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Reconstruction of stochastic nonlinear dynamical models from trajectory measurements

机译:基于轨迹测量的随机非线性动力学模型的重构

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We consider the following general problem of applied stochastic nonlinear dynamics (see e.g.). We observe a time series of signals y(t) = y(t_0 + hn) corrupted by noise. The actual state and the nonlinear vector field of the dynamical system is not known. The question is how and with what accuracy can we determine x(t) and functional form of f(x). In this talk we discuss a novel approach to the solution of this problem based on the application of the path-integral approach to the full Bayesian inference. We demonstrate a reconstruction of a dynamical state of a system from corrupted by noise measurements. Next we reconstruct the corresponding nonlinear vector field. The emphasis are on the theoretical analysis. The results are compared with the results of earlier research.
机译:我们考虑应用随机非线性动力学的以下一般问题(例如参见)。我们观察到信号y(t)= y(t_0 + hn)被噪声破坏的时间序列。动力学系统的实际状态和非线性矢量场是未知的。问题是我们如何以及以何种精度确定x(t)和f(x)的函数形式。在本次演讲中,我们将基于路径积分方法在完整贝叶斯推理中的应用,讨论一种解决该问题的新颖方法。我们演示了从噪声测量结果破坏的系统动态状态的重建。接下来,我们重建相应的非线性矢量场。重点是理论分析。将结果与早期研究的结果进行比较。

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