Simultant: simultaneous curve fitting of functions and differential equations using analytical gradient calculations

Abstract

Background: The initial step in comparing mathematical models to experimental data is to do a fit. This process can be complicated when either the mathematical models are not analytically solvable (e.g. because of nonlinear differential equations) or when the relation between data and models is complex (e.g. when some fitting parameters must be shared between many data sets). Results: We introduce Simultant, a software package that allows complex fitting setups to be easily defined using a simple graphical user interface. Fitting functions can be defined directly as mathematical expressions or indirectly as the solution to specified ordinary differential equations. Analytical gradients of these functions, including the solution of differential equations, are automatically calculated to provide fast fitting even for functions with many parameters. The software enables easy definition of complex fitting setups in which parameters can be shared across both data sets and models to allow simultaneous fits to be performed. Conclusions: Simultant exploits differentiable programming and simplifies modern fitting approaches in a unified graphical interface.