Calibration of stochastic differential equation models using implicit numerical methods and particle swarm optimization

Stochastic differential equation (SDE) is a very important mathematical tool to describe complex systems in which noise plays an important role. SDEs have been widely used to study various nonlinear systems in biology, engineering, finance and economics, as well as physical sciences. Since a SDE can generate unlimited number of trajectories, it is a difficult problem to estimate model parameters based on experimental observations which may represent only one trajectory of the stochastic model. During the last decade substantial research efforts have been made to the development of effective methods for inferring parameters in SDE models. However, it is still a challenge to estimate parameters in SDE models from observations with large variations. In this work, we proposed to use the implicit numerical methods to simulate SDE models in order to generate stable trajectories for estimating parameters in stiff SDE models. In addition, we used the particle swarm optimization to search the optimal parameters from the parameter space that has a complex model error landscape. Numerical results suggested that the proposed algorithm is an effective approach to estimate parameters in SDE models.