EFDA-JET-PR(09)04

Machine Learning Methods for Data Driven Theory in the Physical Sciences with Applications to Confinement Regime Identification in Nuclear Fusion

In various fields of science complex, non linear systems have to be investigated. Given the rapid development of information technology, in many cases a lot of data is available to study the phenomena of interest but, contrary to what happened in previous societies, now very often the bottleneck is the ability to extract the right knowledge from these large repositories of information. In this paper two machine learning tools, Neural Networks and Support Vector Machines, are used for data driven theory formulation, to derive mathematical expressions directly from the database with a minimum of a priori hypotheses. As an example, the methodology is applied to one of the major problems in present day magnetic confinement fusion: the understanding of the scaling laws for the access to the high confinement regime. First the two numerical tools are refined to extract numerical relations from an international database, which are compared with the most widely accepted theoretical models. Since the international database does not contains signals covering the entire evolution of the discharges, a most sophisticated process is developed, using a dedicated and validated database of JET Joint Undertaking discharges, to study in more detail the plasma evolution close to the transition. A specific approach is developed to determine the dimensionality of the problem and then to select the most relevant signals. Specific mathematical relations for the scaling of the temperature threshold are derived again using NNs and SVMs independently. Clear evidence is collected for the existence of two different types of transition to the H mode. Both NNs and SVMs converge on very similar equations which show a success rate in interpreting JET database of practically 100% once the error bars in the measurements are taken into account. The proposed methodology therefore seems to be able to extract, in an automatic, robust and user independent way, the right physics from the database. Additional refinements of the approach to provide also confidence intervals in the derived mathematical equations are also presented.
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EFDP09004 1.53 Mb