{"list":"other","total":185,"rows":[{"id":"1806.07572","title":"Neural Tangent Kernel: Convergence and Generalization in Neural Networks","created":"2018-06-20","cited_by_count":2621},{"id":"1505.05770","title":"Variational Inference with Normalizing Flows","created":"2015-05-21","cited_by_count":2170},{"id":"1806.08734","title":"On the Spectral Bias of Neural Networks","created":"2018-06-22","cited_by_count":1341},{"id":"1502.05767","title":"Automatic differentiation in machine learning: a survey","created":"2015-02-20","cited_by_count":855},{"id":"2011.06225","title":"A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges","created":"2020-11-12","cited_by_count":819},{"id":"1503.02406","title":"Deep Learning and the Information Bottleneck Principle","created":"2015-03-09","cited_by_count":802},{"id":"2404.19756","title":"KAN: Kolmogorov-Arnold Networks","created":"2024-04-30","cited_by_count":649},{"id":"2109.01050","title":"Characterizing possible failure modes in physics-informed neural networks","created":"2021-09-02","cited_by_count":643},{"id":"2007.14527","title":"When and why PINNs fail to train: A neural tangent kernel perspective","created":"2020-07-28","cited_by_count":634},{"id":"1907.04502","title":"DeepXDE: A deep learning library for solving differential equations","created":"2019-07-10","cited_by_count":619},{"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},{"id":"1710.00211","title":"The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems","created":"2017-09-30","cited_by_count":583},{"id":"1703.00810","title":"Opening the Black Box of Deep Neural Networks via Information","created":"2017-03-02","cited_by_count":503},{"id":"2105.09506","title":"Physics-informed neural networks (PINNs) for fluid mechanics: A review","created":"2021-05-20","cited_by_count":473},{"id":"1711.10561","title":"Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations","created":"2017-11-28","cited_by_count":373},{"id":"2003.06097","title":"B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data","created":"2020-03-13","cited_by_count":335},{"id":"2012.10047","title":"On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks","created":"2020-12-18","cited_by_count":284},{"id":"2102.04626","title":"Physics-informed neural networks with hard constraints for inverse design","created":"2021-02-09","cited_by_count":280},{"id":"2003.05385","title":"hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition","created":"2020-03-11","cited_by_count":236},{"id":"2207.10289","title":"A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks","created":"2022-07-21","cited_by_count":236},{"id":"2009.04544","title":"Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism","created":"2020-09-07","cited_by_count":233},{"id":"1912.01198","title":"Towards Understanding the Spectral Bias of Deep Learning","created":"2019-12-03","cited_by_count":174},{"id":"2004.13145","title":"PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain","created":"2020-04-21","cited_by_count":174},{"id":"2201.07766","title":"Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons","created":"2022-01-19","cited_by_count":170},{"id":"2005.03448","title":"Physics-informed learning of governing equations from scarce data","created":"2020-05-05","cited_by_count":167},{"id":"1711.10566","title":"Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations","created":"2017-11-28","cited_by_count":161},{"id":"2203.07404","title":"Respecting causality is all you need for training physics-informed neural networks","created":"2022-03-14","cited_by_count":156},{"id":"1912.00873","title":"Variational Physics-Informed Neural Networks For Solving Partial Differential Equations","created":"2019-11-27","cited_by_count":148},{"id":"1809.08327","title":"Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems","created":"2018-09-21","cited_by_count":147},{"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},{"id":"1701.02440","title":"Machine Learning of Linear Differential Equations using Gaussian Processes","created":"2017-01-10","cited_by_count":140},{"id":"2104.08426","title":"Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks","created":"2021-04-17","cited_by_count":137},{"id":"1811.02033","title":"Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations","created":"2018-11-05","cited_by_count":135},{"id":"2308.08468","title":"An Expert's Guide to Training Physics-informed Neural Networks","created":"2023-08-16","cited_by_count":126},{"id":"2007.04542","title":"Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks","created":"2020-07-09","cited_by_count":123},{"id":"1811.04026","title":"Adversarial Uncertainty Quantification in Physics-Informed Neural Networks","created":"2018-11-09","cited_by_count":120},{"id":"1909.10145","title":"PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs","created":"2019-09-23","cited_by_count":118},{"id":"2408.10205","title":"KAN 2.0: Kolmogorov-Arnold Networks Meet Science","created":"2024-08-19","cited_by_count":118},{"id":"1907.02531","title":"Transfer learning enhanced physics informed neural network for phase-field modeling of fracture","created":"2019-07-04","cited_by_count":116},{"id":"2402.01868","title":"Challenges in Training PINNs: A Loss Landscape Perspective","created":"2024-02-02","cited_by_count":113},{"id":"2104.10013","title":"Parallel Physics-Informed Neural Networks via Domain Decomposition","created":"2021-04-20","cited_by_count":112},{"id":"2104.12325","title":"Efficient training of physics-informed neural networks via importance sampling","created":"2021-04-26","cited_by_count":110},{"id":"2406.02917","title":"A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks","created":"2024-06-05","cited_by_count":104},{"id":"2007.01138","title":"Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs","created":"2020-06-29","cited_by_count":102},{"id":"2007.07442","title":"A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks","created":"2020-07-15","cited_by_count":87},{"id":"1911.03737","title":"Physics-Informed Neural Networks for Power Systems","created":"2019-11-09","cited_by_count":80},{"id":"2007.11207","title":"Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains","created":"2020-07-22","cited_by_count":79},{"id":"2307.12306","title":"Tackling the Curse of Dimensionality with Physics-Informed Neural Networks","created":"2023-07-23","cited_by_count":79},{"id":"1808.08952","title":"Deep Learning of Vortex Induced Vibrations","created":"2018-08-26","cited_by_count":76},{"id":"1905.04817","title":"Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks","created":"2019-05-13","cited_by_count":76},{"id":"2202.11821","title":"Physics-informed