University of Pittsburgh

Parameter Estimation and Time Series Modeling of Ordinary Differential Equations (ODEs) for Wound Healing

Friday, April 17, 2020 - 12:30pm - 1:00pm

Abstract: Ordinary Differential Equations (ODEs) are often used to model dynamic systems and have been successfully applied to many fields including population prediction, decay of radioactive material, electric circuits. Its inverse problem, the parameter fitting problem, is often challenging due to the dimensionality of the parameters and their correlations. Meanwhile, thanks to the rapid development of Machine Learning techniques, it became possible to more accurately predict time series data from systems that can be modeled by ODEs. In this work, we focus on the parameter fitting problem from and the time series data prediction for an ODE application in wound healing process. We use a Markov Chain Monte Carlo method to estimate parameters from data, which can potentially represent customized settings for individuals across population. Long Short-Term Memory (LSTM) based time series models are used to predict tendencies for different concentrations that we measure in wound tissues. Experiments performed on synthesized data show that our models are capable to estimate parameters for an ODE wound healing modeling with 42 parameters and predict time series data given the history.

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