Numerical method for parameter inference of systems of nonlinear ordinary differential equations with partial observations.

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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.





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Chen, Yu, Jin Cheng, Arvind Gupta, Huaxiong Huang and Shixin Xu (2021). Numerical method for parameter inference of systems of nonlinear ordinary differential equations with partial observations. Royal Society open science, 8(7). p. 210171. 10.1098/rsos.210171 Retrieved from

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Shixin Xu

Assistant Professor of Mathematics at Duke Kunshan University

Shixin Xu is an Assistant Professor of Mathematics.   His research interests are machine learning and data-driven models for diseases,  multiscale modeling of complex fluids, Neurovascular coupling, homogenization theory, and numerical analysis.  The current projects he is working on are

  • image data-based for the prediction of hemorrhagic transformation in acute ischemic stroke,
  • electrodynamics modeling of saltatory conduction along a myelinated axon
  • electrochemical modeling
  • fluid-structure interaction with mass transportation and reaction

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