MOFs and COFs are porous materials with a large variety of applications including gas storage and separation. Synthesised in a modular fashion from distinct building blocks, a near infinite number of structures can be constructed and the properties of the material can be tailored for a specific application. While this modularity is a very attractive feature it also poses a challenge. Attempting to identify the best performing material(s) for a given application is experimentally intractable. Current research efforts combine molecular simulations and machine learning techniques to evaluate the simulated performance of hundreds of thousands of materials to identify top performing MOFs and COFs for a given application. These approaches typically rely on moderated brute-force screening which is still resource-intensive as typically between 70‒100 % of the hundreds of thousands of materials must be simulated to create a training set for the machine learning models used, restricting screening to relatively simple molecules. In this work we demonstrate our novel Bayesian mining approach to materials screening which allows 62‒92 % of the top 100 porous materials for a range of applications to be readily identified from large materials databases after only assessing less than one percent of all materials. This is a stark contrast to the 0‒1 % achieved by conventional brute-force screening where porous materials are just chosen at random during a high throughput screening. Through this accelerated virtual screening process, the identification of high performing materials can be used to more rapidly inform experimental efforts and hence lead to an acceleration of the entire research and development pipeline of porous materials.