Numerical method for parameter inference of systems of nonlinear ordinary differential equations with partial observations.
Yu Chen, Jin Cheng, Arvind Gupta, Huaxiong Huang, Shixin Xu
Author Information
Yu Chen: School of Mathematics, Shanghai University of Finance and Economics, Shanghai, People's Republic of China.
Jin Cheng: School of Mathematical Sciences, Fudan University, Shanghai 200433, People's Republic of China.
Arvind Gupta: Computer Science, University of Toronto, Toronto, Ontario, Canada.
Huaxiong Huang: Joint Mathematical Research Centre of Beijing Normal University and BNU-HKBU United International College, Zhuhai, People's Republic of China.
Shixin Xu: Duke Kunshan University, 8 Duke Ave, Kunshan, Jiangsu, People's Republic of China. ORCID
Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a method for parameter inference of a system of nonlinear coupled ordinary differential equations with partial observations. Our method combines fast Gaussian process-based gradient matching and deterministic optimization algorithms. By using initial values obtained by Bayesian steps with low sampling numbers, our deterministic optimization algorithm is both accurate, robust and efficient with partial observations and large noise.
