Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs (Q6143622)

scientific article; zbMATH DE number 7783920

Language	Label	Description	Also known as
English	Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs	scientific article; zbMATH DE number 7783920

Statements

instance of

scholarly article

0 references

title

Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs (English)

0 references

arXiv ID

2303.10913

0 references

DOI

10.4208/cicp.oa-2023-0075

0 references

0 references

0 references

0 references

0 references

George Em. Karniadakis

0 references

published in

Communications in Computational Physics

0 references

publication date

5 January 2024

0 references

full work available at URL

https://arxiv.org/abs/2303.10913

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

scientific machine learning

0 references

uncertainty quantification

0 references

stochastic fractional differential equations

0 references

PINNs

0 references

inverse problems

0 references

MaRDI profile type

MaRDI publication profile

0 references

0 references

0 references

A fractional phase-field model for two-phase flows with tunable sharpness: algorithms and simulations

0 references

Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

0 references

What is the fractional Laplacian? A comparative review with new results

0 references

不确定性量化的高精度数值方法和理论

0 references

Quasi-Linear (Stochastic) Partial Differential Equations with Time-Fractional Derivatives

0 references

Regularity for the Solution of a Stochastic Partial Differential Equation with the Fractional Laplacian

0 references

Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients

0 references

Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation

0 references

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

0 references

Q3583848

0 references

Constructing Least-Squares Polynomial Approximations

0 references

Dynamically orthogonal field equations for continuous stochastic dynamical systems

0 references

Dynamical criteria for the evolution of the stochastic dimensionality in flows with uncertainty

0 references

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms

0 references

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations

0 references

Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

0 references

On the equivalence of dynamically orthogonal and bi-orthogonal methods: theory and numerical simulations

0 references

A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems

0 references

Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations

0 references

Solving parametric PDE problems with artificial neural networks

0 references

Deep learning of vortex-induced vibrations

0 references

Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

0 references

Physics-Informed Neural Networks with Hard Constraints for Inverse Design

0 references

fPINNs: Fractional Physics-Informed Neural Networks

0 references

Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

0 references

Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification

0 references

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

0 references

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

0 references

A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition

0 references

Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

0 references

Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks (PINNs)

0 references

NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations

0 references

Monte Carlo fPINNs: deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations

0 references

A series of high-order quasi-compact schemes for space fractional diffusion equations based on the superconvergent approximations for fractional derivatives

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:6143622