Stirred Tank Reactors (STRs) are a cornerstone of chemical and biotechnology industry, broadly used in countless production and culture processes due to their simplicity, robustness and versatility. Traditionally, the scale-up process of chemical reactors relied on dimensional analysis, rules-of-thumb and the experience and ability of the designer. Although general guidelines are established and accepted, this approach is inherently constrained since full similarity cannot be achieved in a reactor due to its multiscale and multi-physics nature [1]. Over the last decades, Computational Fluid Dynamics (CFD) has acquired a crucial role in the field of reactors, since it can provide insights and information unreachable via experimental techniques. Once a model is validated, it becomes a trustworthy and valuable tool for the design process. The proposed scale-up approach leverages the capacities of CFD and it is demonstrated for a small-scale STR operating with a non-Newtonian fluid in laminar regime, under the variation of the rotation speed, geometric scale, rheological properties of the fluid, the mixing of a tracer released from a feeder and chemical reaction kinetics. Conventional Dimensional Analysis for reactors defines global dimensionless numbers based on characteristic values of the different variables. Instead, in this approach local dimensionless numbers are built for each volume of the domain using the cell values. These quantities can be either formulated manually or automatically from the raw data using unsupervised learning techniques [2]. Standardized Probability Density Functions (PDFs) are constructed for the dimensionless numbers of each simulation in the sparse experiment space. Using an algorithm based on symbolic regression [3], functional relations are discovered between the mentioned dimensionless distributions, which were previously characterized as function of the design variables. Thus, explicit expressions that relate different operating conditions are obtained, allowing to a faster and straightforward scale-up and design for STRs. This results on the definition of optimal partial similarity criteria.