Knowledge-based machine learning to extend scientific knowledge

Machine Learning (ML) applied to scientific domains often neither generates a scientific hypothesis, nor exploits existing knowledge in the domain for learning. Out vision is a Bayesian reasoning framework on data and domain knowledge, outputting a posterior on symbolic solutions that create true scientific hypotheses in domaisn like environmental chemistry. To that end, we develop flexible representations that enable a domain scientist to naturally express knowledge and ML algorithms to systematically exploit it. For instance, the theory of formal tree languages allows assigning proper a-priori probability distributions to the set of syntactically correct mathematical expressions through regular tree expressions. This can be exploited for Bayesian reasoning by contracting a tensor network corresponding to a finite state machine that recognizes the structure of generalized sorption isotherm equations in soil science.