# Pumas-QSP: Robust and High-Performance Complex Systems Analysis

Pumas-QSP is a package and methodology to solve difficult model calibration and analyses in high-performance and user friendly manner. This allows for scaling to large models and datasets without requiring advanced programming. It allows you to focus on the semantics of the model and the interpretation of its behaviour. Clear and flexible code structures provide you with the opportunity to identify wider connections as well as narrow in on areas of interest. At the same time, automatic, under-the-hood parallelizations, enable you to formulate robust hypothesis as it is providing you with the necessary performance to test detailed and explore options widely.

## Overview of Pumas-QSP

Pumas-QSP is centered around solving `InverseProblem`

s, i.e. finding the parameters which cause models to be sufficiently good fits to data. In PumasQSP, model and data pairs are known as `Trial`

s. For example, a trial might be a differential equation model describing a clinical trial with a loading dose of 250mg and the dataset which the model is supposed to fit. A separate trial may define a clinical trial with a loading dose of 150mg and the associated data with said dose. The `InverseProblem`

is then a collection of trials. The purpose of PumasQSP is to then find out how to calibrate the model to all such trials and datasets simultaniously.

Pumas-QSP offers many different analysis functions to enable such model calibration and exploration. At a high level, these are:

`calibrate`

: the fitting of an`InverseProblem`

, i.e. finding the best parameters to simultaniously fit all trials. This function is made to be fast and robust, making it easy to perform difficult calibrations.`vpop`

: the generation of plausible populations, or a set of parameters which are all sufficiently good fits to all datasets. This is an extension of`calibrate`

which is used to convey uncertainty in the model fitting process and allow for analysis with respect to model uncertainty and data noise.`subsample`

: the subsampling of plausible populations to virtual populations. While the`vpop`

result gives a set of parameters which all fit the dataset well, there are no high-level guarentees about the statistics of the fit.`subsample`

allows for subsampling the generated parameter set to allow it to match known characteristics to improve predictions from the uncertainty set.`gsa`

: the analysis of the sensitivity of solutions with respect to parameters. This gives an alternative view of an`InverseProblem`

by demonstrating what parameters have large effects on the solution, improving the calibration process and the understanding of its uncertainties.

## Pumas-QSP's Integration with Julia and SciML

Pumas-QSP is written in Julia and therefore brings all the Julia language advantages with it: this includes, for example, that it has an easy to read and write syntax and a high baseline performance. Additionally, Pumas-QSP is nicely integrated in the existing package ecosystem of Julia. Specifically relevant are the connections to the following packages:

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- DataFrames.jl allows us to manipulate tabular data and hence is useful to handle trail data stored in e.g. csv files.
- ModelingToolkit.jl provides a modeling framework for high-performance symbolic-numeric computation hence allows for smooth model definitions and model handeling.
- SBMLToolkit.jl alows import of models that are

specified in the Systems Biology Markup Language (SBML) to facilitate reuse of models developed with SBML compliant tools such as BioNetGen, Copasi and SimBiology :r:. as well as reuse of models downloaded from databases such as BioModels.

- CellMLToolkit.jl alows import of models specified

in the CellML language to facilitate reuse of models downloaded from databases such as the CellML Model Repository.

- DifferentialEquations.jl can be used to numerically solving differential equations with high efficiency.
- GlobalSensitivity.jl provides several methods to quantify the uncertainty in the model output with respect to the input parameters of the model.
- Plots.jl is a plotting API and toolset that can be used to intuitively analyse and visualise model behaviour and output.