The paper addresses the acceleration of scientific discoveries by developing logical and cognitive ontologies in a special convergent way that ensures the acceleration and purposefulness of collective scientific discussions. It is noted that modern information systems, which have been created to support scientific activities, focus on information and reference work. They help analyse retrospective data to predict the development of events and reveal hidden relationships in big data and knowledge. At the same time, the known methods of creating ontologies are used to build artificial intelligence (AI) models by explicating the knowledge of experts and big data. It is shown in the paper that modern approaches to creating ontologies excessively reduce non-formalized and uncaused cognitive processes of scientific discoveries such as free will, consciousness, unconsciousness, feelings, thoughts, and experience. Attempts to formalize these processes lead to an incorrect and incomplete replacement of infinite-dimensional and continuous cognitive phenomena by finite-dimensional spaces, digital numbers, and discrete symbols. To compensate for the resulting cognitive distortions, a special approach has been developed to represent convergent scientific creativity processes in AI models more correctly and completely by using the capabilities of hybrid (human-machine) AI, the cognitive semantics of AI models, and the method of inverse problem-solving in topological spaces. The idea of using a non-local approach to enrich the cognitive semantics of AI models that considers the subatomic structure of the human mind's biological tissue is also considered. Currently, the proposed approach is successfully used for accelerating collective strategic planning in the real digital economy