Related references
Note: Only part of the references are listed.When and why PINNs fail to train: A neural tangent kernel perspective
Sifan Wang et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2022)
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations
Jian-Bing Chen et al.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2022)
A deep learning approach for the solution of probability density evolution of stochastic systems
Seid H. Pourtakdoust et al.
STRUCTURAL SAFETY (2022)
A unified formalism of the GE-GDEE for generic continuous responses and first-passage reliability analysis of multi-dimensional nonlinear systems subjected to non-white-noise excitations
Meng-Ze Lyu et al.
STRUCTURAL SAFETY (2022)
A Survey of the Usages of Deep Learning for Natural Language Processing
Daniel W. Otter et al.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS (2021)
A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
Ehsan Haghighat et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2021)
DeepXDE: A Deep Learning Library for Solving Differential Equations
Lu Lu et al.
SIAM REVIEW (2021)
Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
Luning Sun et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)
Solving Fokker-Planck equation using deep learning
Yong Xu et al.
CHAOS (2020)
Neural network representation of the probability density function of diffusion processes
Wayne Isaac T. Uy et al.
CHAOS (2020)
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2019)
Machine Learning for Semi Linear PDEs
Quentin Chan-Wai-Nam et al.
JOURNAL OF SCIENTIFIC COMPUTING (2019)
Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
Yinhao Zhu et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2019)
fPINNs: FRACTIONAL PHYSICS-INFORMED NEURAL NETWORKS
Guofei Pang et al.
SIAM JOURNAL ON SCIENTIFIC COMPUTING (2019)
Dimension Reduction of the FPK Equation via an Equivalence of Probability Flux for Additively Excited Systems
Jianbing Chen et al.
JOURNAL OF ENGINEERING MECHANICS (2014)
PDEM-based dimension-reduction of FPK equation for additively excited hysteretic nonlinear systems
Jianbing Chen et al.
PROBABILISTIC ENGINEERING MECHANICS (2014)
Dimension-reduction of FPK equation via equivalent drift coefficient
Jianbing Chen et al.
THEORETICAL AND APPLIED MECHANICS LETTERS (2014)
Probability density function for stochastic response of non-linear oscillation system under random excitation
Xufang Zhang et al.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS (2010)
The principle of preservation of probability and the generalized density evolution equation
Jie Li et al.
STRUCTURAL SAFETY (2008)
The probability density evolution method for dynamic response analysis of non-linear stochastic structures
J Li et al.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2006)