5:15 PM - 6:45 PM
[MGI24-P03] Online state and time-varying parameter estimation using the implicit equal-weights particle filter
Keywords:Data assimilation, Particle filter, Optimization, Parameter estimation
A method is proposed for resilient and efficient estimation of the states and time-varying parameters in nonlinear high-dimensional systems through a sequential data assimilation process. The importance of estimating time-varying parameters lies not only in improving prediction accuracy but also in determining when model characteristics change.
We propose a particle filter-based method that incorporates nudging techniques inspired by optimization algorithms in machine learning by taking advantage of the flexibility of the proposal density in particle filtering. However, as the model resolution and number of observations increase, filter degeneracy tends to be the obstacle to implementing the particle filter. Therefore, this proposed method is combined with the implicit equal-weights particle filter (IEWPF) proposed by Zhu et al. (2016), in which all particle weights are equal. As an example of optimization algorithms, we use the adaptive moment estimation (Adam) proposed by Kingma and Ba (2014), which combines momentum-based and norm-based algorithms. Then, based on the Adam algorithm, we define the parameter nudging term that forces the estimated model parameters closer to their true values. Here, the parameter nudging term is defined using the step-size factor and the gradient of the likelihood.
The method is validated using the 1000-dimensional Lorenz-96 model, where the forcing term is parameterized. From evaluating the impact of the parameter error covariance and the step-size factor on the time-averaged RMSE and the ensemble spread (Spread), the former increases the Spread and decreases the RMSE, while the latter decreases the RMSE. Properly determining these values so that the ratio of the RMSE to the Spread approaches one will allow for good ensemble generation.
The method is shown to be capable of resilient and efficient parameter estimation for parameter changes over time in our application with a linear observation operator. This leads to the conjecture that it applies to realistic geophysical, climate, and other problems.
We propose a particle filter-based method that incorporates nudging techniques inspired by optimization algorithms in machine learning by taking advantage of the flexibility of the proposal density in particle filtering. However, as the model resolution and number of observations increase, filter degeneracy tends to be the obstacle to implementing the particle filter. Therefore, this proposed method is combined with the implicit equal-weights particle filter (IEWPF) proposed by Zhu et al. (2016), in which all particle weights are equal. As an example of optimization algorithms, we use the adaptive moment estimation (Adam) proposed by Kingma and Ba (2014), which combines momentum-based and norm-based algorithms. Then, based on the Adam algorithm, we define the parameter nudging term that forces the estimated model parameters closer to their true values. Here, the parameter nudging term is defined using the step-size factor and the gradient of the likelihood.
The method is validated using the 1000-dimensional Lorenz-96 model, where the forcing term is parameterized. From evaluating the impact of the parameter error covariance and the step-size factor on the time-averaged RMSE and the ensemble spread (Spread), the former increases the Spread and decreases the RMSE, while the latter decreases the RMSE. Properly determining these values so that the ratio of the RMSE to the Spread approaches one will allow for good ensemble generation.
The method is shown to be capable of resilient and efficient parameter estimation for parameter changes over time in our application with a linear observation operator. This leads to the conjecture that it applies to realistic geophysical, climate, and other problems.