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

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2021-07-28

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Abstract

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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10.1098/rsos.210171

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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 https://hdl.handle.net/10161/23926.

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Xu

Shixin Xu

Assistant Professor of Mathematics at Duke Kunshan University

Shixin Xu is an Assistant Professor of Mathematics whose research spans several dynamic and interconnected fields. His primary interests include machine learning and data-driven models for disease prediction, multiscale modeling of complex fluids, neurovascular coupling, homogenization theory, and numerical analysis. His current projects reflect a diverse and impactful portfolio:

  • Developing predictive models based on image data to identify hemorrhagic transformation in acute ischemic stroke.
  • Conducting electrodynamics modeling of saltatory conduction along myelinated axons to understand nerve impulse transmission.
  • Engaging in electrochemical modeling to explore the interactions between electric fields and chemical processes.
  • Investigating fluid-structure interactions with mass transport and reactions, crucial for understanding physiological and engineering systems.

These projects demonstrate his commitment to addressing complex problems through interdisciplinary approaches that bridge mathematics with biological and physical sciences.


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