标题： DeepBayes——一种用于随机非线性动力学模型参数估计的估计器 显示英文标题

标题： DeepBayes -- an estimator for parameter estimation in stochastic nonlinear dynamical models

摘要： 随机非线性动力系统在现代实际应用中无处不在。然而，估计随机非线性动力学模型的未知参数仍然是一个具有挑战性的问题。大多数现有方法采用最大似然估计或贝叶斯估计。然而，这些方法存在一些局限性，最显著的是推理所需的计算时间较长且在应用中的灵活性有限。在这项工作中，我们提出了DeepBayes估计器，利用深度循环神经网络学习估计器的能力。该方法首先通过使用来自感兴趣模型集的模型生成的一组合成数据来训练循环神经网络，以最小化均方估计误差。预先训练好的估计器可以直接用于推理，通过用估计数据评估网络即可实现。深度循环神经网络架构可以在离线时进行训练，并在推理过程中确保显著的时间节省。我们实验了两种流行的循环神经网络——长短期记忆网络（LSTM）和门控循环单元（GRU）。我们展示了所提出的方法在不同示例模型上的适用性，并与最先进的方法进行了详细的比较。我们还研究了一个现实世界中的非线性基准问题。实验评估表明，所提出的方法在渐近意义上与贝叶斯估计器一样好。 显示英文摘要

摘要： Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods employ maximum likelihood or Bayesian estimation. However, these methods suffer from some limitations, most notably the substantial computational time for inference coupled with limited flexibility in application. In this work, we propose DeepBayes estimators that leverage the power of deep recurrent neural networks in learning an estimator. The method consists of first training a recurrent neural network to minimize the mean-squared estimation error over a set of synthetically generated data using models drawn from the model set of interest. The a priori trained estimator can then be used directly for inference by evaluating the network with the estimation data. The deep recurrent neural network architectures can be trained offline and ensure significant time savings during inference. We experiment with two popular recurrent neural networks -- long short term memory network (LSTM) and gated recurrent unit (GRU). We demonstrate the applicability of our proposed method on different example models and perform detailed comparisons with state-of-the-art approaches. We also provide a study on a real-world nonlinear benchmark problem. The experimental evaluations show that the proposed approach is asymptotically as good as the Bayes estimator.