Fibrous filters are used in many applications like face masks, HVAC filters, diesel engine applications etc. The case study has two main objectives both related to Meltblown fibrous filter media production. The first part of the project explores the use of numerical optimization to solve a model which relates process parameters to the fiber diameter produced by the meltblown process. The model is a first principles model based on conservation laws. There are two unknown parameters which need to be set, and an optimization procedure is used for that purpose. The 2nd part of the project explores the use of the Convolutional Neural network to characterize fiber diameters produced in the meltblown process from SEM micrographs. A novel software architecture was developed for this purpose. The biggest obstacle was training the neural network as labeled data wasn’t available. Image generation and augmentation techniques were used to generate labeled images. The predictions from the models were reasonable. Drawbacks in the methodology were identified for future development.