Transient probabilistic solution of stochastic oscillator under combined harmonic and modulated Gaussian white noise stimulations

Nonlinear Dynamics, Journal Year: 2023, Volume and Issue: 111(19), P. 17709 - 17723

Published: Aug. 11, 2023

Language: Английский

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Investigation on optimization-oriented EPC method in analyzing the non-linear oscillations under multiple excitations

International Journal of Non-Linear Mechanics, Journal Year: 2024, Volume and Issue: 164, P. 104771 - 104771

Published: June 3, 2024

Language: Английский

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Theoretical foundations of physics-informed neural networks and deep neural operators

Handbook of numerical analysis, Journal Year: 2024, Volume and Issue: unknown, P. 293 - 358

Published: Jan. 1, 2024

Language: Английский

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Predicting the nonlinear dynamics of spatiotemporal PDEs via physics-informed informer networks

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

Published: Dec. 3, 2024

Language: Английский

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Non-stationary semi-analytical solution of vibro-impact system with multiplicative and external random stimulations

Reliability Engineering & System Safety, Journal Year: 2024, Volume and Issue: 256, P. 110703 - 110703

Published: Dec. 6, 2024

Language: Английский

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DR-PDEE for engineered high-dimensional nonlinear stochastic systems: A physically-driven equation providing theoretical basis for data-driven approaches

Research Square (Research Square), Journal Year: 2024, Volume and Issue: unknown

Published: July 25, 2024

For over half a century, the analysis, control, and optimization design of high-dimensional nonlinear stochastic dynamical systems have posed long-standing challenges in fields science engineering. Emerging scientific ideas powerful technologies, such as big data artificial intelligence (AI), offer new opportunity for addressing this problem. Data-driven techniques AI methods are beginning to empower research on dynamics. However, what is physical essence, theoretical foundation, effective applicable spectrum data-driven AI-aided (DDAA) dynamics? Answering question has become important urgent advancing dynamics more solidly effectively. This paper will provide perspective answering from viewpoint system dimensionality reduction. In DDAA framework, dimension observed studied system, complete state variables fundamentally unknown. Thus, it can be considered that under framework dimension-reduced subsystems real-world systems. Therefore, interest is: To extent probability information predicted by subsystem characterize serve decision basis? The discuss issues density evolution equation (DR-PDEE) satisfied function (PDF) path-continuous non-Markov responses general systems, partial integro-differential PDF path-discontinuous responses, non-exchangeability reduction imposition absorbing boundary conditions. These studies suggest DR-PDEE bases effectiveness applicability boundaries framework.

Language: Английский

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A deep learning method based on prior knowledge with dual training for solving FPK equation

Chinese Physics B, Journal Year: 2023, Volume and Issue: 33(1), P. 010202 - 010202

Published: Oct. 26, 2023

The evolution of the probability density function a stochastic dynamical system over time can be described by Fokker–Planck–Kolmogorov (FPK) equation, solution which determines distribution macroscopic variables in dynamic system. Traditional methods for solving these equations often struggle with computational efficiency and scalability, particularly high-dimensional contexts. To address challenges, this paper proposes novel deep learning method based on prior knowledge dual training to solve stationary FPK equations. Initially, neural network is pre-trained through obtained Monte Carlo simulation (MCS). Subsequently, second phase incorporates differential operator into loss function, while supervisory term consisting local maximum points specifically included mitigate generation zero solutions. This dual-training strategy not only expedites convergence but also enhances efficiency, making well-suited systems. Numerical examples, including two different two-dimensional (2D), six-dimensional (6D), eight-dimensional (8D) systems, are conducted assess efficacy proposed method. results demonstrate robust performance terms both speed accuracy first three While applicable such as 8D, it should noted that may marginally compromised due data volume constraints.

Language: Английский

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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

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

Published: Oct. 12, 2023

Language: Английский

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