论文标题
从随机动态系统的数据中检测最大似然过渡路径
Detecting the maximum likelihood transition path from data of stochastic dynamic systems
论文作者
论文摘要
近年来，通过数据驱动方法发现各个领域中复杂的动态系统引起了广泛关注。该方法起着数据的作用，并已成为我们研究复杂现象的有利工具。在这项工作中，我们提出了一个框架，用于检测来自数据的随机动态系统的动态行为，例如最大似然过渡路径。对于随机动态系统，我们需要使用Kramers-Moyal公式将其转换为确定性形式进行处理，然后使用扩展的Sindy方法来获得随机动态系统的参数，并最终计算最大似然过渡路径。我们给出了由加性和乘法高斯噪声驱动的随机动力系统的两个示例，并通过再现已知的动态系统行为来证明该方法的有效性。
In recent years, the discovery of complex dynamic systems in various fields through data-driven methods has attracted widespread attention. This method has played the role of data and has become an advantageous tool for us to study complex phenomena. In this work, we propose a framework for detecting the dynamic behavior, such as the maximum likelihood transition path, of stochastic dynamic systems from data. For the stochastic dynamic system, we need to use the Kramers-Moyal formula to convert it into a deterministic form for processing, then use the extended SINDy method to obtain the parameters of stochastic dynamic systems, and finally calculate the maximum likelihood transition path. We give two examples of stochastic dynamical systems driven by additive and multiplicative Gaussian noise, and demonstrate the validity of the method by reproducing the known dynamical system behavior.
