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

Area of Science:

• Computational science
• Mathematical modeling
• Data analysis

Background:

• Comparing mathematical models to experimental data requires fitting, which is complex for non-analytically solvable models or when parameters are shared across datasets.
• Existing methods face challenges with nonlinear differential equations and intricate data-model relationships.

Purpose of the Study:

• To introduce Simultant, a software package designed to simplify complex fitting setups.
• To provide an intuitive graphical user interface for defining and performing advanced data fitting procedures.

Main Methods:

• Simultant allows fitting functions to be defined via mathematical expressions or as solutions to ordinary differential equations.
• The software automatically calculates analytical gradients for efficient parameter fitting, even with numerous parameters.
• It supports complex fitting scenarios, including parameter sharing across multiple datasets and models for simultaneous fitting.

Main Results:

• Simultant offers a user-friendly graphical interface for defining complex fitting setups.
• The software enables the definition of fitting functions through direct mathematical expressions or by solving ordinary differential equations.
• Automatic gradient calculation ensures fast fitting performance, even for models with many parameters.

Conclusions:

• Simultant simplifies modern fitting approaches through differentiable programming within a unified graphical interface.
• The software facilitates complex data analysis by enabling easy definition of simultaneous fits and parameter sharing.