相关论文: Accurate predictions of chaotic motion of a free f…

It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependence on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error)…

In this paper, an extremely accurate numerical algorithm, namely the "clean numerical simulation" (CNS), is proposed to accurately simulate the propagation of micro-level inherent physical uncertainty of chaotic dynamic systems. The chaotic…

Due to the butterfly-effect, computer-generated chaotic simulations often deviate exponentially from the true solution, so that it is very hard to obtain a reliable simulation of chaos in a long-duration time. In this paper, a new strategy…

The background numerical noise $\varepsilon_{0} $ is determined by the maximum of truncation error and round-off error. For a chaotic system, the numerical error $\varepsilon(t)$ grows exponentially, say, $\varepsilon(t) = \varepsilon_{0}…

We report a phenomenon that physical perturbations sometimes can benefit the certainty of a free-fall motion with chaotic modes, albeit, as commonly believed, they can ruin it. We statistically compare those factors that may lead to…

It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependance on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error)…

The real-time prediction of chaotic systems requires a nonlinear-reduced order model (ROM) to forecast the dynamics, and a stream of data from sensors to update the ROM. Data-driven ROMs are typically built with a two-step strategy: data…

The famous three-body problem is investigated by means of a numerical approach with negligible numerical noises in a long enough time interval, namely the Clean Numerical Simulation (CNS). From physical viewpoints, position of any bodies…

Ship roll motion in high sea states has large amplitudes and nonlinear dynamics, and its prediction is significant for operability, safety, and survivability. This paper presents a novel data-driven methodology to provide a multi-step…

Turbulence holds immense importance across various scientific and engineering disciplines. The direct numerical simulation (DNS) of turbulence proposed by Orszag in 1970 is a milestone in fluid mechanics, which began an era of numerical…

Turbulent flow has been extensively studied using computational fluid dynamics (CFD) simulations since turbulent flow regime is so frequently encountered in both academic and engineering applications. The high-fidelity simulation of the…

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent…

From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a…

Traditionally, results given by the direct numerical simulation (DNS) of Navier-Stokes equations are widely regarded as reliable benchmark solutions of turbulence, as long as grid spacing is fine enough (i.e. less than the minimum…

Recently, machine learning techniques, particularly deep learning, have demonstrated superior performance over traditional time series forecasting methods across various applications, including both single-variable and multi-variable…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

To predict the future evolution of dynamical systems purely from observations of the past data is of great potential application. In this work, a new formulated paradigm of reservoir computing is proposed for achieving model-free…

Deducing the states of spatiotemporally chaotic systems (SCSs) as they evolve in time is crucial for various applications. However, it is a dramatic challenge for generally achieving so due to the complexity of non-periodic dynamics and the…

In the field of Maritime Autonomous Surface Ships (MASS), the accurate modeling of ship maneuvering motion for harbor maneuvers is a crucial technology. Non-parametric system identification (SI) methods, which do not require prior knowledge…

Yao and Hughes commented (Tellus-A, 60: 803 - 805, 2008) that "all chaotic responses are simply numerical noise and have nothing to do with the solutions of differential equations". However, using 1200 CPUs of the National Supercomputer…