In this work we discuss a variational approach for the determination of the parameters of systems of ordinary differential equations (ODE). We construct a model for fitting observed noisy data into the given dynamical system. Also we explain in detail the advantage of using the adjoint equation method to compute the derivatives or gradients, which are needed for the application of gradient methods and quasi-Newton algorithms to find the minimum of the cost function. In particular we consider two classic iterative algorithms: the conjugate gradient (CG) algorithm and the BFGS algorithm. For educational purposes we try to explain several numerical and computational issues with some detail and illustrate them with the SEIRD epidemiological model.
Abstract In this work we discuss a variational approach for the determination of the parameters of systems of ordinary differential equations (ODE). We construct a model for fitting [...]
Parameter estimation in ODEs. Modelling and computational issues 
