FPINNs
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Software:56270
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Source code repository: https://github.com/lululxvi/deepxde
Related Items (83)
Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learning ⋮ nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications ⋮ Learning to differentiate ⋮ On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton-Jacobi partial differential equations ⋮ Data-driven discovery of coarse-grained equations ⋮ Analysis of Anisotropic Nonlocal Diffusion Models: Well-Posedness of Fractional Problems for Anomalous Transport ⋮ Numerical methods for nonlocal and fractional models ⋮ Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems ⋮ Deep learning of free boundary and Stefan problems ⋮ DeepM\&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks ⋮ Weak form theory-guided neural network (TgNN-wf) for deep learning of subsurface single- and two-phase flow ⋮ A New Artificial Neural Network Method for Solving Schrödinger Equations on Unbounded Domains ⋮ A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder ⋮ Multifidelity modeling for physics-informed neural networks (PINNs) ⋮ MIONet: Learning Multiple-Input Operators via Tensor Product ⋮ A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions ⋮ Adaptive deep density approximation for Fokker-Planck equations ⋮ When and why PINNs fail to train: a neural tangent kernel perspective ⋮ On quadrature rules for solving partial differential equations using neural networks ⋮ A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data ⋮ Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems ⋮ An optimization-based approach to parameter learning for fractional type nonlocal models ⋮ Error estimates for deep learning methods in fluid dynamics ⋮ The deep parametric PDE method and applications to option pricing ⋮ Scientific machine learning through physics-informed neural networks: where we are and what's next ⋮ Convergence Rate Analysis for Deep Ritz Method ⋮ A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs ⋮ Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs ⋮ Data-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learning ⋮ Physics-informed PointNet: a deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries ⋮ Fractional Chebyshev deep neural network (FCDNN) for solving differential models ⋮ HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations ⋮ Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network ⋮ Physics-informed neural networks for high-speed flows ⋮ A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations ⋮ Wasserstein generative adversarial uncertainty quantification in physics-informed neural networks ⋮ Improved deep neural networks with domain decomposition in solving partial differential equations ⋮ The deep learning Galerkin method for the general Stokes equations ⋮ A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks ⋮ DAS-PINNs: a deep adaptive sampling method for solving high-dimensional partial differential equations ⋮ Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons ⋮ A metalearning approach for physics-informed neural networks (PINNs): application to parameterized PDEs ⋮ Surrogate modeling for Bayesian inverse problems based on physics-informed neural networks ⋮ Physics-informed neural networks for data-driven simulation: advantages, limitations, and opportunities ⋮ Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton-Jacobi PDEs ⋮ Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions ⋮ Data-driven forward-inverse problems for Yajima-Oikawa system using deep learning with parameter regularization ⋮ Time difference physics-informed neural network for fractional water wave models ⋮ An overview on deep learning-based approximation methods for partial differential equations ⋮ Greedy training algorithms for neural networks and applications to PDEs ⋮ Deep ReLU networks and high-order finite element methods ⋮ DeepXDE: A Deep Learning Library for Solving Differential Equations ⋮ Parametric deep energy approach for elasticity accounting for strain gradient effects ⋮ Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm ⋮ Artificial neural network approximations of Cauchy inverse problem for linear PDEs ⋮ Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations ⋮ On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs ⋮ A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems ⋮ Physics-Informed Neural Networks with Hard Constraints for Inverse Design ⋮ PPINN: parareal physics-informed neural network for time-dependent PDEs ⋮ \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition ⋮ Data-driven learning of nonlocal physics from high-fidelity synthetic data ⋮ Non-invasive inference of thrombus material properties with physics-informed neural networks ⋮ Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning ⋮ Bilevel parameter learning for nonlocal image denoising models ⋮ Approximation of an optimal control problem for the time-fractional Fokker-Planck equation ⋮ Mosaic flows: a transferable deep learning framework for solving PDEs on unseen domains ⋮ Interpretable machine learning: fundamental principles and 10 grand challenges ⋮ Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning ⋮ On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models ⋮ Data-driven discoveries of Bäcklund transformations and soliton evolution equations via deep neural network learning schemes ⋮ Overcoming the curse of dimensionality for some Hamilton-Jacobi partial differential equations via neural network architectures ⋮ Monte Carlo fPINNs: deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations ⋮ Space-fractional diffusion with variable order and diffusivity: discretization and direct solution strategies ⋮ Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks ⋮ Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs ⋮ Efficient coupled deep neural networks for the time-dependent coupled Stokes-Darcy problems ⋮ Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements ⋮ Schwarz waveform relaxation-learning for advection-diffusion-reaction equations ⋮ Optimal control of PDEs using physics-informed neural networks ⋮ A physics-informed learning approach to Bernoulli-type free boundary problems ⋮ DIFFUSION ON FRACTAL OBJECTS MODELING AND ITS PHYSICS-INFORMED NEURAL NETWORK SOLUTION ⋮ Prediction of optical solitons using an improved physics-informed neural network method with the conservation law constraint
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