Machine Learning of Space-Fractional Differential Equations

DOI10.1137/18M1204991zbMath1419.35209arXiv1808.00931MaRDI QIDQ5230657

Paris Perdikaris, Mamikon Gulian, Maziar Raissi, George Em. Karniadakis

Publication date: 28 August 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.00931

zbMATH Keywords

Gaussian processesanomalous diffusionstable processfractional diffusionmatérn kernel

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Gaussian processes (60G15) Bayesian inference (62F15) Stable stochastic processes (60G52) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Fractional partial differential equations (35R11)

Related Items (17)

Symplectic neural networks in Taylor series form for Hamiltonian systems ⋮ Analysis of Anisotropic Nonlocal Diffusion Models: Well-Posedness of Fractional Problems for Anomalous Transport ⋮ An optimization-based approach to parameter learning for fractional type nonlocal models ⋮ Error estimates for deep learning methods in fluid dynamics ⋮ Discovery of subdiffusion problem with noisy data via deep learning ⋮ Efficient optimization-based quadrature for variational discretization of nonlocal problems ⋮ APIK: Active Physics-Informed Kriging Model with Partial Differential Equations ⋮ Isogeometric collocation method for the fractional Laplacian in the 2D bounded domain ⋮ Efficient Monte Carlo Method for Integral Fractional Laplacian in Multiple Dimensions ⋮ A general framework for substructuring‐based domain decomposition methods for models having nonlocal interactions ⋮ Efficient quadrature rules for finite element discretizations of nonlocal equations ⋮ Discovery of PDEs driven by data with sharp gradient or discontinuity ⋮ Topology optimization based on deep representation learning (DRL) for compliance and stress-constrained design ⋮ A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems ⋮ An ergodic approach to Laplace transforms on time scales ⋮ Towards a unified theory of fractional and nonlocal vector calculus ⋮ fPINNs: Fractional Physics-Informed Neural Networks

Uses Software

• PDE-Net

Cites Work

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