Computational investigations of the BME mapping approach and incorporation of physical knowledge bases

The introduction of the Bayesian Maximum Entropy (BME) spatiotemporal mapping method more than a decade ago addressed successfully a variety of issues and shortcomings of existing mapping methods by means of its theoretically rigorous and epistemically sound framework. Many challenging tasks have been created since; these involve the development of numerically effective and computationally efficient applications of the BME theory. Despite the existence of such tools that have been heretofore successfully tested by substantiating and confirming the BME theory predictions, there are still areas in expectance of investigation. The present work deals with the particular area of considering physical laws as a general knowledge form in the BME framework. Physical laws contain crucial information about physical processes, but have never been before explicitly accounted for in spatiotemporal mapping in a purely numerical manner. Their importance often leads to an implicit acknowledgement of their validity, but this tactic entails the danger of irretrievably ignoring the physical principles dominating over a phenomenon. It is, therefore, necessary to accentuate their role in spatiotemporal mapping, particularly in the presence of little or no other information in the study of a physical process. The research goal is to investigate and numerically develop the incorporation of this fundamental knowledge base into the BME environment. Intermediate objectives in this task include the effective handling of numerical issues associated with this venture, as well as the familiarization with the BME mapping perspective and its various features. In this work a fully numerical incorporation of general knowledge in the form of physical laws is implemented by means of a partial differential equation describing advection-reaction. The objectives are met using study cases taken from the Environmental and Health Sciences areas, thus providing important help in the thorough investigation of the main task. Using a controlled environment, additional uncertain information given as interval and probabilistic data is considered, thus demonstrating the practical aspects of the research goal. These investigations are presented as a key for handling similar tasks when other physical laws are applicable, and to consolidate the rigorousness and diverse character of the BME method.