The software package :sfit is a Common Lisp implementation for parameter estimation and hidden state reconstruction in stochastic differential equation (SDE) and ordinary differential equation (ODE) models with equality and inequality constraints using a multiple shooting discretization and automatic differentiation to generate necessary derivatives. The underlying differential equations are solved using an error-controlled arbitrary order Runge-Kutta scheme (order 1 to 17 are supported). Exact derivatives up to (in principle) arbitrary order are efficiently computed using algorithmic differentiation (AD) and freezing the adaptive parts (internal numerical differentiation, IND). For solving the nonlinear weighted least squares problems, a globalized Gauss-Newton method with backtracking line-search or restricted monotonicity test are available. For sparse problems, bindings to SuperLU are provided.

[1] Andreas Sommer: Numerical methods for parameter estimation in dynamical systems with noise with applications in systems biology, PhD Thesis, Heidelberg University, 2016.  Online: http://archiv.ub.uni-heidelberg.de/volltextserver/22589/

The C++ software package ParaOCP (standing for Para meter estimation in Optimal Control Problems) implement