论文标题
混沌动力学系统逆问题使用贝叶斯人工神经网络的概率解决方案
Probabilistic solution of chaotic dynamical system inverse problems using Bayesian Artificial Neural Networks
论文作者
论文摘要
本文展示了将贝叶斯人工神经网络应用于普通微分方程（ODE）逆问题。我们考虑从状态观察数据估算未知混沌动力学系统过渡模型的情况。混乱系统的反问题在数值上是具有挑战性的，因为模型参数的小扰动可能会导致估计的远期轨迹发生很大变化。贝叶斯人工神经网络可用于同时拟合模型并估计模型参数不确定性。然后可以将模型参数不确定性的知识纳入推断系统的正向时间演变的概率估计中。通过分析混乱的Sprott B系统来证明该方法。该系统的观察结果用于估计参数多项式内核人工神经网络的权重上的后验预测分布。结果表明，所提出的方法能够执行准确的时间预测。此外，所提出的方法能够正确说明模型不确定性并提供有用的预测不确定性界限。
This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state observation data. Inverse problems for chaotic systems are numerically challenging as small perturbations in model parameters can cause very large changes in estimated forward trajectories. Bayesian Artificial Neural Networks can be used to simultaneously fit a model and estimate model parameter uncertainty. Knowledge of model parameter uncertainty can then be incorporated into the probabilistic estimates of the inferred system's forward time evolution. The method is demonstrated numerically by analysing the chaotic Sprott B system. Observations of the system are used to estimate a posterior predictive distribution over the weights of a parametric polynomial kernel Artificial Neural Network. It is shown that the proposed method is able to perform accurate time predictions. Further, the proposed method is able to correctly account for model uncertainties and provide useful prediction uncertainty bounds.
