4.7 Article

Solution of FPK equation for stochastic dynamics subjected to additive Gaussian noise via deep learning approach

Related references

Note: Only part of the references are listed.
Article Computer Science, Interdisciplinary Applications

When and why PINNs fail to train: A neural tangent kernel perspective

Sifan Wang et al.

Summary: This work investigates the Neural Tangent Kernel (NTK) of Physics-informed neural networks (PINNs) and demonstrates that it can converge to a deterministic kernel that remains constant during training under appropriate conditions. A novel gradient descent algorithm is proposed to adaptively calibrate the convergence rate of total training error using the eigenvalues of NTK. A series of numerical experiments are conducted to validate the theory and practical effectiveness of the proposed algorithms.

JOURNAL OF COMPUTATIONAL PHYSICS (2022)

Article Multidisciplinary Sciences

Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations

Jian-Bing Chen et al.

Summary: This paper presents a method for capturing the probabilistic response of high-dimensional nonlinear stochastic dynamic systems involving double randomness. Using a globally-evolving-based generalized density evolution equation, a two-dimensional partial differential equation is derived to describe the evolution of the probability density function. The effective drift coefficients are determined based on data from deterministic dynamic analyses, and a new estimator for these coefficients is developed using vine copulas.

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2022)

Article Engineering, Civil

A deep learning approach for the solution of probability density evolution of stochastic systems

Seid H. Pourtakdoust et al.

Summary: The paper introduces a new deep learning method called DeepPDEM for solving the evolution of probability density. By utilizing the concept of physics-constrained networks, DeepPDEM learns the General Density Evolution Equation of stochastic structures. This method can solve the density evolution problem without prior simulation data and can serve as an efficient surrogate in optimization schemes or real-time applications.

STRUCTURAL SAFETY (2022)

Article Engineering, Civil

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.

Summary: The stochastic response and first-passage reliability analysis of multi-dimensional nonlinear systems under non-white-noise dynamic excitations have been challenging problems. This paper extends the globally-evolving-based generalized density evolution equation (GE-GDEE) for these purposes. A more general derivation of the GE-GDEE is provided, and a new process absorbed at the boundary is constructed for first-passage reliability evaluation. The proposed method is demonstrated to be efficient and accurate through numerical examples.

STRUCTURAL SAFETY (2022)

Article Computer Science, Artificial Intelligence

A Survey of the Usages of Deep Learning for Natural Language Processing

Daniel W. Otter et al.

Summary: This article provides a brief introduction to the recent developments in natural language processing driven by deep learning models, discusses their applications and research findings, and offers recommendations for future research directions.

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS (2021)

Article Engineering, Multidisciplinary

A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics

Ehsan Haghighat et al.

Summary: This study presents the application of Physics Informed Neural Networks (PINN) in solid mechanics, improving accuracy and convergence with a multi-network model and Isogeometric Analysis. The study demonstrates the importance of honoring physics in improving robustness and highlights the potential application of PINN in sensitivity analysis and surrogate modeling.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2021)

Article Mathematics, Applied

DeepXDE: A Deep Learning Library for Solving Differential Equations

Lu Lu et al.

Summary: This article introduces an overview, implementation and applications of Physics-Informed Neural Networks (PINNs), along with a new residual-based adaptive refinement (RAR) method. By comparing with finite element methods, the advantages of PINNs and the versatile applications of the Python library DeepXDE are demonstrated. Overall, DeepXDE contributes to the more rapid development of the emerging scientific machine learning field.

SIAM REVIEW (2021)

Article Engineering, Multidisciplinary

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)

Article Mathematics, Applied

Solving Fokker-Planck equation using deep learning

Yong Xu et al.

CHAOS (2020)

Article Computer Science, Interdisciplinary Applications

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)

Article Mathematics, Applied

Machine Learning for Semi Linear PDEs

Quentin Chan-Wai-Nam et al.

JOURNAL OF SCIENTIFIC COMPUTING (2019)

Article Computer Science, Interdisciplinary Applications

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

Yinhao Zhu et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

Article Mathematics, Applied

fPINNs: FRACTIONAL PHYSICS-INFORMED NEURAL NETWORKS

Guofei Pang et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2019)

Article Engineering, Mechanical

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)

Article Engineering, Mechanical

PDEM-based dimension-reduction of FPK equation for additively excited hysteretic nonlinear systems

Jianbing Chen et al.

PROBABILISTIC ENGINEERING MECHANICS (2014)

Article Mechanics

Dimension-reduction of FPK equation via equivalent drift coefficient

Jianbing Chen et al.

THEORETICAL AND APPLIED MECHANICS LETTERS (2014)

Article Mechanics

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)

Article Engineering, Multidisciplinary

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)