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针对目前有限时间Lyapunov指数(FTLE)计算方法准确度不高和无法获得边界值的问题,基于对偶数理论提出了一种新的高精度计算方法.首先描述了基于有限空间差分方法计算FTLE的缺点和问题:其次介绍了基于对偶数理论的高精度导数计算方法及其显著优点,并将动力系统的柯西一格林形变张量计算问题转化为对偶数空间中非线性微分方程数值求解问题;最后对单摆和非线性Duffing振子两个典型物理动力系统进行了数值实验.结果表明:基于对偶数理论的新方法能有效、方便和高精度地计算出有限时间Lyapunov指数场,并成功识别出所包含的拉格朗日相关结构. 相似文献
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This work addresses the problem of estimating the states of nonlinear dynamic systems with sparse observations.We present a hybrid three-dimensional variation(3DVar) and particle piltering(PF) method,which combines the advantages of 3DVar and particle-based filters.By minimizing the cost function,this approach will produce a better proposal distribution of the state.Afterwards the stochastic resampling step in standard PF can be avoided through a deterministic scheme.The simulation results show that the performance of the new method is superior to the traditional ensemble Kalman filtering(EnKF) and the standard PF,especially in highly nonlinear systems. 相似文献
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MetaPINNs: Predicting soliton and rogue wave of nonlinear PDEs via the improved physics-informed neural networks based on meta-learned optimization
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Efficiently solving partial differential equations(PDEs) is a long-standing challenge in mathematics and physics research. In recent years, the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations. Among them, physics-informed neural networks(PINNs) are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenome... 相似文献
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