Simulation-based inference of dynamical systems with model uncertainty
Date:
Minisymposium presentation at the 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics (WCCM-PANACM). The slides can be found here.
Accounting for model uncertainty during the estimation of dynamical systems is important for generating reliable and generalizable predictions. For state-space systems, quantification of model uncertainty can be achieved through the estimation of an added process noise term in the system dynamics [1]. Within a Bayesian framework, the inclusion of process noise in the model formulation has shown to improve the likelihood smoothness and yield inherent regularization during estimation [2]. The cost of adding process noise, however, is that the system states become uncertain and must be marginalized out when evaluating the likelihood, requiring costly integration. The cost can be mitigated with recursive filtering algorithms, but these algorithms require inversion of covariance matrices, resulting in a computational complexity that scales cubically with the state and measurement dimensions. As a result, the filtering algorithm is unsuitable for even moderate dimensions.
To address the issue of computational cost, we propose a method capable of estimation without requiring a filtering-based evaluation of the likelihood. This method amortizes the inference procedure by training a neural network approximation of the likelihood using sample trajectories drawn from a stochastic dynamics model. Once the network is trained, it can then be used in a variety of inference procedures such as optimization and sampling at a fraction of the cost of the filtering-based evaluation. Moreover, sampling trajectories and evaluating the neural network objective function are easily parallelizable, so training can be completed in a highly efficient manner. In this talk, we outline the details of this approach and compare its performance to the original likelihood-based method. We analyze the cost-accuracy tradeoff of the likelihood-free approach and the relationship between the number of sample trajectories and the accuracy of the approximation.