The digitization of manufacturing processes has led to an increase in the availability of process data, which has enabled the use of data-driven models to predict the outcomes of these manufacturing processes. Data-driven models are instantaneous in simulate and can provide real-time predictions but lack any governing physics within their framework. When process data deviates from original conditions, the predictions from these models may not agree with physical boundaries. In such cases, the use of first-principle-based models to predict process outcomes have proven to be effective but computationally inefficient and cannot be solved in real time. Thus, there remains a need to develop efficient data-driven models with a physical understanding about the process. In this work, we have demonstrate the addition of physics-based boundary conditions constraints to a neural network to improve its predictability for granule density and granule size distribution (GSD) for a high shear granulation process. The physics-constrained neural network (PCNN) was better at predicting granule growth regimes when compared to other neural networks with no physical constraints. When input data that violated physics-based boundaries was provided, the PCNN identified these points more accurately compared to other non-physics constrained neural networks, with an error of <1%. A sensitivity analysis of the PCNN to the input variables was also performed to understand individual effects on the final outputs.
An energy-based population-balance approach to model granule growth and breakage in high-shear wet granulation processes
