提取受非高斯列维噪声扰动随机动力系统的最大似然转移路径 的数据驱动方法 DOI
Linghongzhi Lu, Yang Li, Xianbin Liu

et al.

Acta Mechanica Sinica, Journal Year: 2023, Volume and Issue: 40(1)

Published: Oct. 12, 2023

Language: Английский

Tensor neural networks for high-dimensional Fokker-Planck equations DOI

Taorui Wang,

Zheyuan Hu,

Kenji Kawaguchi

et al.

Neural Networks, Journal Year: 2025, Volume and Issue: 185, P. 107165 - 107165

Published: Jan. 21, 2025

Language: Английский

Citations

3
Deep learning-based state prediction of the Lorenz system with control parameters DOI Open Access
Xiaolong Wang,

Jing Feng,

Yong Xu

et al.

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2024, Volume and Issue: 34(3)

Published: March 1, 2024

Nonlinear dynamical systems with control parameters may not be well modeled by shallow neural networks. In this paper, the stable fixed-point solutions, periodic and chaotic solutions of parameter-dependent Lorenz system are learned simultaneously via a very deep network. The proposed learning model consists large number identical linear layers, which provide excellent nonlinear mapping capability. Residual connections applied to ease flow information training dataset is further utilized. Extensive numerical results show that can accurately forecasted for several Lyapunov times long-term predictions achieved solutions. Additionally, characteristics such as bifurcation diagrams largest exponents recovered from Finally, principal factors contributing high prediction accuracy discussed.

Language: Английский

Citations

7
Evolutionary stochastic characteristics of nonlinear oscillator with one side barrier due to multiple modulated Gaussian white noise DOI
Guo‐Kang Er, Jie Luo, Vai Pan Iu

et al.

Communications in Nonlinear Science and Numerical Simulation, Journal Year: 2025, Volume and Issue: unknown, P. 108696 - 108696

Published: March 1, 2025

Language: Английский

Citations

0
First excursion probability of dynamical systems: A review on computational methods DOI
Youbao Jiang, Xu-yang Zhang, Michael Beer

et al.

Mechanical Systems and Signal Processing, Journal Year: 2025, Volume and Issue: 232, P. 112751 - 112751

Published: April 15, 2025

Language: Английский

Citations

0
Approximate solution of KdV-Burgers equation using improved PINNs algorithm DOI

Harender Kumar,

Neha Yadav

Indian Journal of Pure and Applied Mathematics, Journal Year: 2024, Volume and Issue: unknown

Published: Jan. 31, 2024

Language: Английский

Citations

2
A novel method for response probability density of nonlinear stochastic dynamic systems DOI Creative Commons
Xi Wang, Jun Jiang, Ling Hong

et al.

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: unknown

Published: May 17, 2024

Abstract This paper presents a novel method for analyzing high-dimensional nonlinear stochastic dynamic systems. In particular, we attempt to obtain the solution of Fokker–Planck–Kolmogorov (FPK) equation governing response probability density system without using FPK directly. The consists several important components including radial basis function neural networks (RBFNN), Feynman–Kac formula and short-time Gaussian property process. area solving partial differential equations (PDEs) networks, known as physics-informed network (PINN), proposed an effective alternative obtaining solutions PDEs directly dealing with equation, thus avoids evaluating derivatives equation. approach has potential make network-based more efficient accurate. Several highly challenging examples systems are presented in illustrate effectiveness comparison equation-based RBFNN approach.

Language: Английский

Citations

2
Deep neural network method to predict the dynamical system response under random excitation of combined Gaussian and Poisson white noises DOI
Wantao Jia,

Xiaotong Feng,

Mengli Hao

et al.

Chaos Solitons & Fractals, Journal Year: 2024, Volume and Issue: 185, P. 115134 - 115134

Published: June 13, 2024

Language: Английский

Citations

2
Data-based deep learning for random vibration fatigue life prediction of car seat frame DOI
Shenlong Wang, Cheng Wu, Bowen Sun

et al.

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: unknown

Published: July 11, 2024

Language: Английский

Citations

2
Using Reservoir Computing to solve FPK equations for stochastic dynamical systems under Gaussian or Non-Gaussian excitation DOI

Yanming Liang,

Guo Yong-Feng,

Zifei Lin

et al.

Mathematics and Computers in Simulation, Journal Year: 2024, Volume and Issue: 226, P. 645 - 662

Published: July 30, 2024

Language: Английский

Citations

2
DR-PDEE for engineered high-dimensional nonlinear stochastic systems: a physically-driven equation providing theoretical basis for data-driven approaches DOI
Jianbing Chen, Ting-Ting Sun, Meng‐Ze Lyu

et al.

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: unknown

Published: Dec. 6, 2024

Language: Английский

Citations

2