{"total":72,"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":"2105.09506","title":"Physics-informed neural networks (PINNs) for fluid mechanics: A review","created":"2021-05-20","cited_by_count":473,"area":null},{"id":"2103.12959","title":"Solving and Learning Nonlinear PDEs with Gaussian Processes","created":"2021-03-24","cited_by_count":129,"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":"2304.01294","title":"Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes","created":"2023-04-03","cited_by_count":31,"area":null},{"id":"2203.05071","title":"On the influence of over-parameterization in manifold based surrogates and deep neural operators","created":"2022-03-09","cited_by_count":29,"area":null},{"id":"2203.13648","title":"On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networks","created":"2022-03-25","cited_by_count":23,"area":null},{"id":"2205.08332","title":"Scalable algorithms for physics-informed neural and graph networks","created":"2022-05-16","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":"2202.04648","title":"A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems","created":"2022-02-09","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":"2204.14030","title":"Neural Implicit Representations for Physical Parameter Inference from a Single Video","created":"2022-04-29","cited_by_count":19,"area":null},{"id":"2110.13330","title":"Recipes for when Physics Fails: Recovering Robust Learning of Physics Informed Neural Networks","created":"2021-10-26","cited_by_count":18,"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":"2108.13054","title":"Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks","created":"2021-08-30","cited_by_count":16,"area":null},{"id":"2104.12587","title":"Bayesian Numerical Methods for Nonlinear Partial Differential Equations","created":"2021-04-22","cited_by_count":15,"area":null},{"id":"2305.09017","title":"Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior","created":"2023-05-15","cited_by_count":15,"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":"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":"2110.11847","title":"Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations","created":"2021-10-22","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":"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":"2201.06463","title":"Bayesian Calibration of Imperfect Computer Models using Physics-Informed Priors","created":"2022-01-17","cited_by_count":9,"area":null},{"id":"2206.02563","title":"Learning \"best\" kernels from data in Gaussian process regression. With application to aerodynamics","created":"2022-06-03","cited_by_count":9,"area":null},{"id":"2404.08809","title":"Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning","created":"2024-04-12","cited_by_count":9,"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":"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":"2211.16190","title":"Physics Informed Neural Network for Dynamic Stress Prediction","created":"2022-11-28","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":"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":"2308.02894","title":"Physics-informed Gaussian process model for Euler-Bernoulli beam elements","created":"2023-08-05","cited_by_count":4,"area":null},{"id":"2405.13149","title":"Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulation","created":"2024-05-21","cited_by_count":4,"area":null},{"id":"2510.05433","title":"Physics-Informed Machine Learning in Biomedical Science and Engineering","created":"2025-10-06","cited_by_count":4,"area":null},{"id":"2103.15213","title":"A Temporal Kernel Approach for Deep Learning with Continuous-time Information","created":"2021-03-28","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":"2204.02583","title":"PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations","created":"2022-04-06","cited_by_count":3,"area":null},{"id":"2303.00187","title":"On the Integration of Physics-Based Machine Learning with Hierarchical Bayesian Modeling Techniques","created":"2023-03-01","cited_by_count":3,"area":null},{"id":"2304.03689","title":"EPINN-NSE: Enhanced Physics-Informed Neural Networks for Solving Navier-Stokes Equations","created":"2023-04-07","cited_by_count":3,"area":null},{"id":"2309.02351","title":"Exact Inference for Continuous-Time Gaussian Process Dynamics","created":"2023-09-05","cited_by_count":3,"area":null},{"id":"2309.14334","title":"Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points","created":"2023-09-25","cited_by_count":3,"area":null},{"id":"2508.01519","title":"The Vanishing Gradient Problem for Stiff Neural Differential Equations","created":"2025-08-02","cited_by_count":3,"area":null},{"id":"2511.07347","title":"Walsh-Hadamard Neural Operators for Solving PDEs with Discontinuous