2206.14709","title":"An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equations","created":"2022-06-29","cited_by_count":5,"area":null},{"id":"2506.22555","title":"Spectral Bias in Variational Quantum Machine Learning","created":"2025-06-27","cited_by_count":5,"area":null},{"id":"2110.01532","title":"Differentiable Spline Approximations","created":"2021-10-04","cited_by_count":4,"area":null},{"id":"2112.00220","title":"A generic physics-informed neural network-based framework for reliability assessment of multi-state systems","created":"2021-12-01","cited_by_count":4,"area":null},{"id":"2204.07413","title":"Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networks","created":"2022-04-15","cited_by_count":4,"area":null},{"id":"2210.09546","title":"An Improved Structured Mesh Generation Method Based on Physics-informed Neural Networks","created":"2022-10-18","cited_by_count":4,"area":null},{"id":"2307.12435","title":"A Generalized Schwarz-type Non-overlapping Domain Decomposition Method using Physics-constrained Neural Networks","created":"2023-07-23","cited_by_count":4,"area":null},{"id":"2308.04457","title":"A Critical Review of Physics-Informed Machine Learning Applications in Subsurface Energy Systems","created":"2023-08-06","cited_by_count":4,"area":null},{"id":"2405.01680","title":"Physics-Informed Neural Networks: Minimizing Residual Loss with Wide Networks and Effective Activations","created":"2024-05-02","cited_by_count":4,"area":null},{"id":"2406.05108","title":"Adapting Physics-Informed Neural Networks to Improve ODE Optimization in Mosquito Population Dynamics","created":"2024-06-07","cited_by_count":4,"area":null},{"id":"2601.07760","title":"Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning","created":"2026-01-12","cited_by_count":4,"area":null},{"id":"2110.02296","title":"On the Correspondence between Gaussian Processes and Geometric Harmonics","created":"2021-10-05","cited_by_count":3,"area":null},{"id":"2110.05531","title":"Study of Drug Assimilation in Human System using Physics Informed Neural Networks","created":"2021-10-08","cited_by_count":3,"area":null},{"id":"2111.09705","title":"Learning Free-Surface Flow with Physics-Informed Neural Networks","created":"2021-11-17","cited_by_count":3,"area":null},{"id":"2111.10329","title":"Physics-enhanced Neural Networks in the Small Data Regime","created":"2021-11-19","cited_by_count":3,"area":null},{"id":"2112.05489","title":"Surrogate-data-enriched Physics-Aware Neural Networks","created":"2021-12-10","cited_by_count":3,"area":null},{"id":"2207.09299","title":"Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs","created":"2022-07-19","cited_by_count":3,"area":null},{"id":"2402.02425","title":"DeepLag: Discovering Deep Lagrangian Dynamics for Intuitive Fluid Prediction","created":"2024-02-04","cited_by_count":3,"area":null},{"id":"2410.01786","title":"Learning To Solve Differential Equation Constrained Optimization Problems","created":"2024-10-02","cited_by_count":3,"area":null},{"id":"2501.18582","title":"A Control Perspective on Training PINNs","created":"2025-01-30","cited_by_count":3,"area":null},{"id":"2509.06580","title":"AI for Scientific Discovery is a Social Problem","created":"2025-09-08","cited_by_count":3,"area":null},{"id":"2103.03565","title":"Physics-aware deep neural networks for surrogate modeling of turbulent natural convection","created":"2021-03-05","cited_by_count":2,"area":null},{"id":"2108.01862","title":"Reconstructing a dynamical system and forecasting time series by self-consistent deep learning","created":"2021-08-04","cited_by_count":2,"area":null},{"id":"2109.03956","title":"AdjointNet: Constraining machine learning models with physics-based codes","created":"2021-09-08","cited_by_count":2,"area":null},{"id":"2111.05641","title":"Parallel Physics-Informed Neural Networks with Bidirectional Balance","created":"2021-11-10","cited_by_count":2,"area":null},{"id":"2209.06910","title":"Modelling of physical systems with a Hopf bifurcation using mechanistic models and machine learning","created":"2022-09-07","cited_by_count":2,"area":null},{"id":"2401.14591","title":"Ricci flow regularization in latent spaces for the forward learning of partial differential equations","created":"2024-01-26","cited_by_count":2,"area":null},{"id":"2408.14734","title":"General-Kindred Physics-Informed Neural Network to the Solutions of Singularly Perturbed Differential Equations","created":"2024-08-27","cited_by_count":2,"area":null},{"id":"2412.09752","title":"A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks","created":"2024-12-12","cited_by_count":2,"area":null},{"id":"2505.14595","title":"Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers","created":"2025-05-20","cited_by_count":2,"area":null},{"id":"2506.16443","title":"Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networks","created":"2025-06-19","cited_by_count":2,"area":null},{"id":"2509.20191","title":"Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems","created":"2025-09-24","cited_by_count":2,"area":null},{"id":"2511.11734","title":"Physics-Informed Neural ODEs with Scale-Aware Residuals for Learning Stiff Biophysical Dynamics","created":"2025-11-13","cited_by_count":2,"area":null},{"id":"2105.12307","title":"Optimal Transport Based Refinement of Physics-Informed Neural Networks","created":"2021-05-26","cited_by_count":1,"area":null},{"id":"2111.09930","title":"Learning To Estimate Regions Of Attraction Of Autonomous Dynamical Systems Using Physics-Informed Neural Networks","created":"2021-11-18","cited_by_count":1,"area":null},{"id":"2203.14961","title":"A Deep Learning Approach for Thermal Plume Prediction of Groundwater Heat Pumps","created":"2022-03-29","cited_by_count":1,"area":null},{"id":"2307.13517","title":"Towards Long-Term predictions of Turbulence using Neural Operators","created":"2023-07-25","cited_by_count":1,"area":null},{"id":"2411.11276","title":"Coupled Integral PINN for Discontinuity","created":"2024-11-18","cited_by_count":1,"area":null},{"id":"2502.17597","title":"Unraveling particle dark matter with Physics-Informed Neural Networks","created":"2025-02-24","cited_by_count":1,"area":null},{"id":"2508.03315","title":"Bridging ocean wave physics and deep learning: Physics-informed neural operators for nonlinear wavefield reconstruction in real-time","created":"2025-08-05","cited_by_count":1,"area":null},{"id":"2602.01737","title":"Physics-Informed Chebyshev Polynomial Neural Operator for Parametric Partial Differential Equations","created":"2026-02-02","cited_by_count":1,"area":null},{"id":"2606.23359","title":"Adaptive Hard-Soft Physics-Informed Neural Networks for Robust Boundary-Constrained PDE Solving","created":"2026-06-22","cited_by_count":1,"area":null},{"id":"2608.21818","title":"A Physics-informed Neural Network Approach for Robust Buckling Load Prediction and Reliability-Based Design of Thin Truncated Conical Shells","created":"2026-08-22","cited_by_count":1,"area":null},{"id":"2105.09866","title":"Deep learning in physics: a study of dielectric quasi-cubic particles in a uniform electric field","created":"2021-05-11","cited_by_count":0,"area":null}],"next_cursor":"100"}