neural networks for inverse problems in supersonic flows","created":"2022-02-23","cited_by_count":76},{"id":"2207.02338","title":"Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling","created":"2022-07-05","cited_by_count":73},{"id":"2307.00379","title":"Residual-based attention in physics-informed neural networks","created":"2023-07-01","cited_by_count":72},{"id":"2005.03596","title":"Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks","created":"2020-05-07","cited_by_count":68},{"id":"1905.10866","title":"Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction","created":"2019-05-26","cited_by_count":67},{"id":"2406.11045","title":"Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks","created":"2024-06-16","cited_by_count":67},{"id":"2004.14941","title":"The Information Bottleneck Problem and Its Applications in Machine Learning","created":"2020-04-30","cited_by_count":66},{"id":"2306.15969","title":"Separable Physics-Informed Neural Networks","created":"2023-06-28","cited_by_count":66},{"id":"1905.01205","title":"Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks","created":"2019-05-03","cited_by_count":64},{"id":"2210.00279","title":"Failure-informed adaptive sampling for PINNs","created":"2022-10-01","cited_by_count":64},{"id":"2307.11833","title":"PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks","created":"2023-07-21","cited_by_count":64},{"id":"2203.09346","title":"Error estimates for physics informed neural networks approximating the Navier-Stokes equations","created":"2022-03-17","cited_by_count":63},{"id":"1912.02968","title":"Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport","created":"2019-12-06","cited_by_count":61},{"id":"2012.13294","title":"Multi-fidelity Bayesian Neural Networks: Algorithms and Applications","created":"2020-12-19","cited_by_count":59},{"id":"2407.04192","title":"KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics","created":"2024-07-05","cited_by_count":59},{"id":"2109.09444","title":"When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?","created":"2021-09-20","cited_by_count":58},{"id":"1804.07010","title":"Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations","created":"2018-04-19","cited_by_count":55},{"id":"2205.08304","title":"Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems","created":"2022-05-12","cited_by_count":54},{"id":"2010.02011","title":"A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications","created":"2020-09-28","cited_by_count":53},{"id":"2002.10253","title":"Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structures","created":"2020-02-18","cited_by_count":52},{"id":"2005.00615","title":"A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecture","created":"2020-05-01","cited_by_count":50},{"id":"2110.11286","title":"One-Shot Transfer Learning of Physics-Informed Neural Networks","created":"2021-10-21","cited_by_count":49},{"id":"2011.13511","title":"Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture","created":"2020-11-27","cited_by_count":48},{"id":"2302.14227","title":"A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions","created":"2023-02-28","cited_by_count":48},{"id":"2307.08934","title":"Multi-stage Neural Networks: Function Approximator of Machine Precision","created":"2023-07-18","cited_by_count":48},{"id":"2205.07731","title":"Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios","created":"2022-05-16","cited_by_count":46},{"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},{"id":"2008.13547","title":"Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks","created":"2020-07-28","cited_by_count":42},{"id":"2012.13376","title":"A Physics-Informed Deep Learning Paradigm for Car-Following Models","created":"2020-12-24","cited_by_count":41},{"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},{"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},{"id":"2407.17611","title":"Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks","created":"2024-07-24","cited_by_count":38},{"id":"2106.05863","title":"Learning Functional Priors and Posteriors from Data and Physics","created":"2021-06-08","cited_by_count":37},{"id":"2410.01803","title":"On the expressiveness and spectral bias of KANs","created":"2024-10-02","cited_by_count":37},{"id":"1808.04327","title":"Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data","created":"2018-08-13","cited_by_count":36},{"id":"1912.07443","title":"VarNet: Variational Neural Networks for the Solution of Partial Differential Equations","created":"2019-12-16","cited_by_count":35},{"id":"2009.13291","title":"Physics Informed Neural Networks for Simulating Radiative Transfer","created":"2020-09-25","cited_by_count":35},{"id":"2205.01059","title":"Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)","created":"2022-04-29","cited_by_count":35},{"id":"2406.19662","title":"Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems","created":"2024-06-28","cited_by_count":35},{"id":"2010.06050","title":"A Physics-Guided Neural Network Framework for Elastic Plates: Comparison of Governing Equations-Based and Energy-Based Approaches","created":"2020-10-12","cited_by_count":34},{"id":"2212.03130","title":"Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems","created":"2022-12-06","cited_by_count":34},{"id":"2310.10776","title":"Correcting model misspecification in physics-informed neural networks (PINNs)","created":"2023-10-16","cited_by_count":33},{"id":"2405.04230","title":"Unveiling the optimization process of Physics Informed Neural Networks: How accurate and competitive can PINNs be?","created":"2024-05-07","cited_by_count":31},{"id":"2301.02152","title":"L-HYDRA: Multi-Head Physics-Informed Neural Networks","created":"2023-01-05","cited_by_count":29},{"id":"2310.01433","title":"AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification","created":"2023-09-29","cited_by_count":29},{"id":"2311.11262","title":"Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators","created":"2023-11-19","cited_by_count":28},{"id":"2402.10680","title":"Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics","created":"2024-02-16","cited_by_count":28},{"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},{"id":"2205.02902","title":"Lagrangian PINNs: A causality-conforming solution to failure modes of physics-informed neural networks","created":"2022-05-05","cited_by_count":26},{"id":"1910.11710","title":"Multi-scale Deep Neural Networks for Solving High Dimensional PDEs","created":"2019-10-25","cited_by_count":25}],"next_cursor":"100"}