Deep neural network modeling of unknown partial differential equations in nodal space

DOI10.1016/j.jcp.2021.110782OpenAlexW3205265842WikidataQ114163405 ScholiaQ114163405MaRDI QIDQ2136465

Dongbin Xiu, Kailiang Wu, Zhen Chen, Victor Churchill

Publication date: 10 May 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.03603

zbMATH Keywords

meshfreedeep neural networkgoverning equation discoverynodal space

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Partial differential equations of mathematical physics and other areas of application (35Qxx) Approximation methods and numerical treatment of dynamical systems (37Mxx)

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Uses Software

• DeepXDE
• PDE-Net
• DeepONet

Cites Work

• Discovering governing equations from data by sparse identification of nonlinear dynamical systems
• Data-driven deep learning of partial differential equations in modal space
• Numerical aspects for approximating governing equations using data
• Data driven governing equations approximation using deep neural networks
• Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
• Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
• Extracting Sparse High-Dimensional Dynamics from Limited Data
• Learning partial differential equations via data discovery and sparse optimization
• Data-Driven Learning of Nonautonomous Systems
• Structure-Preserving Method for Reconstructing Unknown Hamiltonian Systems From Trajectory Data
• DeepXDE: A Deep Learning Library for Solving Differential Equations

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