Manuel Mai

I will present two related analyses of systems of ordinary differential equations (ODEs). The first one investigates outcome prediction in several systems of ODEs for the immune response to infection. We show that patient-to-patient variability sets a fundamental limit on the outcome prediction accuracy. However, accuracy can be increased at the expense of delayed prognosis. In the second study, I develop a method to build, general nonlinear ODE models from time series data using machine learning techniques related to sparse coding. I employ sparse basis learning to identify a basis set of functions that accurately represents the system of ODEs. We then employ L1-regularized regression, which finds sparse solutions to underdetermined systems of equations. We use this method to recover a full function (i.e. the right-hand side of an ODE) from a small number of measurements. Results are presented for one, two and three dimensional non-linear ODEs.