Analytical Identification of Design and Multidimensional Spaces Using R-Functions
<|reference_start|>Analytical Identification of Design and Multidimensional Spaces Using R-Functions: The design space (DS) is defined as the combination of materials and process conditions that guarantees the assurance of quality. This principle ensures that as long as a process operates within DS, it consistently produces a product that meets specifications. A novel DS identification method called the R-DS identifier has been developed. It makes no assumptions about the underlying model - the only requirement is that each model constraint (CQA) should be approximated by a multivariate polynomial model. The method utilizes the methodology of Rvachev's R-functions and allows for explicit analytical representation of the DS with only a limited number of model runs. R-functions provide a framework for representing complex geometric shapes and performing operations on them through implicit functions. The theory of R-functions enables the solution of geometric problem such as identification of DS through algebraic manipulation. It is more practical than traditional sampling or optimization-based methods. The method is illustrated using a batch reactor system.<|reference_end|>
@article{kucherenko2024analytical,
    title={Analytical Identification of Design and Multidimensional Spaces Using
  R-Functions},
    author={Segei Kucherenko, Oleksiy Klymenko, Nilay Shah},
    journal={arXiv preprint arXiv:2407.13573},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.13573},
    primaryClass={math.AG cs.NA math.NA}
}