Coefficients","created":"2025-11-10","cited_by_count":3,"area":null},{"id":"2107.01650","title":"Learning ODEs via Diffeomorphisms for Fast and Robust Integration","created":"2021-07-04","cited_by_count":2,"area":null},{"id":"2202.01793","title":"Incorporating Sum Constraints into Multitask Gaussian Processes","created":"2022-02-03","cited_by_count":2,"area":null},{"id":"2210.00518","title":"High Precision Differentiation Techniques for Data-Driven Solution of Nonlinear PDEs by Physics-Informed Neural Networks","created":"2022-10-02","cited_by_count":2,"area":null},{"id":"2312.06625","title":"Decoding Mean Field Games from Population and Environment Observations By Gaussian Processes","created":"2023-12-08","cited_by_count":2,"area":null},{"id":"2406.05020","title":"Scaling up Probabilistic PDE Simulators with Structured Volumetric Information","created":"2024-06-07","cited_by_count":2,"area":null},{"id":"2502.11506","title":"Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problems","created":"2025-02-17","cited_by_count":2,"area":null},{"id":"2508.03926","title":"Next Generation Equation-Free Multiscale Modelling of Crowd Dynamics via Machine Learning","created":"2025-08-05","cited_by_count":2,"area":null},{"id":"2104.12722","title":"Dominant motion identification of multi-particle system using deep learning from video","created":"2021-04-26","cited_by_count":1,"area":null},{"id":"2108.01584","title":"Numerical Solution of Stiff ODEs with Physics-Informed RPNNs","created":"2021-08-03","cited_by_count":1,"area":null},{"id":"2110.08382","title":"A Neural Network Ensemble Approach to System Identification","created":"2021-10-15","cited_by_count":1,"area":null},{"id":"2205.06494","title":"A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantification","created":"2022-05-13","cited_by_count":1,"area":null},{"id":"2304.00909","title":"Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion","created":"2023-04-03","cited_by_count":1,"area":null},{"id":"2305.11586","title":"PDE-constrained Gaussian process surrogate modeling with uncertain data locations","created":"2023-05-19","cited_by_count":1,"area":null},{"id":"2507.22493","title":"LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process","created":"2025-07-30","cited_by_count":1,"area":null},{"id":"2509.14054","title":"Physics-based deep kernel learning for parameter estimation in high dimensional PDEs","created":"2025-09-17","cited_by_count":1,"area":null},{"id":"2510.13601","title":"Physics-augmented Multi-task Gaussian Process for Modeling Spatiotemporal Dynamics","created":"2025-10-15","cited_by_count":1,"area":null},{"id":"2511.00886","title":"HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEs","created":"2025-11-02","cited_by_count":1,"area":null},{"id":"2105.12894","title":"MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamics","created":"2021-05-27","cited_by_count":0,"area":null},{"id":"2210.12154","title":"Use of BNNM for interference wave solutions of the gBS-like equation and comparison with PINNs","created":"2022-08-07","cited_by_count":0,"area":null},{"id":"2302.08309","title":"The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach","created":"2023-02-16","cited_by_count":0,"area":null},{"id":"2312.10023","title":"A Kronecker product accelerated efficient sparse Gaussian Process (E-SGP) for flow emulation","created":"2023-12-13","cited_by_count":0,"area":null},{"id":"2402.03243","title":"PINN-BO: A Black-box Optimization Algorithm using Physics-Informed Neural Networks","created":"2024-02-05","cited_by_count":0,"area":null},{"id":"2408.15393","title":"Linear Stability Analysis of Physics-Informed Random Projection Neural Networks for ODEs","created":"2024-08-27","cited_by_count":0,"area":null},{"id":"2505.00909","title":"Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problems","created":"2025-05-01","cited_by_count":0,"area":null},{"id":"2505.03783","title":"A general physics-constrained method for the modelling of equation's closure terms with sparse data","created":"2025-04-30","cited_by_count":0,"area":null},{"id":"2603.15055","title":"Spatio-temporal probabilistic forecast using MMAF-guided learning","created":"2026-03-16","cited_by_count":0,"area":null},{"id":"2603.22050","title":"Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data","created":"2026-03-23","cited_by_count":0,"area":null},{"id":"2607.06292","title":"A unified perspective of Gaussian process approximation for differential equations","created":"2026-07-07","cited_by_count":0,"area":null},{"id":"2607.14233","title":"LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks","created":"2026-07-15","cited_by_count":0,"area":null},{"id":"2609.30348","title":"Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices","created":"2026-09-24","cited_by_count":0,"area":null}],"next_cursor":